AN4 Abstracts

Abstracts are printed as submitted by the authors.

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AN14 Abstracts 1

IC1

Equilibrium Analysis of Large Populations Dynam-ics

The first part of the talk will review several applica-tions, including bird flocking, information percolation insocial networks, valuation of exhaustible resources, highfrequency market making, emissions regulation, , for whichmodels of large populations dynamics can be brought tobear. These models will be framed in the context of thetheory of mean field games. The second part of the talkwill present recent equilibrium existence results, and dis-cuss some of the nagging computational challenges raisedby the need for reasonable numerical approximations tothese equilibria.

Rene CarmonaPrinceton UniversityDpt of Operations Research & Financial Engineeringrcarmona@princeton.edu

IC2

Solving Stochastic Inverse Problems Using Sigma-Algebras on Contour Maps

We describe recent work on the formulation and numericalsolution of stochastic inverse problems for determining pa-rameters in differential equations with stochastic data onoutput quantities. The new approach involves approximat-ing the generalized contour maps representing set-valuedinverse solutions, using the approximate contour maps todefine a geometric structure on events in the sigma-algebrafor the probability space on the parameter domain, andexploiting the structure to define and approximate proba-bility distributions in the space. We will present variousexamples, including high-dimensional problems involvingspatially varying parameter fields in storm surge models.

Donald EstepColorado State Universityestep@math.colostate.edu or don.estep@gmail.com

IC3

Computational Biology in the 21st Century: Mak-ing Sense out of Massive Data

The last two decades have seen an exponential increasein genomic and biomedical data, which will soon outstripadvances in computing power to perform current methodsof analysis. Extracting new science from these massivedatasets will require not only faster computers; it will re-quire smarter algorithms. We show how ideas from cutting-edge algorithms, including spectral graph theory and mod-ern data structures, can be used to attack challenges insequencing, medical genomics and biological networks.

Bonnie BergerDepartment of MathematicsMassachusetts Institute of Technologybab@theory.lcs.mit.edu

IC4

The Evolution of Combinatorial Solvers for Lapla-cian Linear Systems

Fast solvers that are based on combinatorial techniqueshave been investigated for more than two decades now.The most successful of these (at least theoretically) solvesymmetric diagonally linear systems, a class that includes

Laplacians of graphs. The talk will describe these tech-niques, starting with Vaidya’s 1991 solver and ending withvery recent algorithms by Kelner and others. The talkwill focus on how the graph-matrix isomorphism is usedin these solvers, on the class of matrices that they can beapplied to, and on the gap between theory and practice inthis area.

Sivan A. ToledoTel Aviv Universitystoledo@tau.ac.il

IC5

Optimization Algorithms for Machine Learning

The extraordinary success of search engines, recommenda-tion systems, and speech and image recognition softwaresuggests that future advances in these technologies couldhave a major impact in our lives. In this talk, we discussmodern intelligent-algorithmic systems based on sophisti-cated statistical learning models and powerful optimizationtechniques. One can envision new algorithms that operatein the stochastic or batch settings, and that take full ad-vantage of parallelism. We review our remarkable under-standing of classical stochastic approximation techniques,and pose some open questions. The lecture concludes witha discussion of modern neural nets and the demands theyimpose on optimization methods.

Jorge NocedalDepartment of Electrical and Computer EngineeringNorthwestern Universitynocedal@eecs.northwestern.edu

IC6

The Mathematical Problems of Isotropic-NematicInterface

Liquid crystals represent a vast and diverse class ofanisotropic soft matter materials which are intermediatebetween isotropic liquids and crystalline solids. The vari-ous liquid crystal phases can be characterized by the typeof ordering,one of the most common liquid crystal phasesis the isotropic phase, another is the nematic phase. Inthis talk, a wide spectrum of mathematical problems ofisotropic-nematic interface will be considered. One set ofproblems to be considered is the relationship between thesedifferent levels of modeling, for example how one can makea rigorous passage from molecular/statistical descriptionsto continuum theories. Special consideration will be givento the existence, uniqueness and regularity of the solutionsof the Landau-de Gennes theory.

Pingwen ZhangPeking Universitypzhang@pku.edu.cn

IC7

The Statistics Behind the Discovery of the HiggsBoson

The standard model of particle physics is a wildly suc-cessful theory of fundamental particles and their interac-tions. The Higgs boson is a particle that was predictednearly 50 years ago to address a serious theoretical consis-tency issue in the Standard Model of particle physics, butit has never been observed. The Large Hadron Collider is amulti-national, multi-billion dollar experiment to search forthe Higgs boson and other new phenomena. I will discuss

2 AN14 Abstracts

the statistical aspects of the recent discovery of the Higgsboson, including the collaborative statistical modeling ofthe data and the statistical procedures we employ. Withmulti-petabyte datasets and complex statistical models, weare arguably pushing a frontier of statistical analysis andquickly outstripping our most advanced tools.

Kyle CranmerNew York Universitykyle.cranmer@nyu.edu

IC8

Random Braids

Braids are mathematical objects closely related to knots.They consist of a set of strings embedded in three dimen-sions, anchored at both ends. Plotted in a spacetime di-agram, trajectories of two-dimensional systems naturallyform braids. When the trajectories correspond to peri-odic orbits they form closed braids, and there are powerfulmathematical techniques available to analyze the dynam-ics. If the trajectories are chaotic, then the analysis is notso simple. I will describe the types of braids that arisewhen dealing with chaotic orbits, and discuss their connec-tion to surface dynamics. I will also discuss applicationsto sparse trajectory datasets.

Jean-Luc ThiffeaultDept. of MathematicsUniversity of Wisconsin - Madisonjeanluc@math.wisc.edu

IP1

Age of Networks

Networks are becoming increasingly relevant in a host ofdomains. In the tech industry, we see the Internet, theWWW, and many online social networks. In economics,we are experiencing both the positive and negative effectsof a global networked economy. In biomedical applications,the structure of gene regulatory networks is relevant forthe treatment of many human diseases. In this talk, I de-scribe quite generally models we are using to describe thesenetworks, processes we are studying on the networks, algo-rithms we have devised for the networks, and finally, meth-ods we are developing to indirectly infer network structurefrom measured data. I then focus on a couple of specificapplications, including one to cancer genomics.

Jennifer Tour ChayesMicrosoft Researchjchayes@microsoft.com

IP2

Big Data, Sparse Information: Bayesian Inferencefor Large-scale Models, with Application to InverseModeling of Antarctic Ice Sheet Dynamics

Predictive models of complex geosystems often containnumerous uncertain parameters. Rapidly expanding vol-umes of observational data present opportunities to re-duce these uncertainties via solution of inverse problems.Bayesian inference provides a systematic framework forinferring model parameters with associated uncertaintiesfrom (possibly noisy) data and prior information. How-ever, solution of Bayesian inverse problems via conven-tional MCMC methods remains prohibitive for expensivemodels and high-dimensional parameters. Observationaldata, while large-scale, typically can provide only sparse

information on model parameters. Based on this propertywe design MCMC methods that adapt to the structure ofthe posterior probability and exploit an effectively-reducedparameter dimension, thereby rendering Bayesian inferencetractable for high-dimensional Antarctic ice sheet flow in-verse problems.

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

IP3

Pattern Recognition with Weakly Coupled Oscilla-tory Networks

One outstanding property of biological neural networks isthe ability to perform pattern recognition tasks. To mimicthis property with a man-made device that processes in-formation in parallel has been a great challenge. Tradi-tional approaches employ many interconnected units andare inherently difficult to construct. In the lecture, we willfocus on neural network models of weakly coupled oscilla-tors with time-dependent coupling. In these models, eachoscillator has only one or a few connections to a commonsupport, which makes them predestinated for hardware im-plementation. We will discuss the dynamics of differentnetwork architectures, compare their scalability, presentexperimental realizations of the networks and point outopen challenging mathematically problems.

Katharina KrischerTechnische Universitat Munchenkrischer@ph.tum.de

IP4

Scientific Computing in Movies and VirtualSurgery

New applications of scientific computing for solid and fluidmechanics problems include simulation of virtual materialsfor movie special effects and virtual surgery. Both disci-plines demand physically realistic dynamics for such mate-rials as water, smoke, fire, and brittle and elastic objects.These demands are different than those traditionally en-countered and new algorithms are required. This talk willaddress the simulation techniques needed in these fields andsome recent results including: simulated surgical repair ofbiomechanical soft tissues, extreme deformation of elasticobjects with contact, high resolution incompressible flow,clothing and hair dynamics. Also included is discussion ofa new algorithm used for simulating the dynamics of snowin Disneys animated feature film, ”Frozen”.

Joseph TeranUCLAjteran@math.ucla.edu

IP5

Big Data Visual Analysis

We live in an era in which the creation of new data isgrowing exponentially such that every two days we createas much new data as we did from the beginning of mankinduntil the year 2003. One of the greatest scientific challengesof the 21st century is to effectively understand and makeuse of the vast amount of information being produced. Vi-sual data analysis will be among our most important toolsto understand such large and often complex data. In thistalk, I will present state-of-the-art visualization techniques,

AN14 Abstracts 3

including ways to visually characterize associated error anduncertainty, applied to Big Data problems in science, en-gineering, and medicine.

Christopher JohnsonUniversity of UtahDepartment of Computer Sciencecrj@sci.utah.edu

IP6

Virtual Electrophysiology Laboratory

We present the development of a highly innovative patient-specific MRI-based heart modeling environment that rep-resents cardiac functions from molecular processes to elec-trophysiological and electromechanical interactions at theorgan level. This environment is termed ”virtual electro-physiology lab”. We present our attempts to translate thisenvironment into the clinic and apply it to the non-invasivediagnosis and treatment of heart rhythm and contractiledisorders in patients with structural heart disease. This pi-oneering effort offers to integrate, for the first time, compu-tational modeling of the heart, traditionally a basic-sciencediscipline, within the milieu of contemporary patient care.The robust and inexpensive non-invasive approaches for in-dividualized arrhythmia risk stratification and guidance ofelectrophysiological therapies presented here are expectedto lead to optimized therapy delivery and reduction inhealth care costs.

Natalia A. TrayanovaJohns Hopkins UniversityInstitute for Computational Medicinentrayanova@jhu.edu

IP7

Unilever, Science and eScience: The ChallengesAhead

Unilever is a large multinational and a market leader inthe fast moving consumer goods business, with well knownproducts in the sectors of home care, personal care, re-freshments and foods. We are embracing new ways of do-ing R&D to deliver bigger, better, faster innovations tomarket. The digital revolution, eScience, is already per-meating everything we do at home: how could we pay ourbills without eBanking, connect with our friends withoutFacebook, or find our way around without SatNav? Thesame revolution is helping us move faster at work. But howcan we make this digital eScience revolution work for us?

Massimo NoroUnilever, United KingdomMassimo.Noro@Unilever.com

IP8

Evolutionary or Revolutionary? Applied Mathe-matics for Exascale Computing

The move to exascale computing is expected to be disrup-tive due to significant changes in computer architectures.Advances in applied mathematics will be necessary to re-alize the full potential of these supercomputers, but willthese advances be incremental changes to existing methodsor will exascale computing require a substantial rethinkingof how we compute? To answer this question, the DOEAdvanced Scientific Computing Research Program char-tered a working group, which Dr. Hittinger co-chaired. Inthis talk, he will discuss the findings of the working group:

the opportunities for new applied mathematics researchthat will enable exascale computing. This work performedunder the auspices of the U.S. Department of Energy byLawrence Livermore National Laboratory under ContractDE-AC52-07NA27344. LLNL-ABS-645318.

Jeffrey A. HittingerCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryhittinger1@llnl.gov

IP9

Physics-based Animation Sound: Progress andChallenges

Decades of advances in computer graphics have made itpossible to convincingly animate a wide range of physicalphenomena, such as fracturing solids and splashing water.Unfortunately, our visual simulations are essentially ”silentmovies” with sound added as an afterthought. In this talk,I will describe recent progress on physics-based sound syn-thesis algorithms that can help simulate rich multi-sensoryexperiences where graphics, motion, and sound are syn-chronized and highly engaging. I will describe work on spe-cific sound phenomena, and highlight the important rolesplayed by precomputation techniques, and reduced-ordermodels for vibration, radiation, and collision processing.

Doug L. JamesCornell Universitydjames@cs.cornell.edu

SP1

AWM-SIAM Sonia Kovalevsky Lecture: The Evo-lution of Complex Interactions in Non-Linear Ki-netic Systems

Recent developments in statistical transport modeling,ranging from rarefied gas dynamics, collisional plasmas andelectron transport in nanostructures, to self-organized orsocial interacting dynamics, share a common descriptionbased in a Markovian framework of birth and death pro-cesses. Under the regime of molecular chaos propagation,their evolution is given by kinetic equations of non-linearcollisional (integral) Boltzmann type. We will present anoverview of analytical issues and novel numerical methodsfor these equations that preserve the expected conservedproperties of the described phenomena, while enabling rig-orous stability, convergence and error analysis.

Irene M. GambaDepartment of Mathematics and ICESUniversity of Texasgamba@math.utexas.edu

SP2

Fast, Accurate Tools for Physical Modeling inComplex Geometry

During the last two decades, fast algorithms have broughta variety of large-scale physical and biophysical modelingtasks within practical reach. This is particularly true of in-tegral equation approaches to electromagnetics, acoustics,gravitation, elasticity, and fluid dynamics. The practicalapplication of these methods, however, requires analyticrepresentations that lead to well-conditioned linear sys-tems, quadrature methods that permit the accurate evalu-ation of boundary integrals with singular kernels, and tech-niques for a posteriori error estimation that permit robust

4 AN14 Abstracts

mesh refinement. I will give an overview of recent progressin these areas with a particular emphasis on wave scatter-ing problems in complex geometry.

Leslie GreengardCourant InstituteNew York Universitygreengar@cims.nyu.edu

SP3

W. T. and Idalia Reid Prize in Mathematics Lec-ture: On the Master Equation in Mean Field The-ory

One of the major founders of Mean Field Games, P.L. LI-ONS has introduced in his lectures at College de Francethe concept of Master Equation. It is obtained through aformal analogy with the set of partial differential equationsderived for the Nash equilibrium of a differential game witha large number of players. The objective of this lecture isto explain its derivation, not by analogy, but through itsinterpretation. We do that for both Mean Field Type Con-trol and Mean Field Games. We obtain complete solutionsin the linear quadratic case. We analyze the connectionwith Nash equilibrium.

Alain BensoussanThe University of Texas, at Dallasaxb046100@utdallas.edu

SP4

I. E. Block Community Lecture: Search and Dis-covery in Human Networks

In the past few years, we have seen a tremendous growth inpublic human communication and self-expression, throughblogs, microblogs, and social networks. In addition, weare beginning to see the emergence of a social technol-ogy stack on the web, where profile and relationship in-formation gathered by some applications can be used byother applications. This technology shift, and the culturalshift that has accompanied it, offers a great opportunityfor computer scientists, artists, and sociologists to study(and organize) people at scale. In this talk I will discusshow the changing web suggests new paradigms for searchand discovery. I will discuss some recent projects that useweb search to study human nature, and use human natureto improve web search. I will describe the underlying prin-ciples behind these projects and suggest how they mightinform future work in search, data mining, and social com-puting.

Sep KamvarMassachusetts Institute of Technology, USAsdkamvar@mit.edu

SP5

Julian Cole Lecture: Growth, Patterning, and Con-trol in Nonequilibrium Systems

Dense-branching morphologies are among the most com-mon forms of microstructural patterning in systems drivenout of equilibrium. Prediction and control of the emergentpatterns are difficult due to nonlocality, nonlinearity andspatial heterogeneity. Focusing on viscous fingering in acircular Hele-Shaw cell as a paradigm for such phenomena,we use theory and numerics to demonstrate that by con-trolling the injection rate of the less viscous fluid, we canprecisely suppress the evolving interfacial instabilities and

control the shape of growing bubbles. Experiments confirmthe feasibility of the control strategy. Extensions to otherpattern-forming systems will be discussed.

John LowengrubDepartment of MathematicsUniversity of California at Irvinelowengrb@math.uci.edu

SP6

Theodore Von Karman Prize Lecture: Materialsfrom Mathematics

We present examples of new materials whose synthesis wasguided by some essentially mathematical ideas from pdeand the calculus of variations. These materials undergophase transformations from one crystal structure to an-other, without diffusion. The underlying mathematicaltheory was designed to identify alloys that show excep-tional reversibility of the transformation. The new alloysdo show unprecedented reversibility, but raise fundamen-tal new questions for theory. Some of these alloys con-vert heat to electricity (without a separate electrical gen-erator), and provide an interesting possible route to re-cover the vast amounts of energy stored on earth at smalltemperature difference. The lecture will be mathemati-cally/experimentally nontechnical and suitable for a broadaudience. (http://www.aem.umn.edu/ james/research/)

Richard JamesDepartment of Aerospace Engineering and MechanicsUniversity of Minnesotajames@umn.edu

CP1

Filtering Algorithm For Pod-Based Reduced OrderModeling Techniques

Principal component analysis (PCA) is a technique thatcan be used to determine the most important componentson a set of varying data. PCA algorithms produces stati-cally independent score variables that determines the im-portance of each component. In this manuscript, we in-troduce a new filtering algorithm that can be used todown-select a smaller number of directions from the POD-determined basis in order to render a more effective re-duction of dimensionality. The error resulting from thisfiltering can be upper bounded using a randomized rangefinding algorithm (RFA), employed in some of our previ-ous developments. A neutron transport model is used todemonstrate the proof of principle and exemplify the imple-mentation and mechanics of the proposed algorithm. Theproposed algorithm can be classified as a PCA algorithm,yet, it uses the error metric associated with the RFA togenerate a set of principal components with a certain prob-ability.

Hany S. Abdel-KhalikNorth Carolina State Univ.abdelkhalik@ncsu.edu

Bassam A. KhuwailehNorth Carolina State Universitybakhuwai@ncsu.edu

CP1

An Efficient Output Error Bound for Reduced Ba-sis Methods Applied to Parametrized Evolution

AN14 Abstracts 5

Equations

We present an efficient a posteriori output error bound forthe reduced basis method applied to nonlinear parameter-ized evolution equations. With the help of a dual systemand a simple representation of the residual in the primalsystem, the output error can be estimated sharply. Such anerror bound is successfully applied to reduced order model-ing of nonlinear chromatography, and the underlying opti-mization can be solved efficiently using the reduced model.

Yongjin ZhangMax Planck Institute for Dynamics of Complex TechnicalSystemszhangy@mpi-magdeburg.mpg.de

Lihong FengMax Planck Institute for Dynamics ofComplex Technical Systemsfeng@mpi-magdeburg.mpg.de

Suzhou LiMax Planck Institute for Dynamicsof Complex Technical Systems, Germanysuzhou@mpi-magdeburg.mpg.de

Peter BennerMax Planck Institute, Magdeburg, Germanybenner@mpi-magdeburg.mpg.de

CP1

Employing Non-Converged Iterates for ReducedOrder Modeling

Recently, reduced order modeling (ROM) is being usedin various engineering fields. Model-specific basis can beconstructed utilizing a randomized range finding algorithm(RFA) where snapshots of the models response are used toconstruct the basis. However, this process might be com-putationally taxing. This work proposes an algorithm thatutilizes the non-converged iterates of the model of interestto construct the basis. A mathematical proof showed thatthe resulting subspace in equivalent to that constructed us-ing the converged snapshots. The two subspaces were com-pared numerically in terms of the dominant angle and anerror metric that has been developed in a previous work.Results indicate that the proposed algorithm produces asubspace that is representative and inclusive of the sub-space obtained by the converged snapshots.In addition tothat, a numerical test is implemented to illustrate the ap-plication of the proposed algorithm in nuclear engineeringdesign calculations.

Bassam A. KhuwailehNorth Carolina State Universitybakhuwai@ncsu.edu

Congjian WangNCSUcwang21@ncsu.edu

Youngsuk BangDepartment of Nuclear Engineering, North Carolina StateUniversity, P.O.Box 7909, Raleigh, NC 27695, USAybang@ncsu.edu

Hany S. Abdel-KhalikNorth Carolina State Univ.

abdelkhalik@ncsu.edu

CP1

Using Snapshots of the Derivatives in ProperOrthogonal Decomposition (POD)-Based ReducedOrder Methods (ROM) for Dynamical Systems

POD-based ROM methods use solution snapshots (SS) orsnapshot difference quotients. We explore a POD ROMmethod that, apart from SS, also uses time derivative snap-shots (TDS), calculated from the right-hand side of the dy-namical system. In general, TDS do not belong to the spanof the SS. We develop error estimates, supported by numer-ical tests, suggesting that a ROM utilizing both TDS andSS approximates the solution better than one based onlyon SS.

Tanya Kostova-Vassilevska, Geoffrey Oxberry, KyleChand, Bill ArrighiLawrence Livermore National Laboratorykostova@llnl.gov, oxberry1@llnl.gov, chand1@llnl.gov, ar-righi2@llnl.gov

CP1

Adaptive Proper Orthogonal Decomposition Re-duced Order Models Via Incremental SVD

Meeting approximation error tolerances may require globalreduced order models (ROMs) with unacceptably largenumbers of ROM basis vectors. To overcome this prob-lem, adaptive sampling and incremental singular value de-composition are used to construct smaller, locally accurateproper orthogonal decomposition (POD) ROMs. Replac-ing a global POD ROM with a collection of local PODROMs generally reduces approximation error for a fixednumber of ROM basis vectors.

Geoffrey M. Oxberry, Tanya Kostova-Vassilevska,William Arrighi, Kyle ChandLawrence Livermore National Laboratorygoxberry@gmail.com, kostova@llnl.gov, arrighi2@llnl.gov,chand1@llnl.gov

CP1

Robust Reduced-Order Models Via Fast, Low-Rank Basis Updates

The large computational cost associated with high-fidelityphysics-based simulations has limited their use in practi-cal situations. Model Order Reduction (MOR) is an at-tempt to reduce the computational cost of such simula-tions by approximating the solution in well-chosen, low-dimensional affine subspaces. Recent developments in non-linear MOR theory that achieves increased parametric ro-bustness and additional speedup using fast, online reduced-basis updates will be presented. These new techniques willbe demonstrated on parametric, large-scale, 3D fluid me-chanical problems.

Matthew J. ZahrStanford UniversityUniversity of California, Berkeleymzahr@stanford.edu

Kyle Washabaugh, Charbel FarhatStanford University

6 AN14 Abstracts

kyle.washabaugh@stanford.edu, CFarhat@stanford.edu

CP2

Two-Point Riemann Problem for InhomogeneousConservation Laws: Geometric Construction of So-lutions

We consider the following conservation law: ∂tu(x, t) +∂xf(u(x, t)) = g(u) The following boundary conditions arespecified: u(0 − 0, t) = u0− and u(X + 0, t) = uX+. Inaddition, we specify the initial condition u(x, 0) = ux0 forx ∈ (0, X). Method of characteristics is used to show theevolution of the initial profile and the discontinuities atthe boundaries as well as appearance and in some casesdisappearance of internal discontinuities. For illustrationpurposes the function f(u) will be assumed to have 3 crit-ical points.

Dmitry A. AltshullerDassault Systemesaltshuller@ieee.org

CP2

On Eigenfunction Expansion Solutions for theStart-Up of Fluid Flow

Textbooks describe the process of “subtracting off’ thesteady state of a linear parabolic PDE as means for ob-taining a homogeneous BVP to solve by eigenfunction ex-pansions. While this works for the start-up problem for aNewtonian fluid between parallel plates, it leads to erro-neous solutions to the corresponding problem for a class ofnon-Newtonian fluids. We show this is due to non-rigorousenforcement of the start-up condition, violating the princi-ple of causality.

Ivan C. ChristovPrinceton Universitychristov@alum.mit.edu

CP2

Transport in Confined Structures As a MultiscaleProblem and Numerical Results for Nanopores

Charge transport through confined structures such asnanopores differs from transport in bulk. Confined struc-tures give rise to multiscale problems; more precisely,transport and scattering occur in the longitudinal direc-tion, while the particles are confined in the two transver-sal directions. We have derived a conservation law of theform ∂tρ(x, η, t) + ∂xF

x(x, η, t) + ∂ηFη(x, η, t) = 0 from

the Boltzmann equation, where ρ is the concentration, η isenergy, and F x and F η are fluxes given explicitly by theharmonic confinement potential. We also present severalrecent numerical results for artificial nanopores and for ionchannels such as certain antibiotics.

Clemens F. HeitzingerArizona State University &Technical University Vienna (TU Vienna)Clemens.Heitzinger@asu.edu

Christian RinghoferSchool of Mathematical and Statistical SciencesArizona State University (ASU)

christian.ringhofer@asu.edu

CP2

A Free Boundary Approach for Solving a Two-Dimensional Riemann Problem for the IsentropicGas Dynamics Equations

We consider a two-dimensional Riemann problem for theisentropic gas dynamics equations modeling strong (ortransonic) regular reflection. We write the problem in self-similar coordinates and obtain a free mixed boundary prob-lem for the reflected shock and the subsonic state behindthe shock. Using the theory of 2nd order elliptic equationswith mixed boundary conditions as well as various fixedpoint arguments, we prove existence of a solution to theabove Riemann problem in a neighborhood of the reflec-tion point.

Katarina JegdicUniversity of Houston-DowntownJegdicK@uhd.edu

CP2

Singular Behavior of the Navier Stokes FlowThrough a Non-Convex Polyhedral Cylinder

This result is a mathematical background to solve the com-pressible flow near the sharp edge. We consider the com-pressible viscous Navier-Stokes equations in a non-convexpolyhedral cylinder. We split the edge singularity occur-ring at the non-convex edge from the velocity vector andshow the high regularity for the velocity remainder. Thelocal sound wave is propagated into the region along thestreamline emanated from the non-convex edge and itsderivatives blow up across the streamline.

Oh Sung KwonPostechjamjjari@gmail.com

Jae Ryong KweonPOSTECH(Pohang University of Science and Technology)Koreakweon@postech.ac.kr

CP2

Higher Order Analyses of Laminated CompositeShells and Plates

The free Vibration analyses of laminated cylindrical shellsby using higher order shear deformation theories. Equilib-rium equations are formulated using the equations of stressresultants to attain a system of differential equations andare solved for free vibrations. Boundary conditions con-sidered are simply supported and lamination is cross ply.The third orders shear deformation theory of that considerstransverse normal stress, shear deformation and rotary in-ertia has been developed and used. An exact analytical so-lutions and boundary condition of shell has been obtained.The (first five) natural frequency parameters are reportedand compared with previously published research using afirst order approximation. Results are also compared withan accurate 3D finite element analyses.

Mohammad ZannonCentral Michigan Universityzanno1ms@cmich.edu

AN14 Abstracts 7

Mohamad QatuCMUqatu1ms@cmich.edu

Leela RakeshCentral Michigan UniversityApplied Mathematics GroupLRakesh@aol.com

CP3

Pushing and Showing in Hallways and Doorways

We investigate the location of macroscopic equilibriumstates, both stable and unstable, in systems of interact-ing particles, modelling the evolution of flocks, swarmsand pedestrian crowds constrained by walls and obsta-cles. Unstable equilibrium states provide valuable infor-mation about qualitative system behaviour, boundaries be-tween stability regions, and transitions between modes offlow. Equation-free methods connecting macroscopic andmicroscopic descriptions are employed to perform analysisand parameter continuation of equilibria and bifurcationpoints.

Poul G. HjorthTechnical Univ of DenmarkDepartment of Mathematicspghj@dtu.dk

Kristian Berg Thomsen, Christian MarschlerTechnical University of DenmarkDepartment of Mathematics and Computer Sciencekristianbthomsen@gmail.com, chrms@dtu.dk

Jens StarkeTechnical University of DenmarkDepartment of Mathematicsj.starke@mat.dtu.dk

CP3

Spatial Localization in Heterogeneous Systems

We study spatial localization in the generalized Swift-Hohenberg equation

ut = r(x)u− (1 + ∂xx)2u+N(u)

with either quadratic-cubic or cubic-quintic nonlinearityN(u) subject to spatially heterogeneous forcing throughthe spatially varying parameter r(x). Different types offorcing with different spatial scales are considered and thecorresponding localized structures are computed. The re-sults indicate that spatial heterogeneity exerts a significantinfluence on the location of spatially localized structures inboth parameter space and physical space, and on their sta-bility properties. The results are expected to assist in theinterpretation of experiments where departures from spa-tial homogeneity are unavoidable.

Hsien-Ching KaoWolfram Research Inc.sp000088@gmail.com

Cedric Beaume, Edgar KnoblochDepartment of PhysicsUniversity of California at Berkeley

ced.beaume@gmail.com, knobloch@physics.berkeley.edu

CP3

Billiard Dynamics of Bouncing Dumbbell

A system of two masses connected with a weightlessrod(called dumbbell) interacting with a flat boundary isconsidered. The sharp bound on the number of collisionswith the boundary is found using billiard techniques. Incase the ratio is large and the dumbbell rotates fast, anadiabatic invariant is obtained.

Ki Yeun KimUniversity of Illinois at Urbana-ChampaignDepartment of Mathematicskkim97@illinois.edu

Yuliy BaryshnikovUniversity of Illinois at UrbanaChampaignDepartment of Mathematicsymb@uiuc.edu

Victoria Blumen, Vadim ZharnitskyUniversity of Illinois at Urbana-Champaignveblumen@illinois.edu, vzh@illinois.edu

CP3

Solitary Waves and the N-particle Algorithm for aClass of Euler-Poincare Equations

Nonlinearity arises generically in mathematical models ofphysical phenomena, and the interplay between nonlinear-ity and dispersion is thought to be responsible for manyof these phenomena, such as the existence of travelingwaves. We explore the relation between nonlinearity anddispersion by studying the N-particle system of the Euler-Poincare differential equations, or the EPDiff equations.In particular, we illustrate the existence and dynamics oftraveling wave solutions of the EPDiff equations. Solitarywaves for this class of equations can be made to correspondto interacting particles of a finite-degree-of-freedom Hamil-tonian system. We analyze the dynamics of two-solitarywave interaction and show that two solitons can either scat-ter or capture each other. The scattering or capture orbitsdepend on the singularity level of the solitons, while singu-larity of a soliton is determined by the power of the linearelliptic operator associated with the EPDiff equations.

Long LeeDepartment of MathematicsUniversity of Wyomingllee@uwyo.edu

Roberto CamassaUniversity of North Carolinacamassa@amath.unc.edu

Dongyang KuangUniversity of Wyomingdkuang@uwyo.edu

CP3

The Gaussian Semiclassical Soliton Ensemble

We study a particular family of perturbed initial data forthe focusing nonlinear Schrodinger equation. This family ofdata arises naturally in the analysis of the zero-dispersionlimit. However, the ellipticity of the associated modulation

8 AN14 Abstracts

equations raises questions about the impact of even smallperturbations of the data. Remarkably, our experimentsshow that the rate of convergence of the perturbed datato the true data is propagated to positive times includingtimes after wave breaking.

Gregory LyngDepartment of MathematicsUniversity of Wyomingglyng@uwyo.edu

CP3

Phyllotaxis As a Pattern-Forming Front

Some of the most spectacular patterns in the natural worldcan be found on members of the plant kingdom. Further-more, the regular configurations of organs on plants, collec-tively termed phyllotaxis, exhibit a remarkable predisposi-tion for Fibonacci-like progressions. Starting from a bio-chemical and mechanical growth model, we derive a PDEsimilar to the classic Swift-Hohenberg equation and findthat nearly every property of Fibonacci phyllotaxis can beexplained as the propagation of a pushed pattern-formingfront.

Matthew PennybackerUniversity of New Mexicopennybacker@math.unm.edu

CP4

Automatic Segmentation of Microscopy ImagesBased on the Starlet Wavelet Transform

We propose an automatic method based on starlet waveletsto perform the segmentation of photomicrographs. Theproposed segmentation method is given applying starletsin an input image, resulting in L detail levels. First andsecond detail levels are ignored; then, third to last detaillevels are summed. From the original image and its GroundTruth, Matthews Correlation Coefficient (MCC) is calcu-lated for each level application. Therefore, the optimalsegmentation level has the highest MCC.

Alexandre F. De Siqueira, Flavio Cabrera, WagnerNakasugaDFQB - Faculty of Sciences and TechnologyUNESP - Univ Estadual Paulistasiqueiraaf@gmail.com, flavioccabrera@yahoo.com.br,wamassa@gmail.com

Aylton PagamisseDMC - Faculty of Sciences and TechnologyUNESP - Univ Estadual Paulistaaylton@fct.unesp.br

Aldo JobDFQB - Faculty of Sciences and TechnologyUNESP - Univ Estadual Paulistajob@fct.unesp.br

CP4

The Generalized Haar-Walsh Transform (GHWT)for Data Analysis on Graphs and Networks

We present a new multiscale transform for data on graphsand networks which is a generalization of the classical Haarand Walsh-Hadamard Transforms. Using a recursive parti-tioning of the graph, the transform generates an overcom-

plete dictionary of piecewise-constant orthonormal bases.We adapt the best-basis selection algorithm to this setting,allowing us to choose a basis most suitable for the task athand. We conclude with some results from approximationand classification experiments.

Jeffrey IrionUC Davisjlirion@math.ucdavis.edu

Naoki SaitoDepartment of MathematicsUniversity of California, Davissaito@math.ucdavis.edu

CP4

Alternating Direction Approximate Newton(ADAN) Method for Partially Parallel Imaging

ADAN method is developed for problems that arise inpartially parallel magnetic resonance image reconstruction(PPI). The reconstruction amounts to solving a problem ofthe form min{φ(Bu)+1/2‖Au−f‖2}, where u is the image.It is shown that ADAN converges to a solution of the imagereconstruction problem without a line search. It performsat least as well as the recent variable stepsize Bregman op-erator splitting algorithm (BOSVS), which requires a linesearch and a suitable choice for many algorithm parame-ters.

William Hager, Cuong K. NgoUniversity of FloridaDepartment of Mathematicshager@ufl.edu, ngocuong@ufl.edu

Maryam YashtiniDepartment of MathematicsUniversity of Floridamyashtini@ufl.edu

Hongchao ZhangDepartment of Mathematics and CCTLouisiana State Universityhozhang@math.lsu.edu

CP4

Topology and Numerical Analysis in MolecularSimulations

Topological changes are significant during molecular sim-ulations. Our research focuses upon accurate display ofthese changes through dynamic visualizations to domainscientists. Most topological characteristics are formulatedin terms of infinite precision, raising challenges within theapproximations seen for graphics. Problems and partialsolutions will be presented.

Thomas J. PetersUniversity of Connecticuttpeters@engr.uconn.edu

CP4

Per-Class Pca-Src: Increased Flexibility and Speci-ficity in Sparse Representation-Based Classification

Sparse Representation-based Classification (Wright, et al.)seeks the sparsest decomposition of test samples over thedictionary of training samples. This method assumes that

AN14 Abstracts 9

the number of classes is large and test samples lie in thelinear subspaces spanned by their class’ training data. Wepropose a modification that builds class-specific dictionar-ies containing approximate bases to points on the classmanifold using the “local PCA’ technique of Singer, et al.We show our modifications improve performance.

Chelsea WeaverUniversity of California, Daviscaweaver@math.ucdavis.edu

Naoki SaitoDepartment of MathematicsUniversity of California, Davissaito@math.ucdavis.edu

CP4

Synchrosqueezed Wave Packet Transforms and Dif-feomorphism Based Spectral Analysis for 1D Gen-eral Mode Decompositions

We develops new theory and algorithms for 1D generalmode decompositions. First, we introduce the 1D syn-chrosqueezed wave packet transform (SSWPT) and proveits ability to estimate the instantaneous information ofwell-separated modes from their superposition. The SS-WPT has a better resolution than the synchrosqueezedwavelet transform. Second, we present a new approachbased on diffeomorphisms for the spectral analysis of gen-eral shape functions. These two methods lead to a frame-work for general mode decompositions.

Haizhao YangStanford UniversityMath Dept, Stanford Universityhaizhao@math.stanford.edu

CP5

Two Mode Matrix of Urban Structure

We present an urban network that takes into accounthow streets and neighborhoods interact and influence eachother. This two-mode urban structure presents anotherapproach to analyze urban environments. We use GIS toconstruct a network map of an American city and then ap-ply network analysis to evaluate how the network structureinfluences such features as traffic flow, density and housingconsiderations. Also, given the rise of African cities, wheresome are being completely designed and developed in lieuof developing organically, the results of this project willmake recommendations for effective metropolitan growthstructures.

James R. GatewoodRensselear Polytechnic Institutejames.gatewood@usma.edu

CP5

Classifying Contagion Dynamics on a Noisy Net-work Using Persistent Homology

A contagion can exhibit complicated dynamics on a net-work and its spread may be constrained by an underly-ing geometry. We embed nodes of a complex-contagionmodel on a manifold (e.g. R

2). We study the extent thata contagion adheres to the underlying geometry with noisynon-geometric edges by embedding the nodes as points in ametric space and analyse the geometrical/topological prop-

erties. We leverage our results to obtain insight into non-linear dimension reduction.

Heather HarringtonUniversity of Oxfordharrington@maths.ox.ac.uk

Florian KlimmMaster of Science (Physics)Humboldt-Universitat, Berlinklimm@physik.hu-berlin.de

Miro Kramar, Konstantin MischaikowDepartment of MathematicsRutgers, The State University of New Jerseymiroslav@math.rutgers.edu, mischaik@math.rutgers.edu

Peter J. MuchaUniversity of North Carolinamucha@unc.edu

Mason A. PorterUniversity of OxfordMathematical Instituteporterm@maths.ox.ac.uk

Dane TaylorStatistical and Applied Mathematical Sciences InstituteDept of Mathematics, University of North Carolina,Chapel Hitaylordr@live.unc.edu

CP5

On Continuous Time Bounded Confidence OpinionDynamics with Multidimensional Opinions

In the bounded confidence opinion dynamics model, theopinion of each agent is only affected by other agents whoseopinions lie within a confidence bound. In the case of con-tinuous time bounded confidence opinion dynamics modelwith scalar opinions, trajectories have been proven to reachan equilibrium asymptotically in time. We generalize thisresult for vector opinions by introducing Dissipation func-tions and studying omega-limit sets of the trajectories.

Serap Tay, Muruhan RathinamUniversity of Maryland, Baltimore Countyseratay1@umbc.edu, muruhan@umbc.edu

CP5

Numerical Study on G-Expectation

We will present some numerical methods for the G-Heatequation which is related to the nonlinear expectation, in-troduced by Shige Peng:

ut −G(D2u) = 0, (x, t) ∈ Rn × (0, T ); u(x, 0) = φ(x),

where G(A) = supQ∈Θ(12tr(AQ)), Θ ⊂ S+(n) = {BBt :

B ∈ Rn×n} Numerous numerical experiments will be car-ried out to show the efficiency, accuracy and stability of theproposed methods. The effect of the boundary conditionsis also numerically investigated. Some numerical analysisis given to show the convergence of the numerical solutionsto the viscous solutions of the G-Heat equation.

Xingye YueSoochow University, Suzhou, China

10 AN14 Abstracts

xyyue@suda.edu.cn

CP5

Support System for Mathematical Models Basedon Optimization Problems of Economic Agents

This paper presents a support system for economic model-ing. It supports development, numerical computations andanalytical study of models. It also controls balances and di-mensions of a model for correctness and consistency. It wassuccessfully applied to intertemporal equilibrium models ofthe Russian and the Kazakhstan economies. The system isparticularly efficient for structures similar to general eco-nomic equilibrium with nonstandard descriptions of agents.The system is supplemented by special procedures of reg-ularization of complementary slackness conditions, subsys-tem for analysis of stationary (or more exactly self-similar)solutions, based on the dimensions of the system, as wellas an algorithm for solving the model as a boundary valueproblem and its implementation on a supercomputer.

Aleksandra A. ZhukovaComputing Center of RASDivision of mathematical modelling of economysasha.mymail@gmail.com

Igor PospelovComputing Center of RASna

Mikhail KhokhlovYandex LLCna

Valentin VrzheschComputing Center of RASna

CP6

Solution of a 2D Electrodiffusion Problem: Mathe-matical Modeling of Contact Resistance in SiliconPhotovoltaic Cells

In screen-printed silicon-crystalline solar cells, the presenceof a thin interfacial glass layer of varying thickness betweenthe silicon and silver electrode inhibits electron flow. Inthis paper we analyze a model for electron transport acrossthe glass, based on the 2D drift-diffusion equations. Wesolve the model numerically using a spectral method andcompare results to asymptotic solutions. We are able todetermine the effect of different glass layer topographieson the contact resistance.

Jonathan P. Black, Christopher BrewardUniversity of Oxfordblack@maths.ox.ac.uk, breward@maths.ox.ac.uk

Peter D. HowellUniversity of OxfordMathematical Institutehowell@maths.ox.ac.uk

Gareth FugeDuPont (UK) Ltd

gareth.fuge@dupont.com

CP6

Eigenvalue Problems for Rapidly Growing Opera-tors in Divergence Form

In an Orlicz-Sobolev setting, the spectrum of an exponen-tial type perturbation of the Laplace operator is completelycharacterized by means of an asymptotic analysis of a classof eigenvalue problems involving the p-Laplacian. This talkis based on joint work with Mihai Mihailescu (Universityof Craiova and “Simion Stoilow” Institute of Mathematicsof the Romanian Academy, Bucharest, Romania).

Marian BoceaLoyola University Chicagombocea@luc.edu

CP6

Simulating Non-Dilute Transport in Porous MediaUsing a TCAT-Based Model

Predicting the transport of non-dilute species in fluids ofvariable density in porous media is a challenging problem.We use a thermodynamically constrained averaging theory(TCAT)-based model, which consists of a flow equation,a species transport equation, and closure relations. Werewrite the model as a system of two partial differential-algebraic equations. We use a stiff temporal integrator toperform 1D simulations. The model is nonlinear and non-smooth. We will discuss results and numerical difficulties.

Deena Hannoun GiffenNCSUdhannou@ncsu.edu

C.T. KelleyNorth Carolina State Universityctk@ncsu.edu

Casey Miller, William Gray, Pamela SchultzUniversity of North Carolinacasey miller@unc.edu, wggray@unc.edu,pbs@email.unc.edu

CP6

A General Methodology for Approximating theDiscrete Chemical Master Equation with ShortRange Spatial Correlations in Homogeneous Sys-tems

The chemical master equation is used to describe a widevariety of chemical kinetic processes, however the resultingsystem is posed in an infinite dimensional space. Often,this system is solved via realizations of stochastic differ-ential equations via kinetic Monte Carlo methods, howeverthese techniques may have high computational cost and re-quire statistical sampling over many realizations. In caseswhere the system of interest may be assumed to have shortrange spatial correlations and have translational symme-tries, we demonstrate a general methodology of approxi-mating the chemical master equation by a finite dimen-sional system of ordinary differential equations. We thendemonstrate this methodology with a concrete example ofsurface catalysis and compare our results with those from

AN14 Abstracts 11

kinetic Monte Carlo simulations.

Gregory J. HerschlagDepartment of MathematicsUniversity of North Carolina at Chapel Hillgjh@math.duke.edu

CP6

On the Initial-Boundary Value Problem for theKorteweg-De Vries Equation

The Korteweg-de Vries Equation (KdV Equation) is oneof the most important nonlinear PDEs of applied mathe-matics. We will discuss the initial-boundary problem forthe PDE and show, depending on boundary conditions,that it can behave like a hyperbolic PDE such as the waveequation and has time reversible solutions, and it can alsobehave like a parabolic equation such as the heat equationand has smooth solutions that are not time reversible.

Steve TaylorUniversity of Auckland, New Zealandtaylor@math.auckland.ac.nz

CP6

Transmission Eigenvalues for Regions on a Con-ducting Surface

We consider the interior transmission problem correspond-ing to inverse scattering for a bounded isotropic dielectricmedium lying on an infinite conducting surface. In partic-ular, we investigate the 2-D scalar case where the dielec-tric medium is illuminated by time harmonic Transverse-Electric or Transverse-Magnetic polarized electromagneticwaves. In both cases we show that transmission eigenvaluesexist and form a discrete set. Numerical results are givenshowing that real transmission eigenvalues can be foundfrom near field data.

Fan YangUniversity of Delawarejackie@math.udel.edu

Peter B. MonkDepartment of Mathematical SciencesUniversity of Delawaremonk@math.udel.edu

CP7

Robust Dynamic Shaping of Distributed ParameterSystems Via Recursively Updated Empirical BasisFunctions

We focus on shaping the dynamic response of distributedparameter systems in the presence of parameter uncer-tainty using adaptive model order reduction. The prob-lem is addressed by enforcing the desired spatio-temporaldynamics in the closed-loop system via an observer-basedrobust nonlinear feedback controller specifically designedbased on the reduced order model that is refined by re-cursively updated empirical basis functions. The proposedmethod is illustrated on the thermal dynamic shaping in acatalytic reactor.

Davood Babaei PourkargarDepartment of Chemical EngineeringThe Pennsylvania State University, University Parkdzb158@psu.edu

Antonios ArmaouDepartment of Chemical EngineeringThe Pennsylvania State Universityarmaou@engr.psu.edu

CP7

Anytime A* for Continuous Optimal Path Plan-ning

Eikonal PDE can be used to find the value function ofan isotropic optimal control problem. These PDE can besolved efficiently using the Fast Marching Method, and A*methods provide additional computational savings. Wepresent an Anytime algorithm using FMM and ideas fromWeighted A*, quickly producing an initial suboptimal solu-tion that is iteratively improved. This ensures early avail-ability of a suboptimal path before the completion of thesearch for a globally optimal path.

Zachary D. ClawsonCornell Universityzc227@cornell.edu

Alexander VladimirskyDept. of MathematicsCornell Universityvlad@math.cornell.edu

CP7

A Proper Orthogonal Decomposition BasedMethod for Solving Algebraic Riccati Equations

We present a new method to solve algebraic Riccati equa-tions by employing a projection method based on ProperOrthogonal Decomposition. The method only requires sim-ulations of linear systems to compute the solution of aLyapunov equation. The leading singular vectors of theLyapunov solution are then used to construct a projec-tor which is employed to produce a reduced order sys-tem.Computational results and comparisons to other meth-ods will be discussed.

Boris KramerVirginia Techbokr@vt.edu

CP7

A New Semi-smooth Newton Multigrid Method forParabolic PDE Optimal Control Problems

A new semi-smooth Newton (SSN) multigrid algorithm isproposed for solving the discretized first order necessaryoptimality systems that characterizing the optimal solu-tions of a class of 2D semi-linear parabolic PDE optimalcontrol problems with control constraints. To achieve asecond-order accurate finite difference discretization, weuse a leapfrog scheme (with the second-order backwarddifferentiation formula (BDF2)) in time and a standard5-point stencil in space. The derived well-structured dis-cretized Jacobian matrices greatly facilitate the develop-ment of effective smoother in our multigrid algorithm. Nu-merical simulations are provided to illustrate the efficiencyof the proposed method, which validates the second-orderaccuracy in solution approximations and the optimal linearcomplexity in computational time.

Jun LiuSouthern Illinois University

12 AN14 Abstracts

junliu2010@siu.edu

Mingqing XiaoSouthern Illinois University at Carbondalemxiao@siu.edu

CP7

Computationally-Based Technique for BifurcationControl

In this paper, a computationally-based methodology to ob-tain chaos controllers for PWM buck power converters isproposed, developed and proven. The mathematical modelof a PWM is highly nonlinear (and non-smooth) and sim-ulations show rich phenomena. The controller is easy toimplement with an analog circuit, and it improves the per-formance of the system. Additionally, it reduces the per-centage of regulation error and eliminates non-desired or-bits. Computational and experimental results validate thecontroller design.

Gerard OlivarDepartment of Electrical and Electronics EngineeringUniversidad Nacional de Colombia, sede Manizalesgolivart@unal.edu.co

Daniel MorcilloUniversidad Nacional de Colombia - Manizalesjdmorcillob@unal.edu.co

Daniel BurbanoUniversita degli Studi di Napolidanielalberto.burbanolombana@unina.it

Fabiola AnguloDepartment of Electrical and Electronics EngineeringUniversidad Nacional de Colombia, sede Manizalesfangulog@unal.edu.co

CP8

Accelerated Hierarchical Stochastic Collocation -Finite Element Methods for PDEs with RandomInputs

The dominant cost of stochastic collocation methods forPDEs with high-dimensional random inputs are the cost ofsolving large numbers of linear systems. For non-intrusivemethods like stochastic collocation, each linear system canbe solved separately. Instead we consider global and lo-cal, hierarchical, semi-intrusive methods that acceleratethe performance of the finite element solvers and look atthe conditions under which computational costs can be re-duced.

Diego Galindo, Clayton G. Webster, Guannan ZhangOak Ridge National Laboratorygalindod@ornl.gov, webstercg@ornl.gov, zhangg@ornl.gov

CP8

Uncertainty Qualification Based on Ranking FuzzyNumbers

In this paper, we present a new method for uncertaintyqualification based on ranking fuzzy number. First, wepresent a new method for ranking fuzzy numbers. Itconsiders left and right area deviation. The proposedmethod can overcome the drawback of some existing meth-ods for ranking fuzzy numbers. Then, we apply the pro-

posed method for ranking fuzzy numbers to develop a newmethod for dealing with fuzzy risk analysis problems.

Tayebeh HajjariDepartment of MathematicsFiroozkooh Branch of Islamic Azad Universitytayebehajjari@yahoo.com

CP8

Reduced Basis Methods for Maxwell’s Equationswith Stochastic Coefficients

We consider parametrized partial differential equationsin many-query settings. We discuss the Reduced BasisMethod (RBM) for time-harmonic Maxwell’s equations un-der stochastic parameters. The RBM model reduction sig-nificantly reduces the system size while preserving a certi-fied accuracy by employing rigorous error estimators. Toquantify the statistical outputs like mean and variance forMaxwell’s equations under stochastic uncertainties, we usesparse collocation and weighted RBM. Numerical experi-ments are performed on 3D models of microwave devices.

Martin W. HessMax-Planck-Institute for Dynamics of Complex TechnicalSystems Magdeburghessm@mpi-magdeburg.mpg.de

Peter BennerMax Planck Institute, Magdeburg, Germanybenner@mpi-magdeburg.mpg.de

CP8

Use of Polynomials of Chaos as Regression Func-tions for Universal Kriging Models and Applicationto Numerical Dosimetry

In the computer experiments domain, Universal Krigingand Polynomial Chaos are two widely used metamodel-ing approaches. Considering a sparse representation of thePolynomial Chaos expansion gathering the most influentpolynomials with the Least Angle Regression, this commu-nication proposes to use these polynomials as regressionfunctions in the Universal Kriging model. The optimalperformances of the proposed approach are illustrated withseveral benchmark functions and with a dosimetry exam-ple.

Pierric KersaudyOrange Labspierric.kersaudy@orange.com

Bruno SudretETH Zurichsudret@ibk.baug.ethz.ch

Odile PiconUniversite Paris-Estodile.picon@univ-mlv.fr

Joe WiartOrange Labsjoe.wiart@orange.com

CP8

Quasi Optimal Sparse-Grid Approximations for El-

AN14 Abstracts 13

liptic PDEs with Stochastic Coefficients

Solution of PDEs depending on random coefficients can beconveniently approximated by polynomial expansions onthe parameter space, that suffer however from a perfor-mance degradation as the number of random parametersincreases (“curse of dimensionality’ effect). In this talk wewill propose an “a-priori/a-posteriori knapsack approach’to minimize such effect for sparse grids approximations.The efficiency of the proposed technique will be supportedby theoretical convergence results and numerical tests.

Lorenzo TamelliniEPF-Lausanne, Switzerland,lorenzo.tamellini@epfl.ch

Fabio NobileEPFL, Switzerlandfabio.nobile@epfl.ch

Raul F. TemponeMathematics, Computational Sciences & EngineeringKing Abdullah University of Science and Technologyraul.tempone@kaust.edu.sa

CP9

Subharmonic Response and Threshold of ChirpDriven Microbubbles

Recent experimental results have shown that acousticallydriven microbubbles may exhibit an enhanced subharmonicresponse if driven by nonstationary (chirp) waveforms.However, the previous theory on the subharmonic thresh-old has been limited to single frequency forcing. We presenta method for predication of the threshold using a energyratio of the IMFs from a Empirical Mode Decompositionof the scattered acoustic signal. Results are compared forlinear and finite elastic models of an encapsulating shell forultrasound contrast agent microbubble applications.

John S. AllenUniversity of Hawaii-Manoaalleniii@hawaii.edu

Rintaro HayashiUniversity of Hawaii at Manoarintaro@hawaii.edu

CP9

A Global Bifurcation of Mixed-Mode Oscillations

Mixed-mode oscillations (MMOs) are trajectories of dy-namical systems in which large and small oscillations oc-cur with a distinct gap between the two. Over two decadesago, Koper first observed the seemingly paradoxical emer-gence of complex MMOs in a (now canonical) model. Wedescribe the successful detection of an elusive global bi-furcation that only now resolves this paradoxical dynam-ics. Our techniques are based on computation of invariantmanifolds and continuation methods.

Ian M. LizarragaCenter for Applied MathematicsCornell Universityiml32@cornell.edu

John GuckenheimerCornell University

jmg16@cornell.edu

CP9

Mixing and Piecewise Isometries on a Hemisphere

We study chaotic nonlinear dynamics and mixing on ahemispherical surface using piecewise isometries (PWI)motivated by cutting and shuffling in 3-D granular flow.Mapping singularities with simple PWI for different pa-rameters yield a variety of complex patterns on the hemi-sphere’s surface termed the exceptional set (E). Coarse-grained measures of E suggest that E exhibits propertiesof fat fractals that may provide deeper insight into mixingby cutting and shuffling.

Paul ParkNorthwestern Universitypaul-park@northwestern.edu

Paul Umbanhowar, Julio OttinoNorthwestern UniversityEvanston, IL 60208-3109umbanhowar@northwestern.edu,jm-ottino@northwestern.edu

Richard M. LueptowNorthwestern UniversityDepartment of Mechanical Engineeringr-lueptow@northwestern.edu

CP9

Variational Integrators for Interconnected DiracMechanical Systems

Dirac mechanics simultaneously generalizes Lagrangianand Hamiltonian mechanics to reveal the geometric struc-ture of systems with forces, constraints and degeneracies.Jacobs and Yoshimura recently elucidated the relationshipbetween the Dirac mechanical structure of an intercon-nected system and those of its components. The varia-tional integrator construction derives structure-preservingintegrators from discrete variational principles, producingsymplectic, momentum preserving integrators where ap-plicable. This talk will discuss extensions of existing Diracvariational integrators to accommodate interconnections.

Helen F. ParksUniversity of Pittsburghparks.helen@gmail.com

Melvin LeokUniversity of California, San Diegomleok@ccom.ucsd.edu

CP9

Different Wave Solutions Associated with SingularLines on Phase Plane

The bifurcation phenomena of a compound K(m,m) equa-tion are investigated. Three singular lines have been foundin the associated topological vector field, which may evolvein the phase trajectories of the system. The influence ofparameters as well as the singular lines on the properties ofthe equilibrium points has been explored in details. Tran-sition boundaries have been obtained to divide the param-eter space into regions associated with different types ofphase trajectories. The existence conditions and related

14 AN14 Abstracts

discussions for different traveling wave solutions have beenpresented in the end.

Yu V. WangYork College, The City University of New Yorkvwang@york.cuny.edu

CP10

A Domain Decomposition Method for CavitationComputation in Nonlinear Elasticity

A domain decomposition method is applied to computecavity growth in nonlinear elasticity. The idea is that thematerial is first tailored into nonoverlapping circular ringsub-domains so that each one is a scaling of the other; then,the standard Dirichlet to Neummann boundary conditionsare applied to pass the information from a subproblem toits neighbors; finally, some special measures are taken tostabilize the method. The convergence speed is greatlyimproved by the method.

Zhiping LiSchool of Mathematical Sciences, Peking Universitylizp@math.pku.edu.cn

Wulin LuoSchool of Mathematical SciencesPeking Universitywulinlovely@gmail.com

CP10

On Strong Ellipticity for Implicit and Strain-Limiting Theories of Elasticity

Implicit constitutive theories for elastic material bodieshave received increasing attention in the literature. Thetheories are used to formulate strain limiting models ofelasticity, and to develop nonlinear constitutive relationsbetween linearized strain and stress. We study strong el-lipticity for a general class of elastic implicit constitutiverelations and apply it to specific examples. For the con-sidered examples, strong ellipticity is shown to hold forsufficiently small strain and fail for suitably large strain.

Tina MaiDepartment of Mathematics, Texas A&M UniversityCollege Station, TX 77843-3368mai@math.tamu.edu

Jay R. WaltonDepartment of MathematicsTexas A&Mjwalton@math.tamu.edu

CP10

Direct Numerical Simulation of Anti-Plane ShearFracture in New Class of Elastic Bodies

In this work we study Finite Element Method (FEM) forthe problem of anti-plane shear fracture in the setting of astrain-limiting theory of elasticity. Recently Rajagopal andWalton used a new class of such models to study anti-planestrain fracture. Using asymptotic analysis of the modelnear the tip of crack, they showed that both stress andstrain vanish at the crack-tip, and the crack separationdisplacement has a cusp-shaped profile. The FEM baseddirect numerical simulation indicates that the present ap-proach removes the classical square root singularity and

hence predicts bounded stress and strain at the crack-tip.

Mallikarjunaiah S. MuddamallappaDepartment of MathematicsTexas A&M Universitymmallikarjuna@math.tamu.edu

Jay R. WaltonDepartment of MathematicsTexas A&Mjwalton@math.tamu.edu

CP10

Peridynamics As a Multiscale Method

The peridynamic theory of solid mechanics is a stronglynonlocal theory that contains a length scale represent-ing the maximum interaction distance between materialpoints. Recent work shows that by varying this lengthscale, we can achieve a multiscale model of solids within asingle theory, without the need to couple dissimilar meth-ods. In this talk I will describe a hierarchical multiscalemethod based on the peridynamic equations and appropri-ate coarse graining of material properties.

Stewart SillingSandia National Laboratoriessasilli@sandia.gov

CP10

Light Beam Interaction in Nonlinear Optical Media

The dynamics of light beam interaction in Nonlinear Op-tical Media is studied numerically and analytically. Thebeam dynamics is simulated by the beam propagationmethod. The numerical results agree with the results ofthe analytic model. The results show that the reflectionand transmission can be predicted and controlled by thetrapped beam at the interface of two nonlinear optical me-dia. Some interesting new results will be presented in thistalk.

Rajah P. VaratharajahNorth Carolina A&T State Universityrajah@ncat.edu

CP11

Variance Reduction in the Simulation of StochasticDifferential Equations

Variance reduction techniques are commonly used to en-hance the efficiency of Monte Carlo simulations. This talkfocuses on variance reduction for single and coupled sys-tems of stochastic ordinary differential equations. Variancereduction techniques such as antithetic variates and controlvariates will be described and results presented.

David J. HorntropDept of Mathematical Sciences, Center for Applied MathNew Jersey Institute of Technologydavid.horntrop@njit.edu

CP11

A Guaranteed Automatic Integration Library forMonte Carlo Simulation

This talk introduce the Guaranteed Automatic IntegrationLibrary (GAIL), which was developed within last year. It

AN14 Abstracts 15

contains four algorithms, which perform function approxi-mation, numerical integration(using Monte Carlo methodand 1-D trapezoidal rule) and Monte Carlo for evaluat-ing the mean. All routines come with theoretical guaran-tees of success, something that is missing, say, for MAT-LAB’s integral.m and nearly all other automatic algo-rithms. Moreover, GAIL has been carefully designed witha friendly user-interface, thorough documentation, and ex-tensive testing. Also, this talk discuss the theoretical re-search on the reliable relative error estimation based on theprevious work, which comes with the numerical results andproved theorems.

Lan JiangDpet. of Applied MathematicsIllinois Institute of Technologyljiang14@hawk.iit.edu

CP11

Reliable Error Estimation for Quasi-Monte CarloMethods

This project aims to build an efficient algorithm based onextensible rank-1 lattice rules for multidimensional integra-tion with guarantees. In order to proceed, we compute thea Fast Fourier Transform on the integrand values sampledon an integration lattice and use them to approximate theFourier coefficients of the integrand. The decay rate of theFourier coefficients and the assumption that the integrandslie inside a given cone helps us approximate the error.

Lluis Antoni Jimenez Rugama, Fred J. HickernellIllinois Institute of Technologylluisantoni@gmail.com, hickernell@iit.edu

CP11

Split-Step Balanced Milstein Methods for Multi-Channel Stiff Stochastic Differential Systems

We discuss systems of ordinary SDEs with non-commutative multi-channel noise arising in chemical net-works that involve reactions at different time scales. Suchsystems are inherently stiff, both in deterministic andstochastic components, and can change stiffness with un-certainty. To resolve this issue we consider fully implicitsplit-step balanced methods with optimal parameter selec-tions with respect to the desired convergence, stability andpositivity properties. Numerical examples are provided toshow the effectiveness of these methods.

Viktor Reshniak, Abdul KhaliqMiddle Tennessee State Universityvr2m@mtmail.mtsu.edu, abdul.khaliq@mtsu.edu

David A. VossWestern Illinois Universityd-voss1@wiu.edu

CP11

Local Smoothers for Cdfem with Sub-Element Dis-continuities

The conformal decomposition finite element method (atechnique for handling sub-cell discontinuities) allows forLagrangian-like interfaces in a (basically) Eulerian mesh.As the physics ”chooses” the location of the interface, itcan lie very close to element boundaries, which can hurtmatrix conditioning and the linear solver. We present a

local smoothing multigrid approach, which uses informa-tion about geometry near the interface to perform a singlegeometric coarsening to a problem with volume-averagedmaterials.

Christopher Siefert, Richard KramerSandia National Laboratoriescsiefer@sandia.gov, rmkrame@sandia.gov

CP11

Various Strategies for the Numerical StochasticHomogenization of the Stochastic Poisson andHelmholtz Equations

We consider stochastic versions of the Poisson equationas well as of the Helmholtz equation with discontinuouscoefficients. These equations arise, e.g., when modelingnanowire sensors and metamaterials with a random struc-ture. Although there are some theoretic homogenizationresults, the question of how to compute solutions effi-ciently still remains. Here, we discuss approximations ofthe stochastic dimensions by various quasi-MC strategiesand which boundary conditions and size of the domain touse when approximating the problem on the whole space.

Gerhard TulzerTU Vienna, Austriagerhard.tulzer@tuwien.ac.at

Clemens F. HeitzingerArizona State University &Technical University Vienna (TU Vienna)Clemens.Heitzinger@asu.edu

CP12

Iron-dependent Oxidative Stress Response Path-way in Human Mammary Epithelial Cells

It has been known that iron plays an important role inthe development of breast cancer and cancer cells are un-der persistent oxidative stress. However, the effect of ironoverload on the oxidative stress response pathway in nor-mal and cancer cells is still under study. This project fo-cuses on a mathematical model of an oxidative stress re-sponse pathway in normal human breast cells in order tounderstand how normal cells transition malignant cells.

Seda AratVirginia Techsedag@vt.edu

Julia ChifmanWake Forest School of Medicinejchifman@wakehealth.edu

Suzy Torti, Reinhard LaubenbacherUniversity of Connecticut Health Centerstorti@uchc.edu, laubenbacher@uchc.edu

CP12

A Mathematical Model for Glucose and Fatty AcidMetabolism

A model is presented for the rate of utilization and stor-age of carbohydrates and fats. It is based on differentialequations for the chemical kinetics converting glucose andfatty acids to pyruvate and acetylCoA, which then enterthe Krebs cycle to produce energy. The molecules can also

16 AN14 Abstracts

be stored as glycogen and fat. The conversion rates aremodeled as Hill’s reactions. Results are presented for dif-ferent conditions of supply and usage.

Donald A. DrewRensselaer Polytech InstituteDept of Mathematical Sciencesdrewd3@rpi.edu

Julienne LaChanceRensselaer Polytechnic Institutelachaj3@rpi.edu

CP12

Multiscale Simulation of Reaction-Diffusion Sys-tems in Living Cells

We present a simulation algorithm that allows for dynamicswitching between a microscopic and a mesoscopic model-ing framework for stochastic reaction-diffusion kinetics. Bydiscretizing space with an unstructured mesh we can carryout simulations in complex and realistic geometries. Theaccuracy and efficiency of the algorithm is demonstratedin numerical examples inspired by biological applications.We show that by simulating only parts of a system at themore detailed, microscopic level, we can reduce the compu-tational cost significantly while retaining the accuracy ofthe full microscopic model. The method can be combinedwith microscopic simulations of dynamic lower dimensionalstructures such as DNA or fibers, where the microscopicsimulations are used close to the complex parts of the ge-ometry, and the more efficient mesoscopic simulations areused in the other parts of space.

Stefan HellanderUppsala University, Swedenst.hellander@gmail.com

Andreas HellanderUppsala Universityandreas.hellander@it.uu.se

Linda PetzoldUniversity of California, Santa Barbarapetzold@cs.ucsb.edu

CP12

A Simulator of the Multi-Scale Dynamics of GeneRegulatory Networks

We propose a simulator of an ODEmodel class of the multi-scale dynamics of gene regulatory networks with steep sig-moidal interactions. The threshold-dependent dynamicsdivides the phase space into domains. Under specific as-sumptions, trajectories through any sequence of domainsare derived by iterating a local computation of transitionsbetween domains. The parameter values can be expressedeither qualitatively by inequalities or by probability dis-tribution. In the latter case, the probability of trajectoryoccurrence is calculated.

Liliana IroniIMATI - CNRPavia (Italy)ironi@imati.cnr.it

CP12

Bioechemical Network Structure can be Revealed

with Timecourse Data

Due to the limit of current experimental techniques, iden-tifying biochemical network among genes and proteins un-derlying biological systems is one of the most challengingworks. On the other hand, output of the networks, time-courses of genes and proteins can be easily acquired withrecent advances in technology (e.g. microarray analysis).In this work, we will describe how to use oscillating time-course data to reveal the biochemical network structure byusing a fixed-point criteria.

Jae Kyoung KimDepartment of MathematicsUniversity of Michigan, Ann Arbor, Michigan 48109, USAkim.5052@mbi.osu.edu

Daniel B. Forger IIIUniversity of Michiganforger@umich.edu

CP12

Using Machine Learning andMetabolomic/transportomic Systems Model-ing to Identify Bacterial Ecotype from GenomicSequence of Uncharacterized Environmental OrClinical Isolates

The ability to genomically sequence bacteria from envi-ronmental or clinical isolates that are not or cannot becultured in the laboratory requires development of compu-tational tools to predict bacterial ecotypes from genomicdata. Using Psuedomonads for which complete genomesare available and ecotype is known or inferred, we demon-strate that support vector machines using features derivedfrom computational modeling of bacterial metabolome andtransportome is more predictive of Psuedomonads ecotypethan using only genomic data.

Peter E. Larsen, Frank CollartArgonne National Laboratoryplarsen@anl.gov, fcollart@anl.gov

Yang DaiLaboraory of Computational Functional GenomicsUniversity of Illinois at Chicahoyangdai@uic.edu

CP13

Non-Parametric Clustering with Rank-Constrained Least-Squares

Unsupervised clustering is a problem of great practical im-portance, from genetics to marketing, extreme events mod-elling or even financial engineering. Although most avail-able techniques perform well in practice, most of them re-quire solving an NP-hard optimization problem or requireto know the number of clusters ahead of time. Our goalis to present a simple technique for fast joint estimation ofthe number of clusters and their respective center of mass.Assuming the data can be represented as a d × n matrixX = C + E, where C = MT , E is a matrix-noise, M isthe center of mass matrix, and Tk,i = 1 if Xi belongs tocuster k and Tk,i = 0 otherwise. This representation leadsto searching for a low rank approximation of X. The rankof C is the number of clusters and is efficiently estimatedusing recent work in model selection. The approximationitself can be performed using the power method and its

AN14 Abstracts 17

recent analysis by Hardt.

Stephane ChretienUniversite de Franche Comtestephane.chretien@univ-fcomte.fr

CP13

Stationary Stability for Evolutionary Dynamics inFinite Populations

We extend the theory of evolutionary stability to multidi-mensional finite populations with mutation, connecting thetheory of the stationary distribution of the Moran processwith the Lyapunov theory of evolutionary stability for thereplicator dynamic. We show essentially that the local ex-trema of the stationary distribution minimize the relativeentropy of the current population state and the ”expectednext state” computed by weighting the adjacent states bythe appropriate transition probabilities. This holds fora variety of selection processes including the increasinglypopular Fermi selection. We present several complete com-putational examples for illustration and we show that theclassical stability theory of the replicator dynamic is re-covered in the large population limit. If time allows, wedescribe extensions to populations evolving on graphs.

Dashiell FryerPomona CollegeDashiell.Fryer@Pomona.edu

Marc HarperUCLAmarcharper@ucla.edu

CP13

A Novel Concept of Normal Exponential ROCModel

Receiver Operating Characteristic (ROC) Curve is used toquantify and compare the accuracy of diagnostic tests. Inthis paper, Normal Exponential ROC model is proposedand its properties are studied when healthy test scoresfollow Normal distribution and diseased test scores followExponential distribution. Area under the proposed ROCcurve and its standard error are derived. The utility ofthis model is explored using simulation studies and Serumconcentrations of CA 19-9 (Carbohydrate antigen) for pan-creatic cancer. At the end, it is found that proposed ROCmodel gives better accuracy as compared to the traditionalBinormal ROC model.

Sudesh PundirPondicherry Universitysudeshpundir19@gmail.com

CP13

Storage Allocation Models with Finite Capacity

We consider a stochastic storage allocation model, whichhas m primary holding spaces and R secondary ones. All ofthe spaces are numbered and ordered, and an arriving cus-tomer takes the lowest ranked available space. We definethe traffic intensity ρ to be λ/μ where λ is the customers’arrival rate and μ is the service rate of the processor. If welet m+R = N , the total number of stored items behaves asan M/M/N/N queue, which is the Erlang loss model. Weobtain the joint probability distribution of the numbersof occupied primary and secondary spaces, for ρ → ∞.

We also study the marginal distribution of the number ofoccupied secondary spaces, as well as various conditionaldistributions.

Eunju SohnUniversity of Georgiaesohn@colum.edu

Charles KnesslUniversity of Illinois at Chicagoknessl@uic.edu

CP14

Using Lasso Model to Predict Cell-Type-SpecificTranscription Factors in Low Methylated Regions

Low Methylated Regions (LMRs) have been implied tobe potential distal regulatory regions. Using the tran-scription factor binding sites (TFBSs) predicted from bothLMRs and promoters, we apply LASSO models to pre-dict directions of gene expression among multiple cell typesbased on the similarity score of TFBSs. By analyzing theLASSO results, we demonstrate that the model can fa-cilitate the identification of cell-type-specific transcriptionfactors binding that may potentially regulate directions ofgene expression.

Hong HuBioinformatics Program, Department of BioengineeringUniversity of Illinous at Chicagohhu4@uic.edu

Yang DaiLaboraory of Computational Functional GenomicsUniversity of Illinois at Chicahoyangdai@uic.edu

CP14

Moment Fitting for Parameter Inference in Re-peatedly and Partially Observed Stochastic Biolog-ical Models

The inference of reaction rate parameters in biochemicalnetwork models from time series concentration data is acentral task in computational systems biology. Under theassumption of well mixed conditions the network dynam-ics are typically described by the chemical master equation.Based on the latter we derive closed systems of parameterdependent nonlinear ordinary differential equations thatpredict the time evolution of the statistical moments. Forinferring the reaction rate parameters we suggest to notonly compare the sample mean with the theoretical meanprediction but also to take the residual of higher order mo-ments explicitly into account. Cost functions that involveresiduals of higher order moments may form landscapes inthe parameter space that have more pronounced curvaturesat the minimizer and hence may weaken or even overcomeparameter sloppiness and uncertainty.

Philipp KueglerRICAM, Austrian Academy of SciencesAustriaphilipp.kuegler@uni-hohenheim.de

CP14

Mathematical Modeling of the Antibiotic Er-

18 AN14 Abstracts

tapenem

Ertapenem is an antibiotic commonly used to treat a broadspectrum of infections. A physiologically-based pharma-cokinetic model was developed to investigate the uptake,distribution, and elimination of ertapenem following aonce-a-day, single one gram dose. Blood concentrationsof ertapenem found by the model were compared to datafrom published experimentation for normal height, normalweight males. Simulations were performed to consider thedistribution of the antibiotic in underweight, overweight,and obese men of normal height.

Cammey Cole ManningAWM and Meredith CollegeManningC@meredith.edu

Michele JoynerEast Tennessee State Universityjoynerm@mail.etsu.edu

CP14

Connecting Motifs and Molecular Mechanisms To-ward Control of Complex Networks

Advances in high throughput biological assays have pro-moted statistical inference of large experimental datasets;the subsequent networks are then used as models to dis-cover therapeutic targets. However, these networks yieldlittle mechanistic insight into the cornerstones of complexbiological systems: regulation and dynamics. Comprehen-sive analysis of networks inferred from in silico models thatrepresent biological mechanisms (e.g., competitive inhibi-tion) elucidates our understanding of large network dynam-ics and informs novel control strategies.

Aaron OppenheimerNorthwestern UniversityDepartment of Chemical and Biological Engineeringaaronoppenheimer2016@u.northwestern.edu

Neda BagheriChemical and Biological EngineeringNorthwestern Universityn-bagheri@northwestern.edu

CP14

A Combined Method of Model Reduction for Bio-chemical Reaction Networks

This talk introduces a combined model reduction algorithmwith particular application to biochemical reaction net-works within the context of systems pharmacology. Thismethod brings together versions of proper lumping and em-pirical balanced truncation to reduce nonlinear, stiff dy-namical systems that are typical in the modelling of bio-chemical reactions. Modifications and enhancements to theestablished methods are discussed. Finally, the algorithmis demonstrated with application to two published systemsbiology models, with good results.

Tom J. Snowden, Marcus TindallUniversity of ReadingT.J.Snowden@pgr.reading.ac.uk, m.tindall@reading.ac.uk,

Piet van Der GraafUniversiteit LeidenPfizer

p.vandergraaf@lacdr.leidenuniv.nl

CP14

Discovery of Multi-Dimensional Modules in CancerGenomic Data

Recent technology has made it possible to simultane-ously perform multi-platform genomic profiling of bio-logical samples, resulting in so-called ’multi-dimensionalgenomic data’. However, integrative analysis of multi-dimensional genomics data for the discovery of combina-torial patterns is currently lacking. Here, we develop a setof matrix factorization techniques to address this challenge.We applied this method to the data from the The CancerGenome Atlas project, and show that our tools can uncoverhidden patterns in multi-dimensional cancer ’omic’ data.

Xianghong J. ZhouBiological Science and Computer ScienceUniversity of Southern Californiaxjzhou@dornsife.usc.edu

CP15

Fourth Order Compact Simulation of the One Di-mensional Euler Equations of Gas Dynamics

This paper introduces a class of higher order compactschemes for the solution of one dimensional (1-D) Eulerequations of Gas Dynamics. These schemes are fourthorder accurate in space and second or lower order accu-rate in time and unconditionally stable. To test the effi-ciency of our proposed schemes, we first apply it to threeshock tube problem of gas dynamics, including the famousSOD shock tube problem. Later on, we apply our pro-posed schemes to the subsonic-supersonic isentropic flowthrough a convergent-divergent nozzle and compare oursolution with the exact solutions. In all the cases, ourcomputed numerical solutions are found to be in excellentmatch with the exact ones. Lastly, we show ways to extendthe schemes to problems of higher spatial dimensions.

Jiten C. KalitaIndian Institute of Technology GuwahatiGuwahati INDIAjiten@iitg.ernet.in

Bidyut GogoiIndian Institute of technology Guwahati INDIAb.gogoi@iitg.ernet.in

CP15

High Order Parametrized Maximum-Principle-Preserving and Positivity-Preserving WenoSchemes on Unstructured Meshes

We will talk about the generalization of the maximum-principle-preserving (MPP) flux limiting technique devel-oped in [Z. Xu, Math. Comp., (2013)] to develop a classhigh order MPP finite volume schemes for scalar conser-vation laws and positivity-preserving (PP) finite volumeWENO schemes for compressible Euler system on two di-mensional unstructured meshes. The key idea of this pa-rameterized technique is to limit the high order schemestowards first order ones which enjoy MPP property, bydecoupling linear constraints on numerical fluxes. Erroranalysis on one dimensional non-uniform meshes is pre-sented to show the proposed MPP schemes can maintainhigh order of accuracy. Similar approach is applied to solve

AN14 Abstracts 19

compressible Euler systems to obtain high order positivity-preserving schemes. Numerical examples coupled withthird order Runge-Kutta time integrator are reported.

Yuan LiuDepartment of MathematicsMichigan State Universityliuyuan01@gmail.com

CP15

Scalable High-Order Non Conforming Finite Ele-ment Methods For Time Domain Acoustic-ElasticProblems

High-order numerical methods for solving time-dependentacoustic-elastic coupled problems are introduced. Thesemethods, based on Discontinuous Galerkin and ClassicalFinite Element techniques, allow for a flexible couplingbetween the fluid and the solid domain by using non-conforming meshes and curved elements. Importantly,physical domains may be independently discretized and thestructural geometry is faithfully represented upon a chosendegree of fidelity, enabling for higher flexibility and efficientcomputation. In order to illustrate the accuracy and scal-ability properties of a parallel implementation, we presentrepresentative numerical tests for large-scale seismic wavepropagation.

Angel Rodriguez-RozasCenter for Mathematics and its ApplicationsDepartment of Mathematics - Instituto Superior Tecnicoangel.rodriguez rozas@inria.fr

Julien DiazTeam-Project Magique-3DINRIA Bordeaux Sud-Ouestjulien.diaz@inria.fr

CP15

Advances in Adaptively Weighted Finite ElementMethods

The overall effectiveness of finite element methods maybe limited by solutions that lack smoothness on a rela-tively small subset of the domain. By enhancing normsand and/or inner products in the variational frameworkwith weight functions chosen according to a coarse-scaleapproximation, it is possible to recover near-optimal con-vergence rates. In this talk we give an overview of thegeneral approach, both in the least-squares and Galerkinsettings, and illustrate with numerical examples.

Chad WestphalWabash Collegewestphac@wabash.edu

CP15

Numerical Simulations of Bioresorbable VascularStent with Automatic Patient-Specific GeometryConstruction and Adaptive Meshing

The invention of Bioresorbable Vascular Stent(BVS)opened a new era for cardiovascular intervention technol-ogy as it offers numerous benefits for patients. Patient-specific CFD Simulation of stented vessel is a great toolto analyze potential risks of BVS such as restenosis. Cur-rent work in BVS research is limited to geometries withno clear appearance of the stent. However, we have devel-

oped an algorithm that extracts the 3D geometry of thedeployed stent from real patients OCT images. Visualiza-tion of the blood flow in stented vessel for the first timebecomes a reality. Combined with an adaptive meshingmethod, real inflow, and real vessel curvature, our CFDsimulations can best approximate the real hemodynamicconditions of the stented vessel and provide many desirableresults, which demonstrates the great power of numericalPDEs in biomedical engineering.

Boyi YangEmory UniversityDepartment of Mathematics & Computer Sciencebyang8@emory.edu

Alessandro VenezianiMathCS, Emory University, Atlanta, GAale@mathcs.emory.edu

CP15

A Finite Element Method for the Second OrderLinear Elliptic Equation in Non-Divergence Form

We design a finite element method for the linear ellipticequation in non-divergence form, which satisfies discretemaximum principle. We show that the method guaran-tees convergence to the viscosity solution provided thatcoefficient matrix A(x) and function f(x) are continuous.In order to establish a rate of convergence, we derive adiscrete version of Alexandroff-Bakelman-Pucci estimate.Using this discrete estimate, we show that

‖ u− uh ‖L∞ ≤ C

(h2 ln

1

h

)α/(2+α)

for u ∈ C2,α(Ω), f ∈ Cα(Ω), and

‖u− uh ‖L∞ ≤ C

(ln h2 1

h

)1/2

for u ∈ C3,1(Ω), f ∈ C0,1(Ω).

Wujun ZhangDepartment of MathematicsUniversity of Marylandwujunzhang@gmail.com

Richardo NochettoUniversity of MarylandDepartment of Mathematicsrhn@math.umd.edu

CP16

The Influence of Stochastic Parameters on CalciumWaves in a Heart Cell

In this study, we investigate the effects of stochastic releasefrom calcium release units (CRUs) on generating calciumwaves considering a distribution for the flux density termsampled (i) once for all CRUs and (ii) for each CRU in-dependently. We include a stochastic flux density term asmore physiologically appropriate than a fixed release rate.We use an array of statistical techniques as well as paral-lel computing to facilitate the large number of simulationruns.

Matthew W. BrewsterUniversity of Maryland, Baltimore Countybmatt3@umbc.edu

20 AN14 Abstracts

Xuan HuangDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countyhu6@umbc.edu

Matthias K. GobbertUniversity of Maryland, Baltimore CountyDepartment of Mathematics and Statisticsgobbert@umbc.edu

Bradford E. PeercyDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countybpeercy@umbc.edu

Padmanabhan SeshaiyerGeorge Mason Universitypseshaiy@gmu.edu

CP16

Simulation of Calcium Waves in a Heart Cell onModern Parallel Architectures

Simulating calcium induced calcium flow in a heart cellrequires solving a system of advection-reaction-diffusionequations in three space dimensions. Efficient parallelcomputing is necessary to enable long-time simulations onhigh-resolution meshes. Modern architectures with multi-ple memory hierarchies in CPU and coprocessors such asGPUs and the Intel Phi offer opportunities to speed up thenumerical kernels of PDE solvers dramatically.

Xuan HuangDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countyhu6@umbc.edu

Matthias K. GobbertUniversity of Maryland, Baltimore CountyDepartment of Mathematics and Statisticsgobbert@umbc.edu

Bradford E. PeercyDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countybpeercy@umbc.edu

CP16

A Model of Brain Neuro-Mechanics

Brain tissue is sensitive to mechanical forces and chem-ical imbalances which can alter brains functions and/orstructure and lead to neurological diseases. Mathematicalmodels of brain neuro-mechanics can increase our under-standing of how brain works and help develop better di-agnostic and therapeutic tools. We propose to model thebrain as a mixture material and investigate the linkagesbetween neural activity and mechanical behavior of braintissue through computer simulations.

Bradford J. LapsanskyThe Pennsylvania State Universitybradjlap@comcast.net

Corina DrapacaDepartment of Engineering Science and MechanicsPennsylvania State University

csd12@psu.edu

CP16

Stochastic Homogenization of the One-Dimensional Keller-Segel Chemotaxis System

In this talk, we focus on the one-dimensional Keller-Segelchemotaxis system in a random heterogeneous domain.We assume that the corresponding diffusion and chemo-taxis coefficients are given by stationary ergodic processes,and we apply methods pertaining to stochastic two-scaleconvergence to derive the homogenized macroscopic equa-tions. Special attention is paid to developing numericalalgorithms for approximating the homogenized asymptoticcoefficients. This is joint work with Mariya Ptashnyk.

Anastasios MatzavinosDivision of Applied MathematicsBrown Universitytasos@brown.edu

Mariya PtashnykDivision of MathematicsUniversity of Dundeemptashnyk@maths.dundee.ac.uk

CP16

Neural Implementation of Shape-Invariant TouchCounter Based on Euler Calculus

One goal of neuromorphic engineering is to imitate thebrain’s ability to count the number of objects based onthe global consistency of the information from the pop-ulation of visual or tactile sensory neurons whatever theobjects’ shapes are. To achieve this flexibility, it is essen-tial to utilize topological methods rather than ad hoc algo-rithms. Although latest works by mathematicians tackledfundamental problems for shape-invariant count, they lackthe circuit implementations to save computational time forbig data. Here we propose a fully parallelized algorithmfor a shape-invariant touch counter for 2D pixels. Thetouch number is counted by the Euler integral, a general-ized integral, in which a connected component counter forbinary images (Betti number) was used as elemental mod-ule. Through examples, we demonstrate how the proposedcircuit embodies the Euler integral in the form of recur-sive vector operations, with scalability to high resolutionsof pixels.

Keiji MiuraTohoku Universitymiura@ecei.tohoku.ac.jp

Kazuki NakadaThe University of Electro-Communicationsk.nakada@ieee.org

CP17

Interface Tracking Using Level Set and A Fast Al-gorithm

Although moving interface problem is an interesting prob-lem in physics, it is challenging to obtain accurate and sta-ble numerical solution because interface problems are sin-gular and sensitive with small perturbations. In this talk,we will discuss an interface tracking method for the solutionof 2D incompressible Stokes flow problems within an unitdisk as an application of a fast algorithm [L. Borges and

AN14 Abstracts 21

P. Daripa, A fast parallel algorithm for the Poisson equa-tion on a disk, J. Comput. Phys., 16 (2001), pp. 151–192.]which is based on the principle of convolution of integralsinvolving Green’s function and exact analysis.

JoungDong KimTexas A&M Universityjdkim@math.tamu.edu

Prabir DaripaDepartment of MathematicsTexas A&M Universitydaripa@math.tamu.edu

CP17

Field-split Preconditioned Inexact Newton Algo-rithms

To improve the convergence of systems with unbalancednonlinearities, the field-split preconditioned inexact New-ton (FSPIN) algorithm is introduced as a complementaryform of the additive Schwarz preconditioned inexact New-ton (ASPIN) algorithm, based on partitioning of degrees offreedom in a nonlinear system by field type rather than bysubdomain. We introduce two types of FSPIN algorithms:Jacobi-type and Gauss-Seidel-type, and we augment theclassical Jacobi-type convergence theory for the latter.

Lulu LiuKing Abdullah University of Science and Technologylulu.liu@kaust.edu.sa

David E. KeyesKAUSTdavid.keyes@kaust.edu.sa

CP17

A Dual Iterative Substructuring Method with AnOptimized Penalty Parameter

In this talk, we will present a domain decompositionmethod based on augmented Lagrangian. The proposedmethod imposes the continuity on the interface not onlyby using Lagrange multipliers but also by adding a penaltyterm which consists of a positive penalty parameter and ameasure of the jump across the interface. The study forthe proposed method with an optimized penalty parame-ter will be discussed in terms of its convergence analysisand practical efficiency.

Eun-Hee ParkKAISTeh.park@kangwon.ac.kr

Chang-Ock LeeDepartment of Mathematical SciencesKAISTcolee@kaist.edu

CP17

Redefining a Mimetic Curl Operator Using Gauss’Theorem with Applications in Computational Cli-mate and Weather Modeling

The common way to define a Curl operator considersStoke’s Theorem and the concept of circulation. Com-mon numerical discretizations for this operator also usethis approach. In this work, we present a redefinition of

the Curl operator using Gauss’ Theorem instead. This re-definition allows us to present a discretization frameworkthat naturally inherits all the desirable properties of themimetic differential operators. We present the mathemati-cal justification for this redefinition and we implement thismimetic Curl operator testing it on 2 and 3D test cases.Physical applications concern the computational study ofhurricanes.

Eduardo J. SanchezComputational Science Research CenterSan Diego State Universityejspeiro@gmail.com

Guillermo MirandaSan Diego State UniversityComputational Science Research Centerunigrav7@gmail.com

Jose CastilloComputational Science Research CenterSan Diego State Universityjcastillo@sdsu.edu

CP17

Fast Structured Direct Spectral Methods for Dif-ferential Equations with Variable Coefficients

We study the rank structures of the matrices in Fourier-and Chebyshev-spectral methods for differential equationswith variable coefficients in one dimension. We show ana-lytically that these matrices have a so-called low-rank prop-erty, and develop a matrix-free direct spectral solver, whichhas nearlyO(N) complexity andO(N) memory. Numericaltests for several important but notoriously difficult prob-lems show the superior efficiency and accuracy of the directsolutions, especially when iterative methods have severedifficulties in the convergence.

Yingwei WangPurdue UniversityPurdue Universitywywshtj@gmail.com

Jie ShenPurdue Universityshen7@math.purdue. edu

Jianlin XiaPurduexiaj@math.purdue. edu

CP17

A Hybrid Fd-Fv Method for First-Order Hyper-bolic Systems

We describe a hybrid FD-FV approach to solve first-orderhyperbolic systems. These methods use cell averages andnodal values as dependent variables, and evolve them intime by the method of lines. They use the integral formof the PDE and Hermite interpolation polynomials to dis-cretize the cell averages and nodal values in space, respec-tively. We present the accuracy and stability analysis ofthese methods to solve problems in one and two dimen-sions.

Xianyi ZengDuke University

22 AN14 Abstracts

xy.zeng@duke.edu

CP18

Block Preconditioners for Biot’s Equations

Biot’s equations are a popular model for geomechanicalsimulations of fluid flow in elastic porous media. Thesesimulations are run on a very large scale, resulting in alarge number of unknowns. Further complicating mattersis that the domains have complex geometry and a vastrange of material parameters. The linear systems that ariseafter discretization of Biot’s equations are large enoughthat iterative methods are required. They are also badlyconditioned, making effective preconditioners essential. Inthis work we investigate the effectiveness of several differentpreconditioners over a wide range of material parameters.

Geoffrey DillonTexas Tech Universitygeoffrey.dillon@ttu.edu

Victoria HowleTexas Techvictoria.howle@ttu.edu

Rob KirbyBaylor Universityrobert kirby@baylor.edu

CP18

A Model for Tempo Synchronization in Music Per-formance

A model is derived for the manner in which performersof music establish and maintain tempi in the presence ofa conductor, other performers, and noise. The model as-sumes that a performer sets a tempo in response to severalstimuli. This tempo, or period, correction, occurs as a su-perposition of responses of the form of sensitivity timesstimulus. The model is solved and results obtained forseveral cases. A model for phase correction is also derived.

Donald A. DrewRensselaer Polytech InstituteDept of Mathematical Sciencesdrewd3@rpi.edu

CP18

Recycling and Updating Preconditioners for Se-quences of Linear Systems

For sequences of related linear systems, the computationof a preconditioner for every system can be expensive. Of-ten a fixed preconditioner is used, but this may not beeffective as the matrix changes. We analyze cheap updatesto preconditioners: Incremental updates (Calgaro et al)and sparse approximate inverse updates to ILUTP precon-ditioners and updates to factorized sparse approximate in-verse preconditioners (Bellavia et al.) Applications includemodel reduction, the Quantum Monte Carlo method, andothers.

Arielle K. Grim McnallyVirginia TechEric de Sturlerarielle5@vt.edu

Li Ming, Eric De SturlerVirginia Techliming@vt.edu, sturler@vt.edu

CP18

Sensitivity of Leverage Scores to Perturbations

The leverage scores of a matrix A with full column rankare the squared row norms of any matrix that containsan orthonormal basis for the range of A. Leverage scoresdescribe the importance of rows in regression problemsand are used as sampling probabilities in randomized al-gorithms for matrix computations. We bound the differ-ence between the leverage scores of A and a perturbationA+ΔA when the orthonormal basis is computed by a QRfactorization or SVD.

John HolodnakNorth Carolina State Universityjtholodn@ncsu.edu

Ilse IpsenNorth Carolina State UniversityDepartment of Mathematicsipsen@ncsu.edu

CP18

Symmetric Tensor Decompositions

A tensor is a multi-way or n-way array. A tensor is sym-metric if its entries are invariant to any permutation of itsindices. A tensor may also be symmetric with respect toa subset of its modes, i.e., if its entries are invariant toany permutation of a specific subset of its modes. We sur-vey the landscape of symmetric tensor decompositions andcompare various methods.

Tamara G. KoldaSandia National Laboratoriestgkolda@sandia.gov

CP18

Indefinite Preconditioning of the Coupled Stokes-Darcy System

We propose the use of an indefinite (constraint) precondi-tioner for the iterative solution of the linear system arisingfrom the finite element discretization of coupled Stokes-Darcy flow. We provide spectral bounds for the precon-ditioned system which are independent of the underlyingmesh size. We present numerical results showing that theindefinite preconditioner outperforms both standard blockdiagonal and block triangular preconditioners both withrespect to iteration count and CPU times.

Scott LadenheimTemple Universitysaladenh@temple.edu

Princ ChidyagwaiLoyola Universitypchidyagwai@loyola.edu

Daniel B. SzyldTemple UniversityDepartment of Mathematics

AN14 Abstracts 23

szyld@temple.edu

CP19

Optimisation and Conditioning in Variational DataAssimilation

Data assimilation merges observations with a dynamicalmodel to find the optimal state estimate of a system givena set of observations. It is cyclic in that it is applied atfixed time intervals and the beginning of each cycle in-corporates the previous cycle known as the backgroundor apriori estimate. Variational data assimilation aims tominimise a non-linear, least-squares objective function thatis constrained by the flow of the (perfect) dynamical model(4DVAR).Relaxing the perfect model assumption gives riseto weak-constraint 4DVAR, which has two formulations ofinterest. Gradient-based iterative solvers are used to solvethe problem. We gain insight into accuracy and conver-gence by studying the condition number of the Hessian.Bounds on the condition number are demonstrated using asimple model and are utilised to illustrate the effect of dif-ferent assimilation components on the conditioning whichcan highlight interesting architectural differences betweenboth formulations.

Adam El-SaidUniversity of Readinga.el-said@pgr.reading.ac.uk

Nancy K. NicholsUniversity of ReadingDepartment of Mathematicsn.k.nichols@reading.ac.uk

Amos LawlessUniversity of Readinga.s.lawless@reading.ac.uk

CP19

A Primal-Dual Simplex Algorithm to Enumeratethe Mixed Cells of a Polynomial System

When the polyhedral homotopy continuation method isused to locate all isolated zeros of a polynomial system, theprocess of enumerating all the mixed cells plays a criticalrole: it provides starting points for the solution paths andgoverns the efficiency of the continuation method. Whenlocating mixed cells, one must deal with a large number oflinear programming problems. Rather than the more pop-ular interior point method, the simplex method is used forthose LP problems because its underlying pivoting struc-ture provides indispensable information in the process. Anefficient primal-dual algorithm to enumerate all the mixedcells will be presented.

Tsung-Lin LeeNational Sun Yat-set Universityleetsung@math.nsysu.edu.tw

Tien-Yien LiDepartment of MathematicsMichigan State Universityli@math.msu.edu

CP19

Fitting a Straight Line in Three-Dimensional Space

by Total Least-Squares Adjustment

Over a century ago Pearson (1901) solved the problem offitting lines in 2-space to points with noisy coordinates inall dimensions. Surprisingly, however, the case of fittinglines in 3-space has seen little attention. We solve thisproblem using a new algorithm for the Total Least-Squaressolution within an Errors-In-Variables (EIV) Model, re-spectively an equivalent Gauss-Helmert Model. Follow-ing Roberts (1988), only four parameters are estimated,thereby avoiding over-parameterization that may lead tounnecessary singularities.

Kyle B. Snow, Burkhard SchaffrinSchool of Earth SciencesThe Ohio State Universitysnow.55@osu.edu, aschaffrin@earthlink.net

CP19

A Block-Coordinate Descent Approach for Large-Scale Sparse Inverse Covariance Estimation

The Sparse Inverse Covariance Estimation problem arisesin many statistical applications in Machine Learning. Inthis problem, the inverse of a covariance matrix of a multi-variate normal distribution is estimated, assuming that itis sparse. An l-1 regularized log-determinant optimizationproblem is solved to compute such matrices. Because ofmemory limitations, most algorithms are unable to handlelarge scale instances of this problem. We present a newblock-coordinate descent approach for solving the prob-lem for such large-scale data sets. Our method treats thesought matrix block-by-block using quadratic approxima-tions. Numerical experiments demonstrate the potential ofthis approach.

Eran TreisterComputer Science Department, Technioneran@tx.technion.ac.il

Javier TurekComputer Science DepartmentTechnionjaviert@cs.technion.ac.il

Irad YavnehComputer Science Department, Technionirad@cs.technion.ac.il

CP19

Coupled Spring Forced Multiagent CoordinationOptimization for Mixed-Binary Nonlinear Pro-gramming

Mixed-binary nonlinear programming(MBNP) optimizingthe network structure and network parameters simultane-ously has been seen widely applications in cyber-physicalsystem nowadays. Swarm intelligence based optimizationalgorithms simulate the cooperation and interaction be-haviors from social or nature phenomena as optimizationto solve complex, non-convex and/or ill-conditioned non-linear problems of high efficiency. In this research, we pro-pose a coupled spring forced multiagent coordination op-timization (CSFMCO) algorithm by considering that eachparticle is a spring and is coupled with the optimal solutionfounded so far as the second abstract spring to offer a newefficient algorithm to solve the MBNP problem. Contin-uous optimizer, binary optimizer and the switch between

24 AN14 Abstracts

continuous and binary optimizers will be investigated.

Haopeng Zhang, Qing HuiDepartment of Mechanical EngineeringTexas Tech Universityhaopeng.zhang@ttu.edu, qing.hui@ttu.edu

CP20

Modeling Accidental Explosions and Detonations

The physical mechanism and constraints required for a De-flagration to Detonation Transition (DDT) in a large num-ber of explosive devices is investigated. The Uintah Com-putational Framework is utilized to model explosives usinglarge computational platforms. Current efforts are focusedon a parametric study to determine if inertial confinementcould cause a transition to detonation. These simulationswill give insight into the physical mechanism of DDT forlarge-scale explosions and help determine safe packagingconfigurations to eliminate DDT in transportation acci-dents.

Jacqueline BeckvermitDepartment of ChemsitryUniversity of Utahbeckvermit@gmail.com

Todd HarmanDepartment of Mechanical EngineeringUniversity of Utaht.harman@utah.edu

Andrew BezdjianUniversity of Utahandrewbezdjian@gmail.com

Qingyu MengSCI InstituteUniveristy of Utahqymeng@cs.utah.edu

Alan Humprey, John SchmidtUniversity of Utahahumphrey@sci.utah.edu, john.schmidt@utah.edu

Martin BerzinsScientific Computing and Imaging InstituteUniversity of Utahmb@sci.utah.edu

Chuck WightWeber State Universitycwight@weber.edu

CP20

Finite Elements in Flux Coordinates in GyrokineticTurbulence Simulation

A series of finite elements with C0 and C1 continuity areconstructed in curved flux coordinates in gyrokinetic tur-bulence modeling. The difficulties with flux coordinate Ja-cobian and periodic domain and the solution strategies willbe demonstrated. This is the first time two-dimensional fi-nite elements are constructed in this type of coordinatesystems which are used everywhere in fusion plasma simu-lation.

Jin Chen

Princeton Plasma Physics Laboratoryjchen@pppl.gov

CP20

A Performance-Portable Implementation of the Al-bany Ice Sheet Model: Kokkos Approach

Modern HPC applications need to be run on many differentplatforms and performance portability has become a criti-cal issue: parallel code needs to be executed correctly andperformant despite variation in the architecture, operatingsystem and software libraries. In this talk we’ll presentour progress towards a performance portable implementa-tion of the finite element assembly in the Albany Ice SheetModel code, based on Kokkos programming model fromTrilinos.

Irina Demeshko, H. Carter EdwardsSandia National Laboratoriesipdemes@sandia.gov, hcedwar@sandia.gov

Michael A. HerouxSandia National LaboratoriesAlbuquerque, New Mexico, USAmaherou@sandia.gov

ERIC T. Phipps, ANDREW G. SalingerSandia National Laboratoriesetphipp@sandia.gov, agsalin@sandia.gov

CP20

Matrix-Free Krylov Subspace Methods on ModernCPUs and Many-Core Processors

We study methods to implement Krylov Subspace methodsin matrix-free form that take advantage of the memory hi-erarchy of modern CPUs and many-core processors such asGPUs and the Intel Phi. We also work to develop an effec-tive preconditioner for Krylov subspace methods for linearsystems arising from the discretization of PDEs that is easyto program. We use a finite difference approximation of anelliptic test problem for the computational experiments.

Samuel KhuvisDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countykhsa1@umbc.edu

Matthias K. GobbertUniversity of Maryland, Baltimore CountyDepartment of Mathematics and Statisticsgobbert@umbc.edu

Andreas MeisterUniversity of KasselInstitute of Mathematicsmeister@mathematik.uni-kassel.de

CP20

Parallel Techniques for the Incomplete-LU Factor-ization

The incomplete-LU factorization (ILU) is one of the mostpopular black-box preconditioning techniques. However,incomplete factorizations are challenging to effectively im-plement on massively parallel computer architectures, suchas GPUs. In this talk we present an in-depth study of dif-ferent existing parallelization techniques for ILU, such as

AN14 Abstracts 25

level-scheduling, multi-coloring and multi-level approaches,as well as more recent communication avoiding algorithmsand related power(q)-pattern method. We discuss theirproperties and relationships. Finally, we present relevantnumerical experiments.

Maxim NaumovNVIDIAmaxim.a.naumov@nvidia.com

CP20

Effective Parallel Preconditioners for CFL Appli-cation

We focus on the fast iterative solution of linear systems onGPUs, in particular, for problems from computational fluiddynamics. Krylov subspace solvers mostly can be imple-mented efficiently on GPUs; however, the preconditioneris often a bottleneck. In fact, many of the most effectivepreconditioners perform poorly on GPUs, such as ILUT,taking much more time than the matrix-vector product inspite of similar complexity. Therefore, we discuss precon-ditioners like sparse approximate inverse preconditioners,which are matrix-vector product like, as alternatives, pos-sibly accelerated with deflation techniques like Krylov sub-space recycling.

Katarzyna Swirydowicz, Eric De SturlerVirginia Techkswirydo@vt.edu, sturler@vt.edu

Xiao Xu, Christopher J RoyVirginia Tech, Department of Aerospace and OceanEngineeringxiao6@vt.edu, cjroy@vt.edu

CP21

Equilibrium and Bifurcation Analysis of DiscoidalLipoproteins

A discoidal lipoprotein particle consists of a lipid bilayerbounded by a protein polymer chain. In isolation, the freeenergy of such a particle is the sum of the bending-energyof the bilayer and the bending and torsional energy of thechiral protein loop. The Euler–Lagrange equations gov-erning the equilibrium of such particles are derived. Also,a finite-element solver is employed to obtain approximatenumerical solutions and analyze possible conformations ofthese particles.

Aisa BiriaMcGill Universityaisa.biria@mail.mcgill.ca

Eliot FriedOkinawa Institute of Science and Technologymechanicist@gmail.com

CP21

Swimming and Pumping of Helical Bodies in Vis-cous Fluids

Many flagellated microorganisms including E. coli swimby rotating slender helical flagella, while ciliated organ-isms like Paramecia swim by passing helical waves alongtheir surfaces. We will discuss a framework for study-ing such problems where the Stokes equations describingviscous flow are written in helical coordinates. Analyti-

cal predictions match well with full numerical simulations,and suggest optimal geometries. This work may also aiddesigns in microfluidic manipulation, microswimmer engi-neering, and the mixing of viscous fluids.

Lei Li, Saverio SpagnolieUniversity of Wisconsin-Madisonleili@math.wisc.edu, saverioiv@gmail.com

CP21

Mathematical Model and Simulation of ParticleFlow Around Choanoflagellates Using the Methodof Regularized Stokeslets

Choanoflagellates are unicellular organisms whose intrigu-ing morphology includes a set of collars/microvilli emanat-ing from the cell body, surrounding the beating flagellum.We investigate the role of the microvilli in the feeding andswimming behavior of the organism using the method ofregularized Stokeslets. This model allows us to depict theeffective capture of nutritional particles and bacteria in thefluid and the hydrodynamic cooperation between the cell,flagellum, and microvilli of the organism.

Hoa Nguyen, Niti NararidhTrinity Universityhnguyen5@trinity.edu, nnararid@trinity.edu

CP21

Swimming Efficiently: An Analytical Demonstra-tion of Optimal Strouhal Number in Fish

Using Lighthills large amplitude elongated body theory itis shown that the kinematics of fish swimming can be re-duced to a single variable, Strouhal Number (St). Thisis accomplished by applying mathematical constraints toenforce constant velocity, low drag swimming. Using thisresult, it is demonstrated that Froude efficiency for swim-ming can be defined directly as a function of St. This func-tion correctly predicts the behavior of swimmers across awide range of sizes.

Alexander J. WiensMassachusetts Institute of Technologywiens@mit.edu

Anette HosoiMassachusetts Institute of Technology77 Massachusetts Avenue, Room 3-173, Cambridge MA02139peko@mit.edu

CP22

Analysis of a Large Time Step and OverlappingGrids Method for Hyperbolic Conservation Laws

We propose a numerical method for approximate solvingof hyperbolic conservation laws. The method is based on afinite volume method and our novelties are twofold. First,our method is a Large Time Step method which enables usto march faster in time. Secondly, the method incorporatesoverlapping grids which is a very important issue in manypractical applications. In one space dimension, we provethat the method converges to the entropy solution of theconservation law. We also present numerical simulationsfor Burger’s equation and the Lax problem for the Eulergas dynamics equations.

Ilija Jegdic

26 AN14 Abstracts

Department of Mathematics, University of Houstoni jegdic@yahoo.com

CP22

Filtered Positive PN Closure for Kinetic TransportEquations

We propose a modification to the standard spherical har-monic closure, known as PN closure, used for linear kineticequations. The modification produces smooth, nonnega-tive polynomial particle distributions by using two-step fil-tering on the oscillatory, partially negative PN solutions;closes the moment system using filtered polynomial ansatz;and integrates the closed moment system with filtered mo-ments. We formulate the filtering process as a quadraticprogram, and demonstrate numerical results on the chal-lenging line source benchmark problem.

Ming Tse P. LaiuDepartment of Electrical and Computer EngineeringUniversity of Maryland - College Parkmtlaiu@umd.edu

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

Dianne P. O’LearyUniversity of Maryland, College ParkDepartment of Computer Scienceoleary@cs.umd.edu

Andre TitsUniversity of Maryland at College Parkandre@umd.edu

CP22

Unconditionally Optimal Error Estimates of FullyDiscrete Fems for Parabolic Equations

Error analysis of fully discrete finite element methods fornonlinear parabolic equations often requires certain time-step size conditions (or stability conditions) such as Δt =O(hk), which are widely used in the analysis of the nonlin-ear PDEs from mathematical physic. In this talk, we sug-gest a new approach to analyze the discretization error offully discrete FEMs for nonlinear parabolic equations. Bythis new approach, we found that the time-step size restric-tions are not necessary for most problems. To illustrate ouridea, we analyze some models from mathematical physics,e.g. the thermistor problem, miscible flow in porous mediaand gradient flows, with linearized backward Euler schemefor the time discretization. Previous works on the thesemodels all required certain time-step size conditions.

Buyang LiNanjing University, Chinabuyangli@nju.edu.cn

CP22

Asymptotic-Preserving Semi-Lagrangian Discon-tinuous Galerkin Schemes for a Class of RelaxationSystems

We consider in this work a class of singularly perturbedhyperbolic balance laws that admit a diffusive limit. Suchsystems arise naturally in radiative transport applicationsif one starts with a Boltzmann description and expands

the distribution function in spherical harmonics (i.e., thePn approximation). One key difficulty in solving such sys-tems is that standard numerical schemes have maximumtime-step restrictions that vanish in the singular limit. Sev-eral approaches have been proposed in the literature thatovercome this difficulty, many of which are based on split-ting the equation into stiff and non-stiff pieces and usingappropriate semi-implicit time-stepping methods. In thiswork we employ a different strategy in order to achieveasymptotic-preservation. We develop a scheme using a dis-continuous Galerkin semi-Lagrangian scheme. Several nu-merical test cases are used to validate the proposed scheme.

Anna LischkeIowa State Universityalischke@iastate.edu

James A. RossmanithDeparment of MathematicsIowa State Universityrossmani@iastate.edu

CP22

Positivity-Preserving WENO Schemes with Con-strained Transport for Ideal MHD

We will discuss a novel positivity-preserving flux limitingtechnique developed for WENO schemes to solve idea mag-netohydrodynamic (MHD) equations. There are two mainsteps in our MHD solver: first updating conservative quan-tities by WENO scheme with positivity-preserving limiterand then correcting the magnetic field and total energy bya high-order constrained transport approach. Several ex-amples are presented to verify the order of accuracy and todemonstrate the efficiency of positivity-preserving limiter.

Qi Tang, Andrew J. Christlieb, Yuan LiuDepartment of MathematicsMichigan State Universitytangqi@msu.edu, christlieb@math.msu.edu,liuyuan01@gmail.com

Zhengfu XuMichigan Technological UniversityDept. of Mathematical Scienceszhengfux@mtu.edu

CP22

Partially Penalized Immersed Finite ElementMethods for Elliptic Interface Problems

In this talk, we present new immersed finite element (IFE)methods for the second order elliptic interface problemson Cartesian meshes. Closely related to traditional IFEmethods which are based on Galerkin formulation, thesenew IFE methods contain extra stabilizing terms at inter-face edges to penalize the discontinuity in IFE functions.Error estimation shows that these IFE methods convergeoptimally in an energy norm. Numerical examples demon-strate that these new methods outperform traditional IFEmethods at the vicinity of the interface.

Xu ZhangPurdue Universityxuzhang@purdue.edu

CP23

Lagrangian Particle Methods for Global Atmo-

AN14 Abstracts 27

spheric Flow

We present a particle method for global atmospheric flow inspherical geometry based on the Lagrangian formulation ofthe fluid equations. Poisson equations for the stream func-tion and velocity are solved using integral convolution withGreen’s function for the sphere, which is approximated nu-merically with singular point vortices and point sourcesusing midpoint rule quadrature. An adaptive remeshingprocedure is applied at regular time intervals to maintainspatial accuracy on the Lagrangian particles. Solutions ofthe barotropic vorticity equation are presented, and on-going work with the shallow water equations is discussed.

Peter A. BoslerUniversity of MichiganApplied and Interdisciplinary Mathematicspbosler@umich.edu

CP23

Numerical Derivation of a D−D−κ Relation for AnExpanding Detonation Wave in the Mie-GruneisenEquation of State

The propagation behavior of a detonation wave expansioncan be described asymptotically by Taylor blast wave the-ory (TBW) in the limit of a small, rapid wave, and bygeometrical shock dynamics (GSD) in the limit of a large,steady wave. We use a hydrodynamic solver to find a nu-merical relationship between the curvature, velocity, andacceleration of the detonation wave that describes the tran-sition between the limits in the ideal and Mie-Gruneisenequations of state.

Brandon A. LieberthalUniversity of Illinois at Urbana-Champaignbrandon.lieberthal@gmail.com

D. Scott StewartMechanical Science and EngineeringUniversity of Illinois at Urbana Champaigndss@illinois.edu

CP23

Turbulent Mix in Numerical Simulations for ICFCapsules

We study the turbulent mixing zone in an Inertial Confine-ment Fusion (ICF) capsule, with a focus on the Rayleigh-Taylor (RT) unstable deceleration phase of hot spot forma-tion. Our main results are twofold: (i) a ”post shot” simu-lation with modifications to input parameters that betterresemble experimental observations and (ii) examination ofthe resulting hot spot and turbulent mixing zone proper-ties.

Hyunkyung LimSUNY at Stony BrookDepartment of Applied Mathematics and Statisticshyulim@ams.sunysb.edu

Jeremy MelvinStony Brook UniversityStony Brook NYjmelvin@ams.sunysb.edu

Verinder RanaStony Brook University

verinder.rana@stonybrook.edu

James GlimmState University of New York, Stony Brookglimm@ams.sunysb.edu

Baolian ChengLos Alamos National Labbcheng@lanl.gov

David SharpLos Alamos National Laboratorydcso@lanl.gov

CP23

Continuum Boundary Force Method for MultiscaleModeling of Flows Subject to Slip Boundary Con-ditions

When fluid flow velocity at fluid-solid interfaces is non-zero,the flow is said to have “slip’ at the fluid-solid boundary.This phenomenon is commonly described by the Navierboundary condition or, more generally, Robin-type bound-ary conditions. Here we propose the Continuous BoundaryForce (CBF) method for imposing Robin boundary condi-tions in Smoothed Dissipative Particle Dynamics (SDPD)simulations. We demonstrated the efficiency and accuracyof the SDPD-CBF method for modeling slip flows subjectto the Robin boundary conditions with arbitrary (constant,space-dependent, or non-linear) slip lengths at flat andcurved boundaries. Furthermore, the consistent thermalscaling in the SDPD-CBF method allows it to also be usedfor multiscale modeling, i.e., bridging scales in concurrentcoupling from the continuum hydrodynamic scale all theway to the molecular scale.

Wenxiao PanPacific Northwest National Laboratorywenxiao.pan@pnl.gov

Alexandre TartakovskyUniversity of South Floridatartakovsky@usf.edu

Nathan BakerPacific Northwest National Laboratorynathan.baker@pnnl.gov

CP23

Hydrodynamic Calculations Using Reale: AnArbitrary-Lagrangian-Eulerian Framework withMesh Reconnection

We examine a new ALE hydro scheme that allows for on-the-fly mesh reconnection based on the Voronoi diagram[Loubere et al, ReALE: A Reconnection-Based Arbitrary-Lagrangian-Eulerian Method, JCP, 2010]. Reconnectionallows the mesh to follow Lagrangian features in the flowmore closely than standard ALE schemes while avoidingthe problem of mesh tangling typical of pure Lagrangianschemes. We outline our methodology for ReALE andpresent results demonstrating its effectiveness on severalchallenging compressible hydrodynamic tests.

David Starinshak, John Owen, Douglas MillerLawrence Livermore National Laboratory

28 AN14 Abstracts

starinshak1@llnl.gov, owen@llnl.gov, miller18@llnl.gov

CP23

A Smoothed Particle Hydrodynamics Model forElectrokinetic Flows

Theoretic description of electrokinetic phenomena includesthe Poisson-Boltzmann equation relating the electric fieldto ion concentration and Navier-Stokes equations relatingthe flow velocity to the pressure and electrostatic forcesacting on the system. A Lagrangian particle model basedon smoothed particle hydrodynamics is proposed to nu-merically solve the coupled equations. And a fast multi-level pre-conditioned method by means of auxiliary spaceis incorporated as the linear solver for the associated Pois-son equation. The efficiency and accuracy of the proposedmodel are examined through modeling the electroosmoticflow in microchannels and flow through charged mem-branes. A good agreement is found in comparison with thecorresponding analytical or finite-element solutions. Thediffusion-advection equation relating the species mass con-centration to flow velocity is then coupled to investigatethe influence of surface heterogeneity on electrokineticallydriven microfluidic mixing.

Wenxiao PanPacific Northwest National Laboratorywenxiao.pan@pnnl.gov

Hongxuan Zhang, Xiaozhe HuThe Pennsylvania State Universityhuz114@psu.edu, hu x@math.psu.edu

Jinchao XuPennsylvania State Universityxu@math.psu.edu

CP24

Mutational History Dominates Clonal SelectionWithin Evolving Tumors

Natural selection acting on clonal diversity within tumorsis thought to drive tumor progression, but details remainobscure. Evolutionary mathematical models of the angio-genic switch predict the emergence of hypovascular necro-sis caused by hypertumors—“cheating” clones that free-ride on vasculature organized by cooperative clones. Herewe show that hypertumors should rarely evolve becausethe deterministic evolutionary trajectory is overwhelmedby stochastic mutational history. These results highlightmutation pressure as a significant evolutionary force in can-cer.

Scott T. BickelArizona State UniversityScottsdale Community Collegebickel777@gmail.com

Joseph JulianoArizona State Universityjoejuliano22@gmail.com

John D. NagyScottsdale Community CollegeArizona State University

john.nagy@scottsdalecc.edu

CP24

Modeling the Progression and Development toHepatocellular Carcinoma for Hepatitis C Virus In-fection

The mathematical model considered here is the first at-tempt to encapsulate the long-term dynamics of hepatitisC virus (HCV) infection and the influence of viral and im-mune processes in the gradual progression and developmentto hepatocellular carcinoma (HCC). The key basis for themodel formulation is that the long-term implications arerandom and are very likely caused by cell-mediated im-mune response. The chances of development of cancer aremodeled by way of a stochastic model which takes into ac-count the dynamics over the infection duration. Samplingbased simulations show that the development rate of HCCover a period of 40 years is about 9%, which is in conso-nance with estimates available in literature. Simulationsalso show that the chance of developing HCC increases lin-early along with the length of period of infection at a rateof 2.4 incidents per year for every thousand infected indi-viduals.

Siddhartha P. ChakrabartyDept. of MathematicsIndian Institute of Technology Guwahatipratim@iitg.ernet.in

John MurraySchool of MathematicsUniversity of NSWJ.Murray@unsw.edu.au

CP24

Quantifying the Relationships among Natural Se-lection, Mutation, and Stochastic Drift in Multidi-mensional Finite Populations

The interrelationships of the fundamental biological pro-cesses natural selection, mutation, and stochastic drift arequantified by the entropy rate of Moran processes with mu-tation, measuring the long-run variation of a Markov pro-cess. The entropy rate is shown to behave intuitively withrespect to evolutionary parameters such as monotonicitywith respect to mutation probability (for the neutral land-scape), relative fitness, and strength of selection. Strictupper bounds, depending only on the number of replicat-ing types, for the entropy rate are given and the neutralfitness landscape attains the maximum in the large popu-lation limit.

Marc HarperUCLAmarc.harper@gmail.com

CP24

Competition Between Oysters and Invasive Mus-sels in the Presence of Water Releases

The Asian green mussel competes with oyster populationsin parts of Florida, displacing some reefs in Tampa Bay.However, oysters are more tolerant of salinity changes thatcan occur, such as when large freshwater releases are made.Releases along waterways can take different forms, withsome recent ones being large in volume relative to time. Wepresent an ODE system modeling the population dynamics,

AN14 Abstracts 29

including the effect of fresh water releases. Some numericalresults are included.

Daniel L. KernFlorida Gulf Coast UniversityDept of Chemistry and Mathematicsdkern@fgcu.edu

CP24

A Mixed-Strategy Game Theoretical Approach forInfectious Disease Prevention by Social Distancing

We describe a population game in which individuals are al-lowed to decide between adopting different social distanc-ing strategies in order to lower infection risk and maximizepayoffs. When the reduction in infection risk is a convexfunction of the cost of social-distancing, there is a uniquepure-strategy game equilibrium. When the reduction ininfection risk is not convex, the existence of equilibria be-comes more complicated. We will discuss three cases vis--vis different costs of infection.

Jing LiCalifornia State University Northridgejing.li@csun.edu

Timothy RelugaPennsylvanian State Universitytreluga@math.psu.edu

CP24

Traveling Wave Fronts in Population and DiseaseModels with Nonlocal Reaction and Delay

We will discuss the stability of traveling wavefronts for non-linear reaction diffusion equations with nonlocal reactionand delay. We will prove stability of both non-critical andcritical wavefronts, and their rates of convergence. Appli-cations will be made to a host-vector disease model, a gen-eralized Nicholson blowflies model, and a modified vectordisease model. This work generalizes results of Lv-Wangand Mei-et-al, and allows us to treat more realistic models.

Peter Y. PangNational University of Singaporematpyh@nus.edu.sg

CP25

A Q2−iso−Q1/Q1 Immersed Finite Element forStokes Interface Problems

We present the bilinear immersed finite element (IFE)methods for solving Stokes interface problems with struc-tured Cartesian meshes that is independent of the locationand geometry of the interface. Basic features of the bilin-ear IFE functions, including the unisolvent property, willbe discussed. Numerical examples are provided to demon-strate that the bilinear IFE spaces have the optimal ap-proximation capability, and that numerical solutions pro-duced by a Q2−iso−Q1/Q1 method with these IFE func-tions for Stokes interface problem also converge optimallyin both L2 and H1 norms.

Nabil ChaabaneVirginia Technabilch@vt.edu

Slimane Adjerid

Department of MathematicsVirginia Techadjerids@math.vt.edu

Tao LinVirginia Techtlin@vt.edu

CP25

Flow Control by Adjoints and Sensitivities

I will present an algorithm for flow control which is basedon the derivation of adjoint equation using Lagrange mul-tipliers. This algorithm involves computing gradient of anuser-defined objective function that has the system controlsettings resulting in sensitivity expressions. Characteris-tic analysis is incorporated in this methodology to derivesensitivity expressions that yield more information on flowcontrol as compared to sensitivity expressions that are de-rived without characteristic analysis. Finally, I will showresults obtained by applying these algorithms to partialdifferential equations that model atmospheric flows.

Vani CheruvuDepartment of Mathematics and StatisticsThe University of Toledo, Toledo, OH 43606vani.cheruvu@utoledo.edu

CP25

A Realizability Preserving Discontinuous GalerkinMethod for the M1 Model for Radiative Transfterin 2D

We consider the M1 moment model for radiative transfer.In order to ensure well-possedness the moment variables ofthe model have to satisfy certain realizability conditions.We present the necessary modifications to the Runge-Kuttadiscontinuous Galerkin method in 2D that ensure realiz-ability of the moment variables. Our goal is to resolve thetime evolution of isolated sources or beams of particles inheterogeneous media on unstructured triangular meshes.

Prince ChidyagwaiTemple UniversityDepartment of Mathematicspchidyagwai@loyola.edu

Martin FrankRWTH Aachen UniversityCenter for Computational Engineering Sciencefrank@mathcces.rwth-aachen.de

Florian SchneidTU Kaiserslautenfschneid@mathematik.uni-kl.de

Benjamin SeiboldTemple Universityseibold@temple.edu

CP25

Optimal Error Estimates of a Linearized BackwardEuler Galerkin Fem for the Landau-Lifshitz Equa-tion

We present a fully discrete linearized backward EulerGalerkin FEM for the Landau–Lifshitz equation in whicha new linearization is proposed for the gyromagnetic term.

30 AN14 Abstracts

Optimal error estimates are proved almost unconditionally(i.e. when the stepsizes h and τ are smaller than givenconstants). Numerical results are provided to confirm ourtheoretical analysis and show the unconditional stability ofthe scheme.

Huadong GaoDepartment of Mathematics, CityU of HKKowloon, Hong Kongmahdgao@163.com

CP25

A Particle-In-Cell Method Based on An ImplicitWave Solver

A recently developed implicit wave solver removes the CFLcondition while maintaining computational cost compara-ble to explicit wave solvers. We present the application ofthis wave solver in a particle-in-cell (PIC) method for thesimulation of plasmas in an approach that can handle bothelectrostatic and fully electromagnetic cases. We show theresults of some standard one- and two-dimensional electro-static test problems, and discuss the extension to the fullyelectromagnetic case.

Eric WolfMichigan State Universityeriwolf@gmail.com

CP26

Generalization of Pade Approximation from Ra-tional Functions to Arbitrary Analytic Functions- Applications

We extended the basic idea of Pade approximation to anyarbitrary function holormorphic in a neighborhood of theTaylor series expansion point. This provides the flexibil-ity of using other functions in a Pade-type approximation,yielding highly accurate approximations with additionaldesirable properties such as asymptotic behavior. In thistalk, we present applications of our method to approxima-tion of sine/cosine, Fresnel integral functions, representa-tion of band-limited functions, and constructing multires-olution representations, i.e., chirplet decomposition.

Evren YarmanSchlumbergercyarman@slb.com

Garret FlaggSchlumberger, Houston, TXgflagg@slb.com

CP26

Analysis of a Singular Integral Equation ModelingWaves Propagating in a Fusion Plasma

A singular integral equation models resonant waves in afusion plasma. This resonance called hybrid is linked toheating of a magnetic plasma. This presentation is dedi-cated to the analysis of this equation, see [B. Despres, L.-M.Imbert-Gerard, R. Weder, Hybrid resonance of Maxwell’sequations in slab geometry, J. Math. Pures et Appl., DOI:10.1016/j.matpur.2013.10.001]. A singular solution is ob-tained thanks to a limit absorption principle, which pro-vides a formula for the plasma heating.

Lise-Marie Imbert-GerardCourant Institute of Mathematical sciences, NYU

imbertgerard@cims.nyu.edu

Bruno DespresUPMC Univ Paris 06, LJLLdespres@ann.jussieu.fr

Ricardo WederUniversidad Nacional Autonoma de Mexico, IIMASweder@unam.mx

CP26

Juxtaposition of Evaporation, Gravity and DarcianResistance in Seepage Through a Silt Block Ad-jacent to a Coarse Sand Compartment: SolutionsBased on Theory of Holomorphic Functions andComputer Algebra

2-D wicking of soil water is analytically studied by tension-saturated model. Along 3 sides of a transient flow tube thetype of boundary conditions is fixed but the 4-th side con-sists of no-flow boundary and constant-potential segment.In the complex potential domain, the shrinking rectangle isconformally mapped onto the rectangle in the flow domain.The Schwarz-Christoffel formula and Mobius transforma-tion are used. Cauchys problem for an integro-differentialequation with respect to an affix of the conformal mappingis numerically solved. Physical and mathematical condi-tions of solvability of the equation are established. Theseepage flow rate as a function of time is presented andrelated to the classical hydrological taxonomy of evapora-tion stages. Applications in agricultural engineering, e.g.desiccation of a coarse-textured under-canopy zone of irri-gated trees in arid conditions, is related to the developedmathematical model.

Anvar KacimovSultan Qaboos Universityanvar@squ.edu.om

Yurii ObnosovKazan Federal University, Russiayurii.obnosov@gmail.com

Dani OrEidgenossische Technische Hochschule ZurichSwitzerlanddani.or@env.ethz.ch

CP26

Unexpected Fooling Functions

We often rely on automatic quadrature rules to computedefinite integrals that cannot be expressed in terms of el-ementary functions. Unfortunately, we have found thatnearly all such algorithms can be fooled because their er-ror estimates are based on the difference of two quadraturerules. Using this insight, we have constructed fooling func-tions that are not particularly spiky, but for which theautomatic quadrature rule is grossly incorrect. This high-lights the need for better rules.

Martha RazoIllinois Institute of Technologymrazo@hawk.iit.edu

CP26

Generalization of Pade Approximation from Ra-

AN14 Abstracts 31

tional Functions to Arbitrary Analytic Functions- Theory

We present a method for extending the basic idea of Padeapproximation by using an arbitrary analytic function in-stead rational functions to match a prescribed number ofterms in the Taylor series. The choice of analytic functioncan be used to construct highly accurate approximations.In this talk, we discuss the theory and error analysis be-hind our method. Several examples of its application willbe discussed in a separate talk.

Evren YarmanSchlumbergercyarman@slb.com

Garret FlaggSchlumberger, Houston, TXgflagg@slb.com

CP27

Rate-Limited Sorption in Production TransportCodes

Computational models of contaminant transport are usedregularly for designing subsurface environmental remedi-ation systems. In many soils, the contaminant sorbs tothe solid matrix in the porous media. As a result, therate of removal by traditional pump-and-treat flushing ismuch slower than predicted with equilibrium models. Thisphenomenon is called rate-limited sorption (RLS) and itis particularly problematic in cases where the contaminanthas been in place for a long period of time. Although RLSis well known in academic literature, production modelsused for field work have failed to incorporate the effect.As a result, remediation designs and cleanup time projec-tions are often inaccurate. In this project, a well-validatedproduction subsurface transport model is modified with asimple analytical model for layers and lenses that incor-porates RLS effects with reasonable computational costs.Preliminary results show good agreement with RLS behav-ior.

David L. CoullietteMathematics and Computer Science DepartmentAsbury Collegedavid.coulliette@asbury.edu

Kenneth RietzAsbury Universitykenneth.rietz@gmail.com

Edward HeyseParsons Corporationed.heyse@parsons.com

CP27

Fingering Instability in the Presence of Visco-elasticity

With the motivation of understanding the effect of com-plex rheological properties of complex fluids often used inchemical enhanced oil recovery, we study linear instabil-ity of the displacement of a visco-elastic complex fluid andquantify the effect of elasticity on fingering instability. Anexact formula is provided which shows that the elasticityhas a destabilizing effect on fingering instability. Relevance

of these results to chemical EOR will be discussed.

Prabir DaripaTexas A&M UniversityDepartment of Mathematicsprabir.daripa@math.tamu.edu

CP27

Iterative Algorithms for Geosounding Inversion

For most of Geosounding problems, an iterative scheme isusually implemented after linearization of forward equa-tions. Bachmayr and Burger propossed iterative algo-rithms for TV functionals. Those iterative algorithms arebased on Bregman distance, that can be interpreted as ageneralization of the mean-square distance for general func-tionals. In this contribution, several novel algorithms fornonlinear inversion of electrical, electromagnetic and re-sistivity soundings based on Bregman iterations are pre-sented. Results are reported of algorithm implementationfor several geosounding methods applying Bregman dis-tance to minimize the TV and MS functionals. The linearapproximation for electromagnetic soundings at low induc-tion numbers is implemented on the inversion algorithm.A comparison of developed models for Bregman based al-gorithms with those obtained with a linear programmingpackage is also presented for synthetic and field data.

Hugo HidalgoCICESE-Ciencias de la Computacionhugo@cicese.mx

Enrique Gomez-TrevinoCICESE-Geofisica Aplicadaegomez@cicese.mx

CP27

A Higher-Order Robert-Asselin Type Time Filter

We propose and analyze a higher-order Robert-Asselin(hoRA) type time filter for weather and climate models.While requiring the same amount of computational effortas the Robert-Asselin-Williams filter, the hoRA filter ef-fectively suppresses the leapfrog schemes computationalmodes and achieves third-order accuracy. The hoRA fil-ter is shown to be suitable for long-time simulations. Inaddition, the filter is non-intrusive, and so it would be eas-ily implementable in the existing legacy codes.

Yong LiUniversity of Pittsburghyol34@pitt.edu

Catalin S. TrencheaDepartment of MathematicsUniversity of Pittsburghtrenchea@pitt.edu

CP27

Coupled Multi-Physics Analysis of Caprock In-tegrity and Joint Reactivation During Co2 Seques-tration

Structural trapping beneath a low-permeable caprock layeris the primary trapping mechanism for long-term subsur-face sequestration of CO2. We modeled the effects ofcaprock jointing on the caprock sealing. The modeling ef-fort uses a 3D-FEM based coupled multiphase flow and ge-

32 AN14 Abstracts

omechanics simulator. Various injection schedules as wellas caprock jointing configurations within a proto-typicalsequestration site have been investigated. The resultingleakage rates through the caprock and fault are comparedto those assuming intact material.

Pania NewellSandia National Laboratorypnewell@sandia.gov

Mario, J. Martinez, JOSEPH, E. BishopSandia National Laboratoriesmjmarti@sandia.gov, jebisho@sandia.gov

CP27

Modeling of Arctic Melt Ponds and Sea-IceAlbedo-Feedback

We study possibility of the climate system to pass througha bifurcation point - irreversible critical threshold as thesystem progresses toward ice-free summers. This studyis based on the nonlinear phase transition model for meltponds and bifurcation analysis of a simple climate modelwith the positive sea ice - albedo feedback as a key mech-anism potentially driving the system to the bifurcationpoint.

Ivan A. SudakovUniversity of UtahMathematics Departmentsudakov@math.utah.edu

Sergey VakulenkoInstitute for Mechanical Engineering ProblemsRussian Academy of Sciencesvakulenfr@mail.ru

CP28

Multi-Echelon Supply Chain Inventory Optimiza-tion: An Industrial Perspective

Mathematical programming based multi-echelon inventoryoptimization models developed in the literature quantifyuncertain demand or lead time assuming a Normal or Pois-son distribution. We demonstrate how such assumptionscan severely impact and underestimate optimal inventory,and discuss the drawbacks of mathematical programmingapproaches. We present a novel simulation-optimizationframework that not only generates more accurate resultsby bootstrapping historical data, but is also versatile tocapture non-standard inventory policies and decisions. In-dustrial examples are presented.

Anshul Agarwal, John WassickThe Dow Chemical CompanyAAgarwal2@dow.com, jmwassick@dow.com

CP28

Single Machine Scheduling Problem with IntervalProcessing Times

In this paper, the single machine scheduling problemwith uncertain and interval processing times is addressedwith the objective of minimizing mean weighted comple-tion time. Some polynomial time heuristics, utilizing thebounds of processing times, are proposed. The proposedand existing heuristics are compared by extensive compu-tational experiments. The computational results indicate

that the proposed heuristics perform significantly betterthan the existing heuristics in terms of both error and com-putation time.

Ali AllahverdiKuwait Universityali.allahverdi@ku.edu.kw

Harun Aydilek, Asiye AydilekGulf University for Science and Technologyaydilek.h@gust.edu.kw, aydilek.a@gust.edu.kw

CP28

Computing Spectra of Laplace Beltrami OperatorUsing Cylindrical Radial Basis Functions

The spectrum of the Laplace-Beltrami (LB) Operator isknown to provide an intrinsic shape signature for 3D shapematching. Given point clouds on a 2 manifold, we utilizea novel cylindrical Radial Basis function to efficiently ap-proximate the surface and compute the Eigen values of theLB operator. At the end, we perform numerical tests todemonstrate the generality and efficiency of our method

Emmanuel O. Asante-AsamaniDepartment of Mathematical SciencesUniversity of Wisconsin-Milwaukeeeoa@uwm.edu

Zeyun YuUniversity of Wisconsin-Milwaukeeyuz@uwm.edu

Lei WangUniversity of Wisconsin-MilwaukeeDepartment of Mathematical Sciencewang256@uwm.edu

CP28

Sub-Linear Sparse Fourier Algorithm for High Di-mensional Data

In this talk, we discuss how to implement a sub-linearsparse Fourier algorithm on data in high dimensional space.We already have the efficient algorithm with O(klogk) run-time for one dimensional problem with k data. We proposea method to embed higher dimensional data in lower spacewithout overlap so that the existent algorithm is applica-ble to modified data. In this way, we can retain the com-putational efficiency. It can be shown theoretically andcomputationally.

Bosu ChoiUniversity of Michiganchoibosu@math.msu.edu

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

Yang WangMichigan State University

AN14 Abstracts 33

ywang@math.msu.edu

CP28

Interpolation Using the Min Kernel

We find a relationship between the second derivative ofa function f ∈ C2[0, b], such that f(0) = 0, and thecoefficients cj obtained from the interpolation problemSf (xj) = f(xj) at points xj , j = 1, . . . , n where xj ∈(0, b], Sf (x) =

∑nj=1 cjK(x, xj), and K is the min kernel

K(x, z) = min (x, z). We find an integral representationformula, then, adding the boundary condition f ′(b) = 0,show that min(x, z) is the Green’s function for the Lapla-cian, and we give an elementary derivation of the nativespace of the min kernel.

Martin A. DillonIllinois Institute of Technologymdillon1@hawk.iit.edu

CP28

On the Entringer and Slater Problem

In 1981, Entringer and Slater proposed the problem of de-termining Ψ(r), where Ψ(r) is the maximum number ofcycles in a connected graph G of order p with q edges andr = q − p + 1 (see Aldred R. E. L., Thomassen Carsten,On the maximum number of cycles in a planar graph, J.Graph Theory 57 (2008), no. 3, 255–264). In this talk,some results on this problem and related conjectures aresummarized.

Chunhui LaiZhangzhou Normal Universitylaichunhui@mnnu.edu.cn; laich2011@msn.cn

CP28

Tractability of Function Approximation Problemswith General Kernels

This talk addresses the problem of approximating functionsbelonging to a reproducing kernel Hilbert space H. Oftenconvergence rates deteriorate quickly as the dimension ofproblem increases. Such a behavior is known as the curseof dimensionality. Therefore it is desirable to have dimen-sion independent convergence rates, which corresponds tothe concept of strong polynomial tractability. We studythe conditions for strong tractability on more general ker-nels of product form. The shape parameter, γ�, governsthe horizontal scale of a function in H with respect to thevariable x�. We also introduce a parameter α�, which gov-erns the vertical scale of the function with respect to thevariable x�. The exponent of strong tractability dependson how quickly the sequence (α�γ�)

∞�=1 tends to zero.

Xuan ZhouIllinois Institute of Technologyxzhou23@hawk.iit.edu

Fred J. HickernellIllinois Institute of TechnologyDepartment of Applied Mathematicshickernell@iit.edu

CP29

An Adaptive Mesh Strategy for Convection Diffu-

sion Problems

It is well known that whenever central finite differenceschemes (second order or higher order central schemes) areapplied to solve convection diffusion singularly perturbedproblems (SPP) numerically on uniform meshes, non physi-cal oscillations observed in the numerical solution and theirmagnitude increases in the layers (boundary and interior)regions. The presence of these large non physical oscil-lations in the approximated solution shows that centralfinite difference operators on the uniform meshes are un-stable. To eliminate these oscillations while retaining theorder of accuracy, one needs either a fine mesh at the layer.This maybe done either via uniformly fine meshing or viaan adaptive mesh strategy. In this paper, a new adaptivemesh strategy has been developed for solving SPP withhigher order central compact schemes. Our strategy usesa novel, entropy-like variable as the adaptation parameterfor convection diffusion SPP.

Vivek K. AggarwalAssistant Professor, Department of Applied Mathematics,Delhi Technological Universityvivekkumar.ag@gmail.com

Balaji SrinivasanDeptt. of Applied Mechanics, IIT DelhiHauz Khas, New Delhi - 110016balaji@am.iitd.ac.in

CP29

Are Spectrally-Accurate Radial Basis FunctionsObsolete? Gaussian-Mollified Polynomial Interpo-lation

Spectrally-accurate radial basis functions (RBFs) such asGaussians often succeed where polynomial interpolationfails because of the Runge Phenomenon. Why? Compar-ative analysis of RBF and polynomial cardinal functions(nodal bases) shows that RBF cardinals are much morelocalized. This motivated us to abandon RBFs in favorof Gaussian-mollified polynomial cardinal functions: muchmore accurate, cheaper to construct and much better con-ditioned than RBFs. Using potential theory, we prove anexponential, geometric rate of convergence. On a uniformgrid, the Runge Phenomenon is not completely annulled,but the Runge Zone is an order of magnitude smaller thanfor polynomial interpolation. Applications to solving dif-ferential equations, especially in complicated geometry, arein progress. A note was published as “Hermite FunctionInterpolation ..., Appl. Math. Letters, 26, 10, 995-997(2013).

John P. BoydUniversity of MichiganAnn Arbor, MI 48109-2143 USAjpboyd@umich.edu

CP29

Solutions of Boltzmann Equation for Simulation ofParticle Distributions in Plasmas

We are investigating the time evolution of the electron andexcited state distribution functions. We solve the timedependent Boltzmann equation to overcome some typicallimitations of modeling high pressure plasmas using MonteCarlo methods. Here we focus on the numerical approachto solving the time dependent Boltzmann equation using amulti-term approximation of the electron distribution func-

34 AN14 Abstracts

tion. We also compare Boltzmann results for electron dis-tribution evolution against multiple plasma simulations us-ing experimental collisional cross-section data.

Jason F. HammondUniversity of ColoradoDepartment of Applied Mathematicsjason.hammond.2@us.af.mil

CP29

Investigation and Numerical Solution of Initial-Boundary Value Problem to One NonlinearParabolic Equation

In the presented work the difference scheme for specificinitial-boundary value problem to the following nonlinearparabolic equation

∂U

∂t= a (x, t)

∂2U

∂x2+ U3 + f (x, t)

is investigated. The coefficient a (x, t) is required to becontinuous and positive. The function f (x, t) is requiredto be continuous. For the mentioned difference scheme thetheorem of convergence of its solution to the solution of thesource problem is proved. The rate of convergence is es-tablished and it is equal to O

(τ + h2

). The corresponding

numerical experiments are conducted which confirm thevalidity of the theorem.

Mikheil TutberidzeIlia State UniversityAssociated Professormikheil.tutberidze@iliauni.edu.ge

CP29

Coupled Orbital And Thermal Evolution of MajorUranian Satellites

We have developed a model of the orbital and thermal evo-lution of the five major Uranian satellites over millionsof years. The model consists of detailed ordinary differ-ential equations for the orbital evolution coupled to theone-dimensional heat equation for the thermal evolution.We present preliminary results that show how the differ-ent terms in the orbital equations such as the oblateness ofUranus affect the orbital semi-major axis and eccentricityof the satellites.

Attique Ur RehmanThe University of Aucklandattique.ur-rehman@auckland.ac.nz

CP29

A New Optimal Error Analysis of Characteristics-Mixed Fems for Miscible Displacement in PorousMedia

In this talk, we establish unconditionally optimal error es-timates for a modified method of characteristics with amixed finite element approximation for the miscible dis-placement problem in Rd (d = 2, 3), while all previouswork required certain time-step restrictions. By introduc-ing a characteristic time-discrete system, we prove that thenumerical solution is bounded in W 1,∞-norm uncondition-ally. Thus, optimal error estimates can be obtained in atraditional way. Numerical results are presented to confirmour theoretical analysis.

Jilu Wang

Department of MathematicsCity University of Hong Kongjiluwang2-c@my.cityu.edu.hk

Zhiyong SiSchool of Mathematics and Information ScienceHenan Polytechnic Universitysizhiyong@hpu.edu.cn

Weiwei SunCity University of Hong Kongmaweiw@math.cityu.edu.hk

CP30

The Heuristic Static Load-Balancing AlgorithmApplied to the Community Earth System Model

We propose to use the heuristic static load-balancing al-gorithm for solving load-balancing problems in the Com-munity Earth System Model, using fitted benchmark dataas an alternative to the current manual approach. Theproblem of allocating the optimal number of CPU cores toCESM components is formulated as a mixed-integer non-linear optimization problem which is solved by using anoptimization solver implemented in MINLP/MINOTAUR.Our algorithm was tested on 163,840 cores of IBM BlueGene/P.

Yuri AlexeevArgonne National Laboratoryyuri@alcf.anl.gov

CP30

Roadmapping An Obstacle Forest

A growing spectrum of applications targeted for au-tonomous vehicles drives demand for robust path planners.Environment obstacle information determines route selec-tion in cluttered domains but is only partially exploitedby sample-based algorithms. A geometric terrain-basedroadmapping approach is discussed that builds, exploresand updates Morse navigation functions for forests of ob-stacle trees. Exploiting a known mathematical character-ization of valleys and ridges on the function landscape, ahigh-level roadmap connecting landscape critical points isconstructed.

Thomas A. FrewenUnited Technologies Research Centerfrewenta@utrc.utc.com

CP30

Optimal Control Approach and Numerical Meth-ods for Constrained Smoothing Splines

Constrained smoothing splines are an efficient array of es-timators, whose performance often surpasses that of theirunconstrained counterparts. The computation of smooth-ing splines subject to general dynamics and control con-straints and initial state constraints is considered. Theoptimal control formulation of such splines is developed.Several algorithms to compute these splines, including a di-rectional derivative based nonsmooth Newton method, areintroduced. The convergence analysis of these algorithmsand numerical examples are presented.

Teresa LebairUniversity of Maryland Baltimore County, USA

AN14 Abstracts 35

ei44375@umbc.edu

Jinglai ShenUniversity of Maryland Baltimore Countyshenj@umbc.edu

CP30

A Cut Approach for Solving the Single-Row Ma-chine Layout Problem

A cut approach is developed for the machine configura-tion in a single-row linear layout, with objective to mini-mize the total material movement cost. We show that theabove equidistant linear layout problem is equivalent to thelocale network problem by graph theory. The minimumcut, which has the minimum capacity in each locale net-work, is the corresponding optimal layout that minimizesthe material handling cost. The computational complexityof the cut approach is O(n3), where n is the number ofworkstations in the layout problem. In addition, the non-equidistant linear layout problem can be transformed intoan equidistant linear layout problem.

Shine-Der LeeNational Cheng Kung UniversityDept. of Industrial & Information Managementsdlee@mail.ncku.edu.tw

CP30

Study of Weak Stationarity for a Class of StochasticMpcc Problems

In this talk we shall discuss the weak stationarity for aparticular class of stochastic mathematical programmingproblem with complementarity constraints (SMPCC, forshort). Our aim here is to show why concept of weak sta-tionarity is important for SMPCC problems even if theproblem data is smooth. In fact, a well known techniqueto solve stochastic programming problems, namely sam-ple average approximation (SAA) method will show thestrength of weak stationarity for SMPCC problems.

Arnab SurIndian Institute of Technology, Kanpurarnabsur2002@gmail.com

CP30

Real-Time Power Dispatch with Renewables UsingStochastic Admm

Leveraging stochastic programming techniques, energymanagement problems are formulated to account for theintrinsically stochastic availability of renewable energysources. Both economic dispatch and demand responsesetups are considered to minimize the microgrid net cost.Based on the stochastic alternating direction method ofmultipliers (ADMM), a novel decentralized solver withguaranteed convergence is developed for real-time powerdispatch. Numerical tests illustrate the merits of the novelapproach.

Yu ZhangUniversity of MinnesotaDepartment of ECE and DTCzhan1220@umn.edu

Georgios GiannakisUniversity of Minnesota

georgios@umn.edu

CP31

On the Existence of Classical Solutions for a Two-Point Boundary Value Problem for the Navier-Stokes Equations

We consider the motion of a liquid surface between twoparallel surfaces that are non-ideal, and hence, subject tocontact angle hysteresis effect. This effect implies that thecontact angle of the capillary surface at the interface isset-valued. We study the problem of existence of classicalsolutions to the two point boundary value problem in timewhereby a liquid surface with one contact angle is deformedto another with a different contact angle.

Bhagya U. Athukorallage, Ram IyerTexas Tech Universitybhagya.athukorala@ttu.edu, ram.iyer@ttu.edu

CP31

High-Order L-Stable Schemes for the NonlinearParabolic Equation Using Successive Convolution

We present a numerical implementation of an L-stable, 3rdorder accurate solution of the Cahn-Hilliard model usingsuccessive convolution combined with the high order multi-derivative time integrators. The primary advantage is thatthe operators can be computed quickly and effectively withvarious boundary conditions using parallel computing.

Hana ChoMichigan State Universitychohana@msu.edu

Andrew ChrisliebDept. of MathematicsMichigan State Universitychristlieb@math.msu.edu

David C. SealDepartment of MathematicsMichigan State Universityseal@math.msu.edu

Matthew F. CausleyMichigan State Universitycausleym@math.msu.edu

CP31

A Scalable, Parallel Implementation of Weighted,Non-Linear Compact Schemes

Weighted, non-linear compact finite-difference schemes,such as the CRWENO scheme (Ghosh and Baeder, SIAMJ. Sci. Comput., 2012) and the hybrid compact-WENOscheme (Pirozzoli, J. Comput. Phys., 2002), are well suitedfor the numerical solution of compressible, turbulent flows.We propose a scalable, parallel implementation of theseschemes based on an iterative sub-structuring of the tridi-agonal system. We apply our algorithm to benchmark flowproblems and demonstrate its scalability on extreme-scalecomputing platforms.

Debojyoti GhoshMathematics and Computer Science DivisionArgonne National Laboratoryghosh@mcs.anl.gov

36 AN14 Abstracts

Emil M. ConstantinescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratoryjedbrown@mcs.anl.gov

CP31

Robust Design of Boundary Conditions forStochastic Incompletely Parabolic Systems ofEquations

We consider an incompletely parabolic system in one spacedimension with uncertainty in the boundary and initialdata. Our aim is to show that different boundary con-ditions gives different convergence rates of the variance ofthe solution. This means that we can with the same knowl-edge of data get a more or less accurate description of theuncertainty in the solution. A variety of boundary con-ditions are compared and both analytical and numericalestimates of the variance of the solution is presented.

Jan NordstromDepartment of Mathematics, Linkoping UniversitySE 581 83 Linkoping, Swedenjan.nordstrom@liu.se

Markus WahlstenDepartment of MathematicsLinkoping University SE 581 83 Linkoping, Swedenmarkus.wahlsten@liu.se

CP31

Multilevel Monte Carlo Finite Element Method forTime-Dependent Wave Equation

We propose multilevel Monte Carlo Finite Element method(MLMC-FEM) for time-dependent stochastic wave equa-tion. Our method leads to decrease to log-linear work andmemory in the number of unknowns of a single level calcu-lation of the deterministic wave equation. We analyze theMLMC-FEM of the solution based on the nested mesh forFinite Element spaces.

Imbo Sim, Myoungnyoun KimNational Institute for Mathematical Sciencesimbosim@nims.re.kr, gmnkim@nims.re.kr

CP31

Pointwise Estimate for Elliptic Equations in Peri-odic Perforated Domains

Pointwise estimate for the solutions of elliptic equations inperiodic perforated domains is concerned. Let ε denote thesize ratio of the period of a periodic perforated domain tothe whole domain. It is known that even if the given func-tions of the elliptic equations are bounded uniformly in ε,the C1,α norm and the W 2,p norm of the elliptic solutionsmay not be bounded uniformly in ε. It is also known thatwhen ε closes to 0, the elliptic solutions in the periodic per-forated domains approach a solution of some homogenizedelliptic equation. In this work, the Holder uniform boundin ε and the Lipschitz uniform bound in ε for the ellipticsolutions in perforated domains are proved. The L∞ andthe Lipschitz convergence estimates for the difference be-

tween the elliptic solutions in the perforated domains andthe solution of the homogenized elliptic equation are de-rived.

Li-Ming YehDepartment of Applied MathematicsNational Chiao Tung University, Taiwanliming@math.nctu.edu.tw

MS1

Network Adaption for Leader-Follower Networks

We examine a networked multi-agent system running con-sensus susceptible to mis-information from its environ-ment. The influenced dynamics are modeled with leader-follower dynamics and the impact of the foreign input ismeasured through the open loop H2 norm of the net-work dynamics. The measure has a graph-based effec-tive resistance interpretation which allows one to reasonabout the graph’s topological robustness. Consequently,to dampen the external disturbances, decentralized game-theoretic and online edge rewiring methods are proposed.

Airlie ChapmanAeronautics & AstronauticsUniversity of Washingtonairliec@u.washington.edu

Mehran MesbahiUniversity of Washingtonmesbahi@uw.edu

MS1

On Leader Selection for Performance and Control-lability

A standard approach to controlling multi-agent systemsis to select a subset of agents, denoted as leaders, thatare directly controlled in order to steer the remaining (fol-lower) agents to a desired state. Approaches to selectingthe leader agents currently depend on the design criteria ofthe system, with continuous optimization techniques em-ployed to guarantee performance and robustness to distur-bances, and discrete optimization used to ensure controlla-bility, and hence do not give optimality guarantees for jointselection based on performance and controllability. I willpresent a unifying approach to leader selection in multi-agent systems based on both performance (e.g., robustnessto noise and convergence rate) and controllability. My keyinsight is that leader selection for joint performance andcontrollability can be formulated within a matroid opti-mization framework, implying provable guarantees on theoptimality of the chosen leader set. Furthermore, I definea novel graph controllability index, equal to the cardinal-ity of the largest controllable subgraph from a given leaderset, and prove that it is a submodular function of the leaderset, leading to a submodular relaxation of the problem ofachieving controllability.

Andrew ClarkElectrical EngineeringUniversity of Washingtonawclark@u.washington.edu

MS1

Joint Centrality and Optimal Leader Selection in

AN14 Abstracts 37

Noisy Networks

We discuss the leader selection problem in a model wherenetworked agents, subject to stochastic disturbances, trackan external signal. The optimal leader set minimizessteady-state variance about the external signal. We provethe single optimal leader is the agent with maximal infor-mation centrality and show the optimal set of m leadersmaximizes a measure of joint centrality. Finally, we solveexplicitly for optimal leader locations in special cases.

Katherine FitchMechanical EngineeringPrinceton Universitykfitch@princeton.edu

Naomi E. LeonardPrinceton Universitynaomi@princeton.edu

MS1

Leader Selection in Noisy Multi-agent Systems: AResistance Distance Approach

We select a number of agents and control them to effec-tively reject noise in multi-agent systems. This optimiza-tion problem is equivalent to grounding nodes in resistancenetworks such that total effective resistance is minimized.For structured networks in which resistance distances haveanalytical expressions, we obtain globally optimal selectionof leaders. For unstructured networks in which resistancedistances can be computed efficiently, we speed up existinggreedy algorithms by exploiting sparsity techniques. Weillustrate our results with several examples.

Fu LinMathematics and Computer Science DivisionArgonne National Laboratoryfulin@mcs.anl.gov

MS2

Bayesian Estimation for Mixtures of Linear Sub-spaces with Variable Dimension

We assume i.i.d. data sampled from a finite mixture distri-bution over variable dimension linear subspaces. An em-bedding of linear subspaces onto a Euclidean sphere allowsus to define a joint prior on each subspace and its dimen-sion. The embedding and use of a Gibbs posterior yieldmodel parameter estimates.

Brian St. ThomasDepartment of Statistical Science - Duke Universitybrian.st.thomas@duke.edu

Sayan MukherjeeDuke Universitysayan@stat.duke.edu

Lek-Heng LimUniversity of Chicagolekheng@galton.uchicago.edu

MS2

Distributed Coordinate Descent Method for Learn-ing with Big Data

In this paper we develop and analyze Hydra: HYbriD co-

oRdinAte descent method for solving loss minimizationproblems with big data. We initially partition the coor-dinates (features) and assign each partition to a differentnode of a cluster. At every iteration, each node picks arandom subset of the coordinates from those it owns, inde-pendently from the other computers, and in parallel com-putes and applies updates to the selected coordinates basedon a simple closed-form formula. We give bounds on thenumber of iterations sufficient to approximately solve theproblem with high probability, and show how it depends onthe data and on the partitioning. We perform numericalexperiments with a LASSO instance described by a 3TBmatrix.

Martin Takac, Peter RichtarikUniversity of Edinburghm.takac@sms.ed.ac.uk, peter.richtarik@ed.ac.uk

MS2

Efficient Quasi-Newton Proximal Method for LargeScale Sparse Optimization

Recently several methods were proposed for sparse opti-mization which make careful use of second-order informa-tion [10, 28, 16, 3] to improve local convergence rates.These methods construct a composite quadratic approx-imation using Hessian information, optimize this approxi-mation using a first-order method, such as coordinate de-scent and employ a line search to ensure sufficient de-scent. Here we propose a general framework, which in-cludes slightly modified versions of existing algorithms andalso a new algorithm, and provide a global convergence rateanalysis in the spirit of proximal gradient methods, whichincludes analysis of method based on coordinate descent.

Xiaocheng TangLehighxct@lehigh.edu

MS2

Nomad: Non-Locking, Stochastic Multi-MachineAlgorithm for Asynchronous and DecentralizedMatrix Factorization

Abstract not available at time of publication.

S V N VishwanathanDepartment of Statistics - Purdue Universityvishy@stat.purdue.edu

MS3

Krylov Subspaces for Approximation of the Spec-tral Embedding

Spectral embedding problems are solved with truncatedspectral decompositions (tSDs); approximation of the tSDmay allow for substantial compute savings. MinimalKrylov subspaces have been advocated as tSD alterna-tives; minimal Krylov subspaces present the greatest po-tential for compute savings over the tSD, but they alsohave nontrivial approximation error. We observe that thiserror is due both to lack of convergence of eigenvaluesused in the spectral embedding and convergence of unde-sired eigenvalues from the opposite end of the spectrum.We also note that eigenvalue approximations may be farmore converged than canonical error bounds suggest. Wepropose preconditioning to produce lower-error minimalKrylov subspaces without incurring much extra computa-tional cost. We demonstrate polynomial preconditioning

38 AN14 Abstracts

for approximations of the spectral embedding and developerror bounds for more tightness. These results hint towardsminimal Krylov subspace-specific preconditioners.

Alexander BreuerU.S. Army Research Laboratoryalexander.m.breuer.civ@mail.mil

MS3

Algebraic Distance on Graphs with Applications toLarge-Scale Optimization and Data Analysis

Measuring the connection strength between vertices in agraph is one of the most important concerns in many nu-merical tasks in graph mining. We consider an iterativeprocess that smooths an associated value for nearby ver-tices, and we present a measure of the local connectionstrength (called the algebraic distance) based on this pro-cess. Algebraic distance is attractive in that the process issimple, linear, and easily parallelized.

Jie Chen, Ilya SafroArgonne National Laboratoryjiechen@mcs.anl.gov, isafro@g.clemson.edu

MS3

Numerical Analysis of Spectral Clustering Algo-rithms (SCAs)

An SCA employs eigensolves to cluster vertices and edgesso that graph topology is better understood. Given agraph, a desired cluster type, and an SCA, howmany eigen-solver iterations are required for the constituent eigenprob-lems to have adequate data mining quality? We presentin-depth analysis of the simplest cases: power method ap-plied to synthetic data mining problems, with an eye fordeveloping convergence theory for real-world problems andfaster iterative methods.

Geoffrey D. SandersCenter for Applied Scientific ComputingLawrence Livermore National Labsanders29@llnl.gov

Lance WardLawrence Livermore National Labward48@llnl.gov

Tobias JonesUniversity of Colorado, BoulderDept. of Applied MathematicsTobias.Jones@colorado.edu

MS4

Pressure Forcing and Time Splitting for Discontin-uous Galerkin Approximations to Layered OceanModels

This work concerns the application of DG methods to thenumerical modeling of the general circulation of the ocean.One step performed here is to develop an integral weakformulation of the pressure forcing that is suitable for us-age with a DG method and with a generalized vertical co-ordinate that includes level, terrain-fitted, and isopycniccoordinates as examples. The computation of pressure atcell edges is facilitated by some ideas that are also usedfor barotropic-baroclinic time splitting. This formulationis tested, in special cases, with some computational ex-

periments and with analyses of well-balancing, dispersionrelations, and numerical stability.

Robert L. HigdonOregon State Universityhigdon@math.oregonstate.edu

MS4

Analysis of Adaptive Mesh Refinement for ImexDiscontinuous Galerkin Solutions of the Compress-ible Euler Equations with Application to Atmo-spheric Simulations

We investigate the performance of a tree-based AMR algo-rithm for the high order discontinuous Galerkin method onquadrilateral grids with non-conforming elements. We payparticular attention to the implicit-explicit (IMEX) timeintegration methods and show that the ARK2 method ismore robust with respect to dynamically adapting meshesthan BDF2. Preliminary analysis of preconditioning re-veals that it can be an important factor in the AMR over-head.

Michal A. Kopera, Francis X. GiraldoNaval Postgraduate Schoolmakopera@nps.edu, fxgirald@nps.edu

MS4

A Unified Discontinuous Galerkin Approach forSolving the Two- and Three-Dimensional ShallowWater Equations

In this talk, we present a novel discontinuous Galerkin(DG) method that provides a unified approach for solv-ing the two- (depth-integrated) and three-dimensional shal-low water equations. A key feature of the developed DGmethod is the discretization of all the primary variables us-ing discontinuous polynomial spaces of arbitrary order, in-cluding the free surface elevation. In a standard Cartesian-coordinate system, this results in elements in the surfacelayer having mismatched lateral faces (a staircase bound-ary). This difficulty is avoided in the current method byemploying a sigma-coordinate system in the vertical, whichtransforms both the free surface and bottom boundariesinto coordinate surfaces. The top sigma coordinate surface,which corresponds to the free surface, is discretized usingtriangular and/or quadrilateral elements that are extendedin the vertical direction to produce a three-dimensionalmesh of one or more sigma layers of triangular prism andhexahedral elements. The polynomial spaces over theseelements are constructed using products of Jacobi polyno-mials of varying degrees in both the horizontal and verticaldirections. The DG approach is unified in the sense thatin the case of a single sigma layer and a piecewise constantapproximation in the vertical, the method collapses to a“standard” DG method for the two-dimensional, depth-integrated shallow water equations. The approach alsomakes use of new (in many cases optimal) sets of nonprod-uct integration rules and strong-stability-preserving timesteppers that have been specifically designed for efficientcalculation when used with DG spatial discretizations. Theefficiency, robustness and h (mesh) and p (polynomial or-der) convergence properties of the method will be demon-strated on a set of test cases.

Ethan KubatkoDepartment of Civil, Environmental and GeodeticEngineeringThe Ohio State University

AN14 Abstracts 39

kubatko.3@osu.edu

MS4

A Discontinuous Galerkin Non-Hydrostatic Modelwith An Operator-Split Semi-Implicit Time Step-ping Scheme

A new two-dimensional non-hydrostatic (NH) DG model(compressible Euler or Navier-Stokes system) based on ef-ficient spatial discretization has been developed on (x, z)plane. However, the fast-moving acoustic waves togetherwith a high aspect ratio (Δx = 1000Δz) between the hori-zontal and vertical spacial discretization impose a stringentrestriction on explicit time-step size for the resulting ODEsystem. We consider a semi-implicit time-split methodwhich employs so-called horizontally explicit and verticallyimplicit (HEVI) approach through an operator-split pro-cedure for the DG discretization. The vertical componentof the dynamics, which deals with the acoustic waves andvery small grid-spacing (Δz), is solved implicitly while thehorizontal part solved in an explicit manner. For the DGmodel with HEVI time integration, the CFL limit is onlyrestricted to the horizontal grid-spacing (Δx). The modelis tested for various NH benchmark test-cases, and the re-sults will be presented in the seminar.

Ram NairNCARInstitute for Mathematics Applied to Geosciencesrnair@ucar.edu

Lei BaoUniversity of Colorado, Boulderlei.bao@colorado.edu

MS5

My Intertwined Paths: Career and Family

A rich mixture of both career and family characterizes mylife during the past twenty years since I earned a PhD inapplied mathematics. I’ll discuss my intertwined paths –as a researcher at Argonne National Laboratory and as aparent. I will highlight career paths at national laborato-ries, with emphasis on the diverse opportunities for impactin interdisciplinary computational science. Also, I will re-flect on my ongoing choices for work-life balance, includingaddressing the ’two-body’ problem, parenting, and care foraging parents.

Lois Curfman McInnesArgonne National Laboratorycurfman@mcs.anl.gov

MS5

Beating the Imposter Syndrome

Many competitive and successful students and profession-als at times feel like impostors. ”I am not as smart asthey think I am”, or ”One sure day, I will disappoint myadvisor” are frequently occurring thoughts. In a study ofseveral hundred graduate students at Stanford, we askedabout this Impostor Syndrome. I’d like to share some ofthe results, as well as my own thoughts on how the oftennegative and sometimes paralyzing thoughts that surfacecan be turned around. We all need mentors and to connectwith a community in our work, and we need this at everycareer stage. I will tell some stories of successes and fail-ures with these from my own career. I will draw some key

conclusions about what to look for in a mentor. And I willreflect on the related topic of community, where the sup-ports and the engagement are bi-directional and dynamic.

Margot GerritsenDept of Energy Resources EngineeringStanford Universitymargot.gerritsen@stanford.edu

MS5

From Law of Large Numbers...

I would like to share some aspects from my own academicexperiences, such as holding positive attitudes, planningand making preparation, and the importance of havinggood mentors.

Fengyan LiRensselaer Polytechnic Institutelif@rpi.edu

MS5

On the Road Again: My Experience as an Early-career Mathematician

As a mathematician in the transition between postdoc andtenure-track, I will reflect on my experiences thus far andhighlight some of the resources that have supported my ca-reer. I will also discuss my experience with the academicjob market, the two-body problem, pursuing funding op-portunities, and seeking a balance between work and per-sonal/family commitments.

Anne ShiuUniversity of Chicagoannejls@math.uchicago.edu

MS5

On the Importance of Good Mentoring and havingan Engaging Community

We all need mentors and to connect with a community inour work, and we need this at every career stage. I will tellsome stories of successes and failures with these from myown career. I will draw some key conclusions about what tolook for in a mentor. And I will reflect on the related topicof community, where the supports and the engagement isbi-directional and dynamic.

Mary SilberNorthwestern UniversityDept. of Engineering Sciences and Applied Mathematicsm-silber@northwestern.edu

MS6

Parallel Preconditioning for All-at-Once Solutionof Time-Dependent Navier-Stokes OptimizationProblems

We explore domain decomposition strategies for accelerat-ing the convergence of all-at-once numerical schemes forthe solution of time-dependent Navier-Stokes optimizationproblems on parallel computers. Special attention is paidto developing preconditioners that are robust with respectto parameters, such as the regularization parameter, theReynolds number, and the timestep size. We describea parallel preconditioning strategy for these systems that

40 AN14 Abstracts

uses domain decomposition algorithms in the time domainand Schur complement approximations for the resultinglocal saddle point systems. Finally, we present numericalresults and discuss possible applications.

Andrew BarkerMax Planck Institut, Magdeburgbarker@mpi-magdeburg.mpg.de

MS6

A Block Diagonal Preconditioner for All-at-OnceSolution of Time-Dependent PDE-Constrained Op-timization Problems

All-at-once schemes aim to solve all time-steps of parabolicPDE-constrained optimization problems in one coupledcomputation, leading to exceedingly large linear systemsrequiring efficient iterative methods. We present a newblock diagonal preconditioner which is both optimal withrespect to the mesh parameter and parallelizable over time,thus can provide significant speed-up. We will present nu-merical results to demonstrate the effectiveness of this pre-conditioner.

Eleanor McDonaldUniversity of Oxfordeleanor.mcdonald@new.ox.ac.uk

Andrew J. WathenOxford UniversityNumerical Analysis Groupwathen@maths.ox.ac.uk

MS6

Fast Iterative Solvers for Reaction-Diffusion Con-trol Problems from Biological and Chemical Pro-cesses

In this talk, we develop fast and robust preconditioned it-erative methods for solving matrix systems arising fromreaction-diffusion control formulations of biological andchemical processes. To construct these methods, we ex-ploit the saddle point structure of the matrices to derivegood approximations of the (1,1)-block and Schur comple-ment. For the problems considered, we motivate our rec-ommended preconditioners, discuss parallel solution strate-gies, and present numerical results to demonstrate the per-formance of our methods.

John W. PearsonUniversity of Edinburghj.pearson@ed.ac.uk

Martin StollMax Planck Institute, Magdeburgstollm@mpi-magdeburg.mpg.de

MS6

All-at-Once Multigrid Methods for Optimal Con-trol Problems

In this talk we will discuss the solution of all-at-once multi-grid methods for optimal control problems of tracking typewith inequality constraints, which might look as follows:

Minimize J(y, u) =1

2‖y − yD‖2L2(Ω) +

α

2‖u‖2L2(Ω)

subject to −Δy = u on Ω and y = 0 on ∂Ω and box con-

straints (α, yD and Ω are given). The box constraintsmight be state constraints (y ≤ y ≤ y) or control con-

straints (u ≤ u ≤ u). One possibility to solve such prob-lems using multigrid methods is to use a (semi-smooth)Newton solver. Here, a standard multigrid method wouldbe used as an solver for linear sub-problems that occurwithin this iteration. Recently, it was possible to con-struct and analyze multigrid solvers that can be directlyapplied to elliptic problems with box constraints (like ob-stacle problems). Those methods have shown good con-vergence behavior in practice. In the present talk we willdiscuss how the ideas of such methods can be extended tocontrol problems.

Stefan TakacsTU Chemnitzstefan.takacs@numa.uni-linz.ac.at

MS7

Algorithms That Satisfy a Stopping Criterion,Probably

Numerical algorithms are typically equipped with a stop-ping criterion where the calculation is terminated whensome error or misfit measure is deemed to be below a giventolerance. However, in practice such a tolerance is rarelyknown; rather, only some possibly vague idea of the de-sired quality of the numerical approximation is available.Indeed, fast codes for initial value ODEs and DAEs heavilyrely on the underlying philosophy that satisfying a toler-ance for the global error is too rigid a task; such codesproceed to control just the local error. Another instanceof soft error control is when a large, complicated modelfor fitting data is reduced, say by a Monte Carlo samplingmethod. If calculating the misfit norm is in itself veryexpensive then the option of satisfying the stopping crite-rion only in a probabilistic sense naturally arises. We willdiscuss this in the context of inverse problems involvingsystems of PDEs, when many experiments are employed inorder to obtain reconstructions of acceptable quality. Ma-jor computational savings can then be realized by usingunbiased estimators for the misfit function in the stoppingcriterion.

Uri M. AscherUniversity of British ColumbiaDepartment of Computer Scienceascher@cs.ubc.ca

Farbod Roosta-KhorasaniComputer ScienceUBCfarbod@cs.ubc.ca

MS7

Time Varying RBFs for Wave-Like Solutions ofPdes

We introduce radial basis functions (RBFs) whose time-varying coefficients determine not only the amplitude andposition of each RBF but also their shape. The intendeduse of these Time Varying-RBFs (TV-RBFs) is in the local-in-time representation of low-dimensional approximationsof functions that arise in solving spatiotemporal evolutionproblems; in particular, for time-varying spatially local-ized solutions with a temporal translation component suchas traveling waves, modulated pulses or soliton-like solu-tions of evolutionary differential equations. This paperis restricted to the one-dimensional spatial case. We also

AN14 Abstracts 41

present an algorithm that places the Time Varying-RBFs(TV-RBFs) over spatiotemporal data that may come fromexperiments, from finely discretized PDE simulations, oreven from multiscale, particle-based simulations. It firstapproximates the function at a single time instant (a tem-poral snapshot) as a sum of RBFs using a novel weightedminimization that causes each RBF to primarily approx-imate one of the localized parts of the function. It thenextends that approximation to TV-RBFs over a sequenceof snapshots of the function at different times. We con-clude by discussing the potential uses of these TV-RBFs.

C.W. GearPrinceton UniversityDepartment of Chemical Engineeringwgear@princeton.edu

Arta JamshidiPrinceton Universityarta.jamshidi@gmail.com

Yannis KevrekidisDept. of Chemical EngineeringPrinceton Universityyannis@princeton.edu

MS7

On High Index Differential-Algebraic Equations

In this talk we discuss solvability of high index differentialalgebraic equations. In this context, exponentially fastertime scale of evolution of the algebraic variables is pointedout. A numerical method that elucidates the above resultby regularizing the Jacobian of the method and producingsmoothed solutions is given. The results are illustratedwith numerical examples.

Soumyendu RahaSERC, Indian Institute of Science, Bangalore 560012,Indiaraha@serc.iisc.ernet.in

MS7

Sensitivity Analysis of Stochastic Chemical Kinet-ics

Monte Carlo methods of parametric sensitivity analysis forstochastic dynamics consist of the Girsanov Transforma-tion (GT), Pathwise Derivative (PD) and Finite Difference(FD) methods. The GT differs significantly from the PDand FD methods which are closely related. While eachmethod has its advantages and drawbacks, it has been ob-served that PD and FD have lower variance than GT inmany examples. We provide a theoretical explanation forthis in the chemical kinetics context.

Muruhan RathinamUniversity of Maryland, Baltimore Countymuruhan@math.umbc.edu

Ting WangDepartment of Mathematics and StatisticsUniversity of Maryland Baltimore County

ting1@umbc.edu

MS8

Optimizing Snake Locomotion in the Plane

We develop a numerical scheme to determine which planarsnake motions are optimal for locomotory efficiency, acrossfrictional parameter space. With large transverse friction,retrograde traveling waves are optimal. Our asymptoticanalysis shows that the optimal wave amplitude decays asthe -1/4 power of the coefficient of transverse friction. Atthe other extreme, zero transverse friction, we find a tri-angular direct wave which is optimal. Between these ex-tremes, a variety of locally optimal motions are found, in-cluding ratcheting motions. We also extend the study tomotion on inclines.

Silas AlbenUniversity of Michigan, USAalben@umich.edu

Matt OsborneUniversity of Toledomatthew.osborne@rockets.utoledo.edu

Xiaolin WangGeorgia Institute of Technologyxiaolin.wang1987@gmail.com

MS8

From Animal to Robot and Back: Sidewinding onGranular Media

Sidewinders locomote in granular medium through compli-cated internal shape changes and body-terrain interactions,hence making it is difficult to predict their trajectories. Wepropose an approach which predicts motions according tobody shapes. This approach is built on geometric tech-niques to prescribe the internal motions and observationsfrom live sidewinders moving on sandy terrain. We demon-strate these ideas on the CMU snake robot.

Howie ChosetRobotics InstituteCarnegie Mellon Universitychoset@cmu.edu

Chaohui Gong, Matthew TraversCarnegie Mellon Universitychaohuig@cmu.edu, botics11@gmail.com

MS8

Lessons from Animal Locomotion: Extending Flo-quet Theory to Hybrid Limit Cycle Oscillators

Animal locomotion is often modeled as a limit cycle oscilla-tor with hybrid (discontinuous) vector field, where classicalresults of Floquet theory do not apply. We will discuss sev-eral recent theoretical results extending Floquet theory tohybrid limit cycle oscillators, as well as ongoing work onnumerical/statistical tools for Data Driven Floquet Anal-ysis of legged locomotion systems.

Shai RevzenUniversity of Michigan

42 AN14 Abstracts

shrevzen@umich.edu

MS8

Chaotic Scattering during Legged Locomotion onGranular Media

We study locomotion on heterogeneous granular media us-ing laboratory experiments and a granular resistive forcetheory (RFT). By combining RFT with a multi-body simu-lator, we model in detail the dynamics of a small open-loopcontrolled legged sand-running robot. To gain insight intothe long-term trajectories, we use cycle expansion theoryto study a simplified (scattering potential) model of thelocomotor.

Tingnan ZhangGeorgia Institute of Technologytingnan1986@gatech.edu

Chen LiUniversity of Califonia, Berkeleychen.li@berkeley.edu

Predrag CvitanovicCenter for Nonlinear ScienceGeorgia Institute of Technologypredrag@gatech.edu

Daniel GoldmanGeorgia TechSchool of Physicsdaniel.goldman@physics.gatech.edu

MS9

An Initial Modeling of Fractal Nets for the Sier-pinski Gasket

The Sierpienski tetrahedron is obtained by applying an it-erated function system (IFS) method to a regular tetrahe-dron. We give a sketch and algorithm for a folding methodthat allows us to construct the n-th iteration of a modi-fied Sierpinski gasket, then fold it to form the Sierpienskitetrahedron. We also provide an initial exploration of con-struction methods for minimal volume objects that retaintheir surface area under refinement. This idea has potentialapplications at nanoscale. Advisor: Gregory Fasshauer

Barrett LeslieIllinois Institute of Technologybleslie@hawk.iit.edu

MS9

A Bioinformatic Approach to Cancer Research

The purpose of the study was to identify potential proto-oncogenes and tumor suppressor genes for further researchby culture. The R programming language was used to ac-cess metadata from the cBio portal. Methylation, muta-tion, and phosphorylation data were used to distinguish themost likely candidate genes. As a result of this study, twosignificant candidates were identified, and the oncogenicnature of a family of genes was characterized. Researchis ongoing. Advisors: Mingli Yang and Yeatman, GibbsCancer Research Center, Spartanburg, SC

Nicolas LimogiannisWofford College

limogiannisna@email.wofford.edu

MS9

Billiard Motion of Microorganisms in Confined Do-mains

Models of ciliated ”squirmer” microorganisms indicate thatthe body rotates passively away from a wall before, during,and after collision. We explore the billiard-like motion ofsuch a body as it swims inside a confined domain. Solutionsfor stable periodic trajectories inside of regular polygonsare derived, and criteria for the existence of other trajec-tories in complex domains are investigated. The resultsmay provide insight on entrapment and sorting of microor-ganisms and other active particles. Advisors: Jean-LucThiffeault and Saverio E. Spagnolie, UW-Madison

Colin Wahl, Joseph LukasikUW-Madisoncwhal@wisc.edu, jglukasik@wisc.edu

MS10

Multiscale Modeling and Numerical Simulation ofCalcium Cycling in Cardiac Myocyte

In this talk we present the detailed model of the intra-cellular calcium dynamics in a cardiac myocyte and theirefficient numerical techniques. We adopted a detailed CRUmodel to describe the source functions in the PDE modeland the dynamics of the membrane potential is based onthe Mahajan membrane Model. We developed a finite el-ement simulator interface for the 452 CRUs arrangement.The numerical convergence of solutions and parallel resultsare demonstrated.

Nagaiah ChamakuriRadon Institute for Computational and AppliedMathematicsAustrian Academy of Sciencesnagaiah.chamakuri@oeaw.ac.at

MS10

Modeling the Molecular Basis of Calcium En-trained Arrhythmia

Heart disease is the leading cause of death in the devel-oped world and an increasing problem developing nationsmost often as result of cardiac arrhythmia. Here we exam-ine the cellular and subcellular basis of calcium dependentarrhythmias. In order to understand how calcium dynam-ics, plays a role in arrhythmogenesis, we have investigatednormal and dysfunctional calcium signaling in heart cellsat high temporal and spatial resolution using multiscalestochastic models.

Aman UllahDepartment of Molecular NeuroscienceGeorge Mason University, Fairfax, VA 22030ullah.aman@gmail.com

Tuan Hoang-TrongSchool of Systems BiologyGeorge Mason University, Manassas, VA 20110hoangtrongminhtuan@gmail.com

Geoge Williams, William LedererBiomedical Engineering and TechnologyUniversity of Maryland, Baltimore, MD 21201

AN14 Abstracts 43

gswill@gmail.com, jlederer@umaryland.edu

Mohsin S. JafriDepartment of Molecular NeuroscienceGeorge Mason University,Manassas,VA 20110sjafri@gmu.edu

MS10

Cellular Mechanisms of Calcium-Mediated Trig-gered Activity in Cardiac Myocytes

The main chambers of the heart are made up of electricallycoupled ventricular myocytes, which are excitable cells thatonly transit from the resting to the excited states (fire anaction potential) under a finite current stimulus. However,under abnormal conditions, those cells can spontaneouslyfire a single action potential, or even a burst of severalaction potentials, after a normal stimulated action poten-tial. This talk will present results of a computational studythat sheds new light on the dynamical origin of those ar-rhythmogenic ”afterdepolarizations” by quantifying the re-lationship of stochastic intracellular calcium dynamics andwhole-cell voltage dynamics.

Alain KarmaDistinguish ProfessorNortheastern Universitya.karma@neu.edu

Zhen SongPhysics DepartmentNortheastern Universitya.karma@neu.edu

MS10

Alternans As An Order-Disorder Transition inHeart Cells

Electrical alternans is a beat-to-beat alternation in the am-plitude of the electrocardiogram (ECG) which has beenshown to be a precursor to various cardiac arrhythmias.In this talk I will argue that nonlinear signaling betweenstochastic ion channels can explain the onset of alternans.Furthermore, I will present evidence that the transitionto alternans occurs via an order-disorder phase transitionwhich exhibits universal features common to a wide rangeof physical systems.

Yohannes ShiferawCalifornia State UniversityNorthridgeyshiferaw@csun.edu

MS11

Computing Eigenvalues and Eigenvectors of Sym-metric Tensors: A Survey

Eigenvalues and eigenvectors of symmetric tensors havefound applications in automatic control, data analysis,higher order diffusion tensor imaging, image authenticityverification, optimization, and other areas. In the past fewyears several algorithms have been proposed for comput-ing certain eigenpairs of symmetric tensors. In this talk, wewill survey these methods. We will also describe some newideas such as the use of deflation method that can assistthe existing algorithms to find other eigenpairs.

Lixing Han

University of Michigan at Flintlxhan@umflint.edu

MS11

Dynamical Systems Analysis of Swamps in ALS

The Alternating Least Squares (ALS) algorithm for ap-proximating a tensor by a low-rank tensor is prone to peri-ods of very slow convergence, known as swamps. Althoughthe existence of swamps is well-known and various fixeshave been proposed, the mechanisms that cause swampsare mysterious. I will discuss progress on analyzing andunderstanding swamps using tools from Dynamical Sys-tems.

Martin J. MohlenkampOhio Universitymohlenka@ohio.edu

MS11

Canonical Polyadic Decomposition for SymmetricTensor

We propose a method for finding symmetric outer prod-uct decomposition for fully and partially symmetric ten-sor. These are iterative algorithms which are based onmatricizations, least-squares and finding roots of quarticpolynomials. The methods work well for third-order par-tially symmetric tensors and fourth-order fully symmetrictensors. Our numerical examples indicate a faster con-vergence rate than the standard alternating least-squaresmethod.

Carmeliza NavascaUniversity of Alabama at Birminghamcnavasca@gmail.com

Na LiMathWorksnalitensor@gmail.com

MS11

Towards Better Computation-statistics Trade-off inTensor Decomposition

New approaches for tensor decomposition with worst caseperformance guarantee have recently emerged. O(rnd−1) isthe number of samples required for recovering an n×n××nd-way tensor that admits a Tucker decomposition withr × r × × r core proved for one of these methods calledoverlapped trace norm. Although this method is com-putationally very efficient, the rate is rather disappoint-ing. A newer approach called square norm achieves lowerO(rd/2nd/2) samples at the cost of higher computationaldemand. There is also a more theoretical approach thatcould achieve optimal O(rnd−1) but seem to be computa-tionally intractable. I will overview these recent develop-ments and discuss how we could achieve a better trade-offbetween what we can provably achieve in terms of statisti-cal accuracy and how much computation we need to spend.

Ryota TomiokoToyota Technological Institute at Chicago

44 AN14 Abstracts

tomioka@ttic.edu

MS12

Mixing and Transport by Ciliary Flows: A Numer-ical Study

Motile cilia often serve the dual function of transportingfluid across the cell surface and sensing of environmentalcues. The performance of cilia in fluid transport was stud-ied extensively. However, the way by which cilia serve thesimultaneous tasks of transport and sensing is less well un-derstood. We use a 3D computational model to examinethe transport and mixing properties of ciliary flows. Wefind that the metachronal wave improves both the trans-port and mixing rates, often simultaneously. These resultssuggest that cilia use chaotic advection and mixing as amechanism to enhance sensing.

Eva KansoUniversity of Southern Californiakanso@usc.edu

MS12

The Capture of Symbiotic Bacteria from the Envi-ronment by Host Ciliated Epithelia

Most, if not all, animals have epithelial cells whose apicalsurfaces have cilia, elongate mechanosensory appendagesthat are evolutionarily conserved in their structure andbiochemical composition. Cilia often occur in dense,behaviorally- coordinated assemblages along the mucosalsurfaces. In these locations, the cilia work in concert withthe secreted mucus to capture and translocate suspendedmaterials, notably environmental bacteria. This presen-tation will focus on what is known about the biology ofcilia-bacteria interactions.

Margaret McFall-NgaiUniversity of Wisconsin-Madisonmjmcfallngai@wisc.edu

MS12

A Cilia-Driven Hydrodynamic Sieve for SelectiveParticle Capture

Juvenile Hawaiian bobtail squids reliably capture and iso-late a single species of bacteria from inhaled coastal watercontaining a huge background of other particles. Here Ipresent experimental data showing how arrangement andcoordination of the cilia that capture the bacteria create a3D flow field that facilitates advection, sieving and selectiveretention of flow-borne particles, including bacteria. Thesestudies may inspire novel microfluidic tools for detectionand capture of specific cells and particles.

Janna C. NawrothHarvard School of Engineeringjnawroth@gmail.com

MS12

Cilia Generated Flows: Insights from Cell Culturesand Engineered Arrays

The lung stays sterile due to the cilia-generated flow ofmucus that sweeps the airway clean. We are studying eachaspect of this process: Using a magnetic microbead assayto measure the force developed by individual cilia, usingdriven microbead rheology to understand strain thickening

behavior at nano sized structures, using cell cultures tostudy biological fluid flow against gravity, and engineeringartificial cilia to study directed flow and enhanced mixingin actuated arrays.

Richard SuperfineDepartment of Physics & AstronomyUniversity of North Carolinarsuper@email.unc.edu

MS13

Frictional and Heat Transfer Characteristics ofFlow in Square Porous Tubes of Diesel ExhaustParticulate Filters

In the 1D modeling of flow in the channels of wall-flowmonoliths used in diesel particulate filters for engine ex-haust emissions control, it is common to use friction coeffi-cients and Nusselt numbers from idealized 2D/3D channelflows. Previously, this idealization suffered from lack offlow through the porous filter walls. As wall flow increasesfor the simpler geometries of circular tubes and parallelplanes, there is a rich literature describing multiple solu-tions. We extend the practical portion of these results tothe computationally challenging, but realistic, square chan-nel geometry that is necessary for mathematical modelingand settle certain long-standing controversies.

Edward BissettGamma Technologies, IncWestmont, IL 60559e.bissett@gtisoft.com

Margaritis KostoglouAristotle University of Thessalonikitba@tba.edu

Athanasios KonstandopoulosAristotle University of Thessalonikitba@tba.edu

MS13

Solution Verification in Simulations of Drop Impactof Flexible Containers

Solution Verification is an important part of the credibilityof a computational model. This activity is focused on de-termining the rate of convergence of the computed solutionas the computational grid gets refined, with the assump-tion that it will reach an asymptotic regime of convergence.The talk will show some approaches on verifying the solu-tion of a fluid structure interaction problem where flexiblecontainer filled with fluid impacts the ground after beingdropped.

Carlos A. CorralesBAXTER HEALTHCARE CORPORATIONRound Lake, IL 60073carlos corrales@baxter.com

Mark PerryBaxter Healthcare Corporationmark perry@baxter.com

MS13

Estimating Shape and Motion Information from

AN14 Abstracts 45

Radar Data

Due to the relatively short microwave wavelengths in-volved, radar imaging relies on exquisite knowledge of therelative geometry between the antenna(s) and the sceneto be imaged (i.e., the target). Radar image formation ofnon-cooperative targets, such as ships in a rolling sea, isparticularly challenging because the target may undergosignificant unknown and unpredictable motion. In this talkwe discuss our recent progress in estimating arbitrary tar-get motion from radar measurements.

Matthew Ferrara, Gregory ArnoldMatrix Research, Inc.matthew.ferrara@matrixresearch.com,greg.arnold@matrixresearch.com

Mark StuffMichigan Tech Research Institutemastuff@mtu.edu

Jason T. ParkerAFRL/RYRTjason.parker@wpafb.af.mil

MS13

Regularization in the Real World

The inverse problem of determining cardiac electrical pat-terns from measurements on internal or external electrodeshas received increasing attention from medical-device com-panies in recent years. This talk will describe new ideasfor regularization methods, simulation and preclinical ex-periments to evaluate and optimize them, and some of theclinical factors that make reliable solutions more difficultin vivo.

Eric VothSt. Jude Medical, USAevoth@sjm.com

MS14

Towards τ Adaptivity for Lithosphere Dynamics:Nonsmooth Processes in Heterogeneous Media

We propose a new form of adaptivity based on FAS multi-grid, allowing fine grid work to be avoided in regionswith nearly-linear behavior, despite arbitrarily rough co-efficients. We present preliminary experiments with non-linear solvers for localized plastic yielding in lithospheredynamics.

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratoryjedbrown@mcs.anl.gov

Mark AdamsColumbia Universitymfadams@lbl.gov

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

Dave MayETH Zurich

dave.may@erdw.ethz.ch

MS14

Hybrid Parallelism for Large-scale Adaptive-meshSimulations

With the advent of supercomputers featuring one millionprocessing units or more, maybe the most important guide-line for algorithm development is to maximize the concur-rency of computational tasks. This is at odds with commonsolution algorithms for elliptic or hyperbolic PDEs, whichare most effective in the mathematical sense but rely on amultilevel structure of causality. In this talk, we discussoptions in parallel algorithm design to reduce causality infavor of concurrency.

Carsten BursteddeUniversitat Bonnburstedde@ins.uni-bonn.de

Donna CalhounBoise State Universitydonnacalhoun@boisestate.edu

Bram MetschUniversity of Bonnmetsch@ins.uni-bonn.de

MS14

Plate Boundary-resolving Nonlinear Global Man-tle Flow Simulations using Parallel High-order Ge-ometric Multigrid Methods on Adaptive Meshes

The simulation of global mantle flow with associated platemotion at global scale is challenging due to the extremenonlinearity, the viscosity variations, and the different spa-tial scales inherent in the problem. We discretize thegoverning nonlinear incompressible Stokes equations usinghigh-order finite elements on highly adapted meshes, whichallow us to resolve plate boundaries down to a few hundredmeters. Crucial components in our scalable solver are anefficient, collective communication-free, parallel implemen-tation of geometric multigrid for high-order elements, theuse of a Schur complement preconditioner that is robustwith respect to extreme viscosity variations, and the use ofan inexact Newton solver combined with grid continuationmethods. We present results based on real data that arelikely the most realist global scale mantle flow simulationsconducted to date.

Johann RudiICESThe University of Texas at Austinjohann@ices.utexas.edu

Hari SundarInstitute for Computational and Engineering SciencesUniversity of Texas at Austinhari@ices.utexas.edu

Tobin Isaac, Georg StadlerUniversity of Texas at Austintisaac@ices.utexas.edu, georgst@ices.utexas.edu

Michael GurnisCalifornia Institute of Technologygurnis@gps.caltech.edu

46 AN14 Abstracts

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

MS14

Title Not Available at Time of Publication

Abstract not available at time of publication.

Olaf SchenkUSI - Universita della Svizzera italianaInstitute of Computational Scienceolaf.schenk@usi.ch

MS15

Geometric Locomotion with Passive Internal De-grees of Freedom: Hovering Flight and PassiveSwimming

This talk presents a general modeling approach for loco-motion dynamics of mobile multibody systems contain-ing passive internal degrees of freedom concentrated intojoints and/or distributed along deformable bodies of thesystem. The approach embraces the locomotion systemsbioinspired by animals that exploit the advantages of softappendages to improve their locomotion performance. It isillustrated through the passive swimming in von KarmanVortex Street (KVS), and the hovering flight with twistableflapping wings.

Frederic BoyerDepartment of Automatic ControlEcole des Mines de Nantesfrederic.boyer@mines-nantes.fr

MS15

Mapping Effort: Cartographically-Inspired Meth-ods for Representing the Energetic Cost of Loco-motion

In kinematic motion planning, Euclidean configuration dis-tance metrics often fail to encode nonlinear effort or powerfrom changing shape. Cartographic techniques can projectthe distorted configuration coordinates into representationsthat more accurately portray such distances. We show thatthe kinematic cartography problem may be reformulatedinto one of nonlinear dimensionality reduction (NLDR),and compare the results of applying a well-known NLDRtechnique against a previous spring relaxation algorithmon a three-link low Reynolds swimmer.

Howie ChosetRobotics InstituteCarnegie Mellon Universitychoset@cmu.edu

MS15

Numerical-Geometric Analysis of Sandswimming

Sand-swimming, a form of desert burrowing, offers inter-esting potential as a locomotion mode for robots operat-ing in loose, granular environments. Unfortunately, thecomputational cost of modeling the relevant physics raisesobstacles to a thorough exploration of the system dynam-ics. Geometric mechanics offers techniques for reducing thecomplexity of evaluating gaits, thereby offering the poten-tial for exploring a gait design space; unfortunately, these

tools have historically been restricted to systems with lin-ear, analytical dynamics. We have recently developed aframework for combining empirical data from nonlinearmodels with geometric gait evaluation methods. The re-sulting tools both reduce the computational costs of de-scribing sand-swimming and reveal fundamental aspects ofthe motion.

Ross L. HattonSc. of Mechanical, Industrial, and ManufacturingEngineeringOregon State Universityross.hatton@oregonstate.edu

MS15

Coupling of Locomotion Control and Sensing in Bi-ological Systems

The hawkmoth Manduca sexta has a keen ability to nav-igate dense environments with incredible robustness. Al-though these animals utilize relatively simple, noisy sen-sors, they harness massively distributed sensing to estimatetheir state and the state of the surrounding environment.Observability tools give us insight into what informationthese sensing systems can encode and how locomotion canbe used to enhance sensing capabilities.

Brian Hinson, Kristi MorgansenDept. of Aeronautics and AstronauticsU. of Washingtonbthinson@u.washington.edu, mor-gansen@aa.washington.edu

MS16

Fully-Automated Multi-Objective Optimization forFitting Spatial and Temporal Constraints in a Neu-ronal Model with Real Morphology

We introduce a fully automated optimization methodologyfor fitting spatially extended neuronal models with mul-tiple time scales. Using multi-objective optimization andtargeted experimental protocols, we model a hippocampalCA1 pyramidal cell, which exhibits a sodium channel withwidely-separated time constants of recovery from inacti-vation. Our implementation uses Python to control theNEURON simulator on a multi-core cluster and featuresa clickable interface to explore the Pareto-optimal front ofsolutions.

Aushra AbouzeidDepartment of Applied Mathematics, NorthwesternUniversityDepartment of Neurobiology, Northwestern Universityaushra.abouzeid@northwestern.edu

William KathNorthwestern UniversityEngineering Sciences and Applied Mathematicskath@northwestern.edu

MS16

Intrinsically Bursting AII Amacrine Cells DriveOscillations in the Degenerated Rd1 Retina

In retinal degeneration, spontaneous oscillations are ob-served in retinal output neurons, interfering with signalprocessing. Using compartmental modeling, based on sliceexperiments, we show these oscillations are generated by

AN14 Abstracts 47

intrinsic bursting of individual AII amacrine cells, whichare instrumental in transmitting photoreceptor signals tothe output cells. We explain the bursting mechanism by de-coupling the fast and slow subsystems, and investigate thebistability between bursting and tonic firing in the model.

Hannah ChoiNorthwestern Universityhannahchoi2014@u.northwestern.edu

Lei ZhangUniversity of Marylandvdxiaozhang@gmail.com

Mark CembrowskiHHMI Janelia Farmcembrowskim@janelia.hhmi.org

Joshua SingerUniversity of Marylandjhsinger@umd.edu

William KathNorthwestern UniversityEngineering Sciences and Applied Mathematicskath@northwestern.edu

Hermann RieckeApplied MathematicsNorthwestern Universityh-riecke@northwestern.edu

MS16

Synchrony and Phase-Locking of Mixed-Mode Os-cillations in a System of Pulse-Coupled Neurons

Our study is motivated by the experimental observationof fast and slow rhythms in the mammalian olfactory sys-tem. We develop a minimal model in which the interac-tion of three relevant populations of neurons is reduced toan effective pulse-coupling amongst a single population ofmixed-mode oscillators, and explore the dynamics of thissystem as a function of the shape and delay of the pulses.We interpret our findings in the context of the observedrhythms.

Avinash J. KaramchandaniDepartment of Engineering Sciences and AppliedMathematicsNorthwestern Universityavijka@u.northwestern.edu

Hermann RieckeApplied MathematicsNorthwestern Universityh-riecke@northwestern.edu

MS16

Network Restructuring Guided by AssociativeFeedback for Enhanced Stimulus Discrimination

The neuronal network performing the initial informationprocessing of olfactory stimuli in mammals exhibits ex-tensive neuronal turnover and a slow restructuring of itsconnectivity. This network evolution and the activity onthis network are modulated by feedback from a networkthat has properties of an associative memory. Using simple

computational models we investigate how these processesallow these coupled networks to learn to discriminate stim-uli depending on their familiarity or their association withnon-olfactory cues.

Hermann RieckeApplied MathematicsNorthwestern Universityh-riecke@northwestern.edu

Wayne Adams, James Graham, Cameron Dennis, TomZhao, Siu Fai ChowNorthwestern Universitywayneadams2014@u.northwestern.edu, jngra-ham@u.northwestern.edu, jcdennis0411@gmail.com,tomzhao2014@u.northwestern.edu, siu-chow2008@u.northwestern.edu

MS17

Hardcore Efficient Computation of AtmosphericFlows Using High-Order Local DiscretizationMethods

The High-order Adaptively Refined Dynamical Core(HARDcore) composes several compact numerical methodsto easily facilitate intercomparison of atmospheric flow cal-culations on the sphere and in rectangular domains. Thisframework includes the implementations of Spectral Ele-ments, Discontinuous Galerkin, Flux Reconstruction, andHybrid Finite Element methods with the goal of achievingoptimal accuracy in the solution of atmospheric problems.Several advantages of this approach are discussed such as:improved pressure gradient calculation, numerical stabil-ity by vertical/horizontal splitting, arbitrary order of accu-racy, etc. The local numerical discretization allows for highperformance parallel computation and efficient inclusion ofparameterizations. These techniques are used in conjunc-tion with a non-conformal, locally refined, cubed-spheregrid for global simulations and standard Cartesian gridsfor simulations at the mesoscale. A complete implemen-tation of the methods described is shown with verificationtest case simulation results based on standard literature.

Jorge E. GuerraDepartment of Land, Air and Water ResourcesUniversity of California, Davisjeguerra@ucdavis.edu

Paul UllrichUniversity of California, Davispaullrich@ucdavis.edu

MS17

Using the Multilayer Shallow Water Equations forStorm Surge Modeling

Coastal hazards related to strong storms, in particularstorm surge, are one of the most frequently recurring andwide spread hazards to coastal communities. In this talkwe will present a modification of the standard shallow wa-ter model that adds an additional layer to represent theboundary layer of the ocean so that the storm wind forc-ing is properly taken into account. A demonstration of theutility of this approach will also be presented as applied toHurricane Ike.

Kyle T. MandliUniversity of Texas at AustinICES

48 AN14 Abstracts

kyle@ices.utexas.edu

MS17

Transport Methods for the Community Atmo-sphere Model’s Spectral Element Dynamical Core

Transport algorithms are highly important in atmosphericmodeling for climate where hundreds of tracer species mustbe efficiently transported and it is critical that they satisfyphysical bounds and conservation laws. We describe andcompare two new transport algorithms that are being de-veloped for the Community Atmosphere Model’s (CAM)Spectral Element (SE) Dynamical Core for use on unstruc-tured meshes. The first is a finite-volume based approachwhere cell intersections between a Lagrangian departuregrid and the Eulerian computational grid are computedwith the Mesh Oriented Data Base (MOAB). This methodis stable for large time steps and is efficient for large num-bers of tracer species because the computationally inten-sive intersection algorithm needs to be called only onceper timestep for multiple tracers. The second method isa nodal semi-Lagrangian scheme that has the advantageof directly using the spectral element degrees-of-freedom.This method is coupled with an optimization algorithm toenforce mass conservation and bounds preservation. Weevaluate the new methods using several standard two- andthree-dimensional transport problems on the sphere andcompare to existing approaches.

Kara PetersonSandia Natl. Labskjpeter@sandia.gov

Mark A. TaylorSandia National Laboratories, Albuquerque, NMmataylo@sandia.gov

MS18

Interpreting the Impact of Constraints for MeanVariance and Cvar Optimization

In this presentation, we study the effect linear constraintshave on risk in the context of both mean variance opti-mization (MVO) and conditional value at risk (CVaR) opti-mization. Jagannathan and Ma (2003) establish an equiva-lency between certain constrained and unconstrained MVOproblems via a modification of the covariance matrix. Weextend their results to both the general case of arbitraryconstraints in MVO problems and to CVaR optimization,where the joint density is modified.

Chris BemisWhitebox AdvisorsMinneapolis, MN 55416chris.bemis@gmail.com

MS18

Addressing the Potential Non-Robustness of Sub-additive Portfolio Risk Measures

The modern approach to managing financial market riskis to define an acceptance set for portfolio net asset valueat some fixed time horizon according to some probabilitymeasure and to impose limits in the current period on theportfolio composition in order to assure acceptable out-comes. Estimating these limits present practical and theo-retical challenges (cf Cont et al. [2010]), particularly whereoutcomes are highly leptokurtotic. We present a concise

description of the problem and how it can be addressed.

John A. DodsonOptions Clearing CorporationChicago, IL 60606jdodson@theocc.com

MS18

Using Social Influence to Predict Subscriber Churn

With the saturation of mobile phone markets operators fo-cus their energies on identifying potential churners for re-tention campaigns. Typical churn prediction algorithmsidentify churners based on service usage metrics, net-work performance indicators, and demographic informa-tion while social influence to churn is usually not consid-ered. We present a churn prediction algorithm that incor-porates the influence churners spread to their social peersand show that social influence improves churn predictionand is among the most important factors.

Veena MendirattaBell Labs, ALCATEL-LUCENTNaperville, IL 60563veena.mendiratta@alcatel-lucent.com

Chitra Phadke, Huseyin Uzunalioglu, Dan KushnirBell Labs, Alcatel-Lucentchitra.phadle@alcatel-lucent.com,huseyin.uzunalioglu@alcatel-lucent.com,dan.kushnir@alcatel-lucent.com

MS18

Efficient High-Precision Numerical Computation

This talk provides an overview of the methods used to com-pute numerical functions using high precision in Mathe-matica. The main focus will be on computation of elemen-tary functions, but applications to special functions willalso be mentioned. An outline of the algorithms used willbe given together with a description of recent work on moreefficient implementation. A comparison with some state-of-the-art special purpose software will also be presented.

Mark SofroniouWolfram Research Inc40139 Bologna, Italymarks@wolfram.com

MS19

Changing Directions

We were often told to choose a research area we love. Butthere are a lot of different kinds of math I love; in fact, anymath is fun! In this talk I will share my reflections on howI came to the research area I work in now and factors youcan consider when making that difficult choice yourself.

May BoggessArizona State UniversityMay.Boggess@asu.edu

MS19

Two Jobs, Two Children, and Two Cars: What canPossibly go Wrong?

Some time in the last millennium but it seems longer ago

AN14 Abstracts 49

than that my husband and I set out to start a family andfind permanent academic jobs, more or less at the sametime. Employer-provided daycare, spousal accommoda-tion, and parental leave were yet to be invented. Nonethe-less, we benefited from many factors: The novelty of thesituation, our willingness to explore different parts of thecountry and different types of institutions, and our opti-mism and our determination to do the best we could forour careers and for our family. This talk will summarizeour strategies, and will consider what we could have donebetter.

Barbara Lee KeyfitzThe Ohio State UniversityDepartment of Mathematicsbkeyfitz@math.ohio-state.edu

MS19

Perspectives of an Assistant Professor

I will reflect on my career path, which did not follow thetrajectory I expected. Instead of continuing in a career fo-cused solely on teaching, I moved from being an assistantprofessor at a teaching university to one at a research uni-versity. Along with my career path, I will share the adviceI received along the way that shaped this journey. In addi-tion, I will reflect on my experiences of being an assistantprofessor at two different types of institutions.

Joan LindUniversity of Tennesseejlind@utk.edu

MS20

A Linear Algebra Perspective on Modeling andComputation with Stochastic PDEs

Computational solutions of PDE models with uncertaininputs often begin by representing the randomness in thesystem with a set of random variables, which become ad-ditional coordinates of the PDE solution. One must dis-cretize both the physical domain (space, time) and therandom domain (added coordinates) to approximate thesolution numerically. Discretization methods yield a hostof interesting linear systems to solve. We will compare thelinear systems arising in Galerkin methods, pseudospectralmethods, and least-squares methods with the goal of offer-ing some practical guidelines for discretization.

Paul ConstantineColorado School of MinesApplied Mathematics and Statisticspconstan@mines.edu

David F. GleichPurdue Universitydgleich@purdue.edu

MS20

Strategies for the Efficient Solution of Parameter-ized or Stochastic PDEs

Many applications, such as stochastic PDEs and uncer-tainty quantification, lead to a large collection or sequenceof parameterized PDEs. Taking into account that we needto solve a collection or sequence of related PDEs can leadto a substantially shorter total solution time (over all sys-tems). We provide a brief overview of methods that help

solve systems of parameterized PDEs faster, such as modelreduction for parameterized systems, Krylov subspace re-cycling, and updating preconditioners, and we discuss linksbetween these approaches, and results from recent projects.

Eric De SturlerVirginia Techsturler@vt.edu

MS20

Computational Complexity of Stochastic Galerkinand Collocation Methods for PDEs with RandomCoefficients

We developed a rigorous cost metric, used to compare thecomputational complexity of a general class of stochas-tic Galerkin methods and stochastic collocation methods,when solving stochastic PDEs. Our approach allows us tocalculate the cost of preconditioning both the Galerkin andcollocation systems, as well as account for the sparsity ofthe Galerkin projection. Theoretical complexity estimateswill also be presented and validated with use of severalcomputational examples.

Nick DexterUniversity of Tennesseendexter@utk.edu

Clayton G. Webster, Guannan ZhangOak Ridge National Laboratorywebstercg@ornl.gov, zhangg@ornl.gov

MS20

Compressive Sensing Method for Solving Stochas-tic Differential Equations

We solve stochastic partial differential equations (SPDEs)with random coefficients by expanding the solution withgeneralized polynomial chaos (gPC). We employ the com-pressive sensing method to recover the coefficients of thegPC expansion given the knowledge that the solution is”sparse”. We also combine this method with a specialsampling strategy to further increase the accuracy of therecovery of the gPC coefficients. Our method is especiallysuitable for exploiting information from limited sources.

Xiu YangBrown Universityxiu yang@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

MS21

Stochastic Turing Patterns: Analysis ofCompartment-based Approaches

Turing patterns can be observed in reaction-diffusion sys-tems where chemical species have different diffusion con-stants. In recent years, several studies investigated theeffects of noise on Turing patterns and showed that theparameter regimes, for which stochastic Turing patternsare observed, can be larger than the parameter regimespredicted by deterministic models. In this talk, thedependence of stochastic Turing patterns on the com-

50 AN14 Abstracts

partment size is investigated. we propose and study acompartment-based model of Turing patterns where eachchemical species is described using a different set of com-partments. It is shown that the parameter regions wherespatial patterns form are different from the regions ob-tained by classical deterministic PDE-based models, butthey are also different from the results obtained for thestochastic reaction-diffusion models which use a single setof compartments for all chemical species. In particular, itis argued that some previously reported results on the ef-fect of noise on Turing patterns in biological systems needto be reinterpretted.

Yang CaoComputer Science DepartmentVirginia Techycao@cs.vt.edu

Radek ErbanUniversity of OxfordMathematical Instituteerban@maths.ox.ac.uk

MS21

Adaptive Accelerated Spatial Stochastic Simula-tion of Biochemical Systems

Spatial stochastic simulation is an extremely computation-ally intensive task. This is due to the large number ofmolecules, which along with the refinement of the dis-cretized spatial domain, results in a large number of dif-fusive transfers between voxels (sub-volumes). Previously,we presented a novel formulation of the Finite State Pro-jection (FSP) method, called the Diffusive FSP (DFSP)method, for the efficient and accurate simulation of diffu-sive processes. Using the FSP method’s ability to providea bound on the error, we are able to take large diffusiontimesteps with confidence in our solution. We used this toconstruct an operator split algorithm for spatial stochasticsimulation of reaction-diffusion processes that solves diffu-sion with DFSP and reactions with SSA. However, one ofthe biggest challenges faced by scientists utilizing DFSPis correct selection of the appropriate operator splittingtimestep. A correctly chosen timestep will produce resultsat the optimum speed without violating the specified errortolerance. Choosing an appropriate timestep requires esti-mation of the error due to operator splitting. The error isa function of the spatial discretization of the domain, thediffusion coefficients of the molecules within the system,and the stiffness of the chemical reaction channels. Here,we present an extension to the DFSP algorithm that auto-matically and adaptively selects the appropriate timestepfor performance and error control. We demonstrate theutility of this method with a traditional CPU implemen-tation, and its parallel efficiency with a many-core imple-mentation.

Brian DrawertUniversity of California Santa Barbarabdrawert@cs.ucsb.edu

MS21

Stochastic Simulation of Biochemical Networks:Diffusion and Parameter Sensitivity

At the level of a single biological cell, random fluctuationshave a significant effect on the biochemistry of the cell. Theintrinsic noise in the system with reactions and diffusionis simulated on an unstructured mesh. The parameters

in the models will vary due to external sources. We willdiscuss how diffusion can be modeled on meshes of poorquality and how to include and analyze extrinsic noise inthe simulations of an oscillatory system.

Per LotstedtDepartment of Information TechnologyUppsala University, SwedenPer.Lotstedt@it.uu.se

MS21

SParSE: Efficient Stochastic Parameter Search Al-gorithm for Events

High-performance computing empowers scientists to runlarge in-silico stochastic models that accurately mimicthe behavior of the represented system. As the predic-tive power of such models improve, the need for an algo-rithm that efficiently determines system configurations forachieving a specific outcome increases. In this presenta-tion, we present a novel parameter estimation algorithm—Stochastic Parameter Search for Events (SParSE)—thatautomatically computes parameter configurations for prop-agating the system to produce an event of interest at user-specified success rate and error tolerance.

Min K. RohIntellectual Ventures Laboratorymroh@intven.com

MS23

Machine Learning Models for Terrestrial SpaceWeather Forecasting

Earths magnetosphere experiences loading and unloadingprocesses in response to the incoming energy from the so-lar wind, creating geomagnetic storms. Predicting thesestorms is a key priority of space agencies. Due to thescarcity of available data, this system is difficult to sim-ulate with first-principle techniques, inspiring significantresearch in data-driven models. We investigate the useof advanced graphical machine learning methods includ-ing Elman Recurrent Neural Networks and Hidden MarkovModels for predicting solar storms. Advisor: Dhruv Batra,Virginia Tech

Brendan Avent, Nicholas SharpVirginia Techbavent@vt.edu, nsharp@vt.edu

MS23

Optimal Control in Time-Varying Velocity Fieldsusing Alpha Hulls

Vehicles in current fields present a difficult optimizationproblem in charting optimal navigational paths. Recentprogress has been made on the general optimal controlproblem by using front propagation to track the bound-ary of a reachable set. This work presents a significantadvancement by using alpha hulls to dynamically mesh aset boundary in three dimensional space. This method per-mits higher order optimization, including mixed time-fuelcost metrics and trajectories in three dimensions. Advisor:Shane Ross, Virginia Tech

Nicholas SharpVirginia Tech

AN14 Abstracts 51

nsharp3@vt.edu

MS23

An Extensible Test Matrix Collection

We describe the design and implementation of a test ma-trix collection. The matrices are grouped into subclassesand their key properties are documented, such as struc-ture, eigenvalues, inverse and condition number. Userscan access to matrices by matrix name, by number andby property. They can also include their own matrices bycreating new subclasses, which can be easily shared withothers. The package is written in Fortran 95 and includesa Python interface. Advisor: Nicholas Higham, Universityof Manchester

Weijian ZhangUniversity of Manchesterweijian.zhang@student.manchester.ac.uk

MS24

Mathematical Modelling of Excitation ContractionCoupling

We present a spatially resolved Ca2+ release unit model. Itreproduces experimental findings like gain and gradedness,spark life time and the dependence of release currents andRyR open probability on lumenal Ca2+. A crucial questionfor the early phase of release is whether the activation ofthe RyRs is triggered by one or by multiple open LCCs.We address the problem by modelling. We conclude thatthe activation of RyRs requires multiple open LCCs.

Martin FalckeMDC for Molecular MedicineBerlin, Germanymartin.falcke@mdc-berlin.de

MS24

Ca2+ Signaling in the Cardiomyocyte: An Atom-istic to Cellular Multi-Scale Perspective

Abstract not available at time of publication.

Peter Kekenes-HuskeyUCSDpkekeneshuskey@ucsd.edu

MS24

Subcellular Calcium Dynamics in a Whole-cellModel of an Atrial Myocyte

Intracellular calcium waves play a crucial role in coordi-nating contraction of cardiac myocytes. I will presentan innovative mathematical modelling approach that al-lows detailed characterisation of calcium movement withinthe 3-dimensional volume of an atrial myocyte. Essentialaspects of the model are the geometrically realistic rep-resentation of calcium release sites and physiological cal-cium flux parameters, coupled with a computationally in-expensive framework. By translating non-linear calciumexcitability into threshold dynamics, we avoid the compu-tationally demanding time-stepping of the full parabolicpartial differential equations that are often used to modelcalcium transport. Our approach successfully reproduceskey features of atrial myocyte calcium signalling observedduring excitation-contraction coupling. Beyond this val-idation of the model, our simulation reveals novel obser-

vations about the spread of calcium within an atrial my-ocyte. Furthermore, I will demonstrate that altering thestrength of calcium release, the refractoriness of calciumrelease channels, the magnitude of initiating stimulus, orthe introduction of stochastic calcium channel activity cancause the nucleation of pro-arhythmic travelling calciumwaves.

Ruediger ThulUniversity of Nottinghamruediger.thul@nottingham.ac.uk

Steve CoombesUniversity of NottinghamDivision of Applied Mathematics, School of MathematicalSciestephen.coombes@nottingham.ac.uk

Martin BootmanThe Open Universitymartin.bootman@open.ac.uk

MS25

Complexity and Approximability of Tensor NuclearNorm

We show that computing the nuclear norm of a 3-tensoris an NP-hard problem. We discuss its approximabilityand deduce polynomial-time computable upper and lowerbounds.

Shmuel FriedlandDepartment of Mathematics ,University of Illinois,Chicagofriedlan@uic.edu

Lek-Heng LimUniversity of Chicagolekheng@galton.uchicago.edu

MS25

Combinatorial Interpretation of the Mesner-Bhattacharya Algebra with Application to Hyper-matrix Spectral Decomposition

In this talk we will present an overview of the hyperma-trix generalization of matrix algebra proposed by Mesnerand Bhattacharya in 1990. In connection with the Mesner-Bhattacharya algebra we discuss a spectral decompositiontheorem for hypermatrices, a generalization of the Cayley-Hamilton theorem to Hypermatrices with application tocomputing new hypergraph invariants.

Edinah GnangInstitute of Advanced Studykgnang@gmail.com

Vladimir RetakhRutgers Universityvretakh@math.rutgers.edu

Ahmed ElgammalDepartment of Computer ScienceRutgers Universityelgammal@cs.rutgers.edu

Ori ParzanchevskiInstitute of Advanced Study

52 AN14 Abstracts

parzan@math.ias.edu

MS25

Randomized Methods for Higher-Order SVD

We adapted the work of Halko, Martinsson and Tropp ofthe randomized range finder in finding the low multilinearrank of tensors.

Deonnia Pompey, Carmeliza NavascaDepartment of MathematicsUniversity of Alabama at Birminghamnicholep@uab.edu, cnavasca@gmail.com

MS25

Tensor Linear Discriminant Analysis for ObjectRecognition

In this talk we explore a tensor based approach to lineardiscriminant analysis and object recognition. Similar tomatrix LDA we determine a basis for projection by mini-mizing the within class scatter and maximizing the betweenclass scatter. We measure the accuracy of the method andcompare to the traditional LDA approach by varying thenumber of eigenvectors and eigenmatrices used for classifi-cation.

William E. SorensonSouth Dakota School of Mines and TechnologyWilliam.Sorenson@mines.sdsmt.edu

Randy Hoover, Karen S. BramanSouth Dakota School of Minesrandy.hoover@sdsmt.edu, Karen.Braman@sdsmt.edu

Nels LeonardSouth Dakota Schoold of Mines and Technologynels.leonard@mines.sdsmt.edu

MS26

Leaf Compliance and Foliar Disease Transmission

Foliar diseases in plants are a major cause of crop lossworldwide. Following a recent study which identified vari-ous modes of foliar pathogen ejections from contaminatedleaves during rainfalls, we here present a theoretical modelthat rationalizes the effect of foliage compliance on suchmechanisms. The laws of fluid dynamics set tight limitson this epidemiological problem of foliar disease transmis-sion and suggest mitigation strategies to the onset of foliardisease spread.

Lydia BourouibaDepartment of Mathematics #2-348Massachusetts Institute of Technologylydia.bourouiba@math.mit.edu

MS26

Hydrodynamic Contributions to Amoeboid CellMotility

Understanding the methods by which cells move is a funda-mental problem in modern biology. Cell locomotion is inte-gral to physiological processes such as wound healing, can-cer metastasis, embryonic development, and the immuneresponse. Recent evidence has shown that the fluid dy-namics of cytoplasm can play a vital role in cellular motil-

ity. The slime mold Physarum polycephalum provides anexcellent model organism for the study of amoeboid mo-tion. In this research, we develop a computational modelof crawling Physarum. Our model incorporates the effectsof the cytoplasm, cellular cortex, the internal cytoskeletonand adhesions to the substrate. Of particlary interest arestresses generated by cytoplasmic flow and how transmis-sion of stresses to the substrate is coordinated. In our nu-merical model, the Immersed Boundary Method is used toaccount for such stresses. We investigate the relationshipbetween contraction waves, flow waves, adhesion, and loco-motive forces in an attempt to characterize conditions nec-essary to generate directed motion. Cytoplasmic flows andtraction stresses generated by the model are compared toexperimentally measured stresses generated by Physarum.

Owen LewisUniversity of California, Davisollewis@math.ucdavis.edu

MS26

Simulation of Fluid Flow Past Conic Obstacles withApplications to Leaves

We present findings from 2 and 3 dimensional simulationsof fluid flow past conic obstacles to compare to experimentsof leaves in wind tunnels conducted by the Miller Lab. Thegoal is to study vortex formation at different cone angles,compare boundary layers to asymptotics and if given timepotentially measure the impact of elasticity on the obstacle.

Jeremy L. MarzuolaDepartment of MathematicsUniversity of North Carolina, Chapel Hillmarzuola@math.unc.edu

MS26

Plant Leaves Reconfigure into Cone Shapes to Re-duce Drag and Flutter

We examine how leaves roll up into drag reducing shapes instrong flows. The dynamics of the flow around the leavesof the wild ginger and tulip poplar are described and com-pared to simplified sheets using 3D numerical simulationsand physical models. In the actual leaf, a stable recircu-lation zone is formed within the wake of the reconfiguredcone. In physical and numerical models that reconfigureinto cones, a similar recirculation zone is observed.

Laura A. MillerUniversity of North Carolina - Chapel HillDepartment of Mathematicslam9@email.unc.edu

MS27

Demon Design: Circumnavigating Landauer’sLimit

Maxwells Demon is a century old thought experimentwhich has challenged physicists understanding of thermo-dynamics. We develop a new classical formalism for con-structing generalized Maxwellian Demons. We call thisnew class of systems information engines. These enginesuse ”intelligent” information processing to extract energyfrom a thermal bath. Although these processes appear toviolate the second law of thermodynamics on first inspec-tion, information processing has an energy cost. This cost

AN14 Abstracts 53

was once thought to be described by Landauers limit onerasure. We discuss how to design the microscopic andmacroscopic architecture of the information engine in or-der to circumnavigate Landauers Principle, developing adifferent set of energetic bounds on information process-ing.

Alec Boyd, James P. CrutchfieldUniversity of California Davisalecboy@gmail.com, chaos@cse.ucdavis.edu

MS27

Information Processing and the Second Law ofThermodynamics: An Inclusive, Hamiltonian Ap-proach

We obtain generalizations of the Kelvin-Planck, Clausius,and Carnot statements of the second law of thermodynam-ics for situations involving information processing. To thisend, we consider an information reservoir (representing,e.g., a memory device) alongside the heat and work reser-voirs that appear in traditional thermodynamic analyses.We derive our results within an inclusive framework inwhich all participating elementsthe system or device of in-terest, together with the heat, work, and information reser-voirsare modeled explicitly by a time-independent, classicalHamiltonian. We place particular emphasis on the limitsand assumptions under which cyclic motion of the deviceof interest emerges from its interactions with work, heat,and information reservoirs.

Sebastian DeffnerUniversity of Marylandsebastian.deffner@gmail.com

MS27

Towards A Physics of Information: Bit by Bit

Energy and information are fundamental concepts in sci-ence, and yet, most would struggle to cite results relat-ing the two, with Landauer’s principle, perhaps, being themost well-known. However, there has been renewed inter-est in relating these concepts, especially as researchers en-gage the nanoscale. We review information-theoretic mea-sures of memory and organization as developed in compu-tational mechanics, an approach that emphasizes informa-tion storage and processing in physical systems. Existingand future applications will also be discussed.

Christopher J. EllisonCenter for Complexity and Collective ComputationUniversity of Wisconsin-Madisoncellison@wisc.edu

MS27

Predictive Inference in Non-equilibrium SteadyState

Biological sensory systems could be very efficient lossy pre-dictive feature extractors, and a common goal is to engineersystems which learn to extract predictive features of sen-sory input. One theoretical framework for lossy predictivefeature extraction is that of predictive rate-distortion the-ory. We discuss how to find predictive information curvesof output generated by partially-deterministic finite au-tomata. We discuss how input-dependent dynamical sys-tems can extract predictive features of their input automat-ically. And finally, we ask whether or not an energetically-

efficient machine which merely copied the input would nec-essarily predict the input.

Sarah MarzenUniversity of California Berkeleymarzen.sarah@gmail.com

James CrutchfieldComputational Science & Engineering Center and PhysicsDept.University of California at Davischaos@cse.ucdavis.edu

MS28

Scalable Nonlinear Solvers for Geophysical Prob-lems

Robustness and efficiency of nonlinear solvers, especiallyfor complex multiphysics problems, is a major concernfor large scale problems. We present the new frameworkfor nonlinear preconditioning developed in PETSc, andshow its application to problem in crustal dynamics fromthe PyLith package, and lithospheric dynamics from thepTatin3d package.

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

MS28

Performance and Scalability of Multigrid Solversfor Geophysical Flow

this talk, we present the abstract concept of hierarchicalhybrid grids to design scalable and fast multigrid solversfor the incompressible Stokes that lead to saddle point for-mulations. Based on a hierarchy of block-wise uniformlyrefined grids, a semi-structured mesh is obtained that con-stitutes the starting point for the design and implementa-tion of a massively parallel Stokes solver. In this presen-tation, we investigate and analyze experiments for EarthMantle Convection simulations on peta-scale clusters.

Bjorn GmeinerComputer Science 10 - System SimulationFriedrich-Alexander-University Erlangen-Nuremberg,Germanybjoern.gmeiner@informatik.uni-erlangen.de

Christian WalugaM2 Center of MathematicsTechnical University of Munichwaluga@ma.tum.de

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ruede@informatik.uni-erlangen.de

MS28

Computational Environments for Modeling Multi-phase Flow, Geochemistry, and Geomechanics

We discuss multiphase models for modeling coupled flow,geochemistry and geomechanics in a porous medium thatincludes history matching using EnKf. We will presentresults for a carbon sequestration storage problem and a

54 AN14 Abstracts

chemical flood.

Mary F. WheelerCenter for Subsurface Modeling, ICESUniversity of Texas at Austinmfw@ices.utexas.edu

MS29

A Hyperspherical Method for Discontinuity Detec-tion

The objects studied in uncertainty quantification may in-conveniently have discontinuities or be contained in an im-plicitly defined irregular subvolume. Standard techniquesare likely to fail; even an adaptive sparse grid method mayrequire excessive sampling to achieve a tolerance. The hy-persphere approach detects and unfolds discontinuity sur-faces, greatly reducing the influence of highly curved ge-ometry, and allowing good estimates of shape and proba-bilistic volume.

Guannan Zhang, Clayton G. WebsterOak Ridge National Laboratoryzhangg@ornl.gov, webstercg@ornl.gov

John BurkardtDepartment of Computational ScienceFlorida State Universityjburkardt@fsu.edu

MS29

A Hierarchical Stochastic Collocation Method forAdaptive Acceleration of PDEs with Random In-put Data

We will present an approach to adaptively accelerate a se-quence of hierarchical interpolants required by a multilevelsparse grid stochastic collocation (aMLSC) method. Tak-ing advantage of the hierarchical structure, we build newiterates and improved pre-conditioners, at each level, by us-ing the interpolant from the previous level. We also providerigorous complexity analysis of the fully discrete problemand demonstrate the increased computational efficiency, aswell as bounds on the total number of iterations used bythe underlying deterministic solver.

Peter JantschUniversity of Tennesseejantsch@math.utk.edu

Guannan Zhang, Clayton G. WebsterOak Ridge National Laboratoryzhangg@ornl.gov, webstercg@ornl.gov

MS29

Improving Performance of Sampling-Based Uncer-tainty Quantification on Advanced Computing Ar-chitectures Through Embedded Ensemble Propa-gation

We explore approaches for improving the performanceof sampling-based uncertainty quantification methods onemerging computational architectures. Our work is moti-vated by the trend of increasing disparity between floating-point throughput and memory access speed. We describerearrangements of sampling-based uncertainty propagationmethods to propagate ensembles of samples simultaneouslyleading to improved memory access patterns and increased

fine-grained parallelism. We then measure the resultingperformance improvements on emerging multicore archi-tectures in the context of sparse linear algebra.

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

H. Carter EdwardsSandia National Laboratorieshcedwar@sandia.gov

MS29

A Generalized Clustering-based Stochastic Collo-cation Approach for High-dimensional Approxima-tion of SPDEs

We developed a novel generalized clustering-based stochas-tic collocation (gSC) approach, constructed from, e.g., alatinized hCV tessellation (hCVT), with locally supportedhierarchical radial basis function defined over each hCVTcell. This gSC method permits low-discrepancy adaptivesampling according to the input probably density function(PDF), and whose accuracy decreases as the joint PDF ap-proaches zero; effectively approximating the solution onlyin the high-probability region. Theoretical and computa-tional comparisons to classical sampling and SC methodswill also be examined.

Clayton G. Webster, Guannan ZhangOak Ridge National Laboratorywebstercg@ornl.gov, zhangg@ornl.gov

MS30

Matching Exponential and Resolvent Based Cen-trality Measures in Complex Networks

Centrality measures are used to numerically define the no-tion of importance of a node to the entire network. In thistalk we consider in particular centrality measures based onthe matrix exponential and resolvent functions. It has beenobserved that the ordinal node ranking the resolvent basedmeasure yields can be particular sensitive to the choice ofthe parameter involved. We show that the parameter canbe chosen so that the resolvent measure gives similar rank-ings to the exponential measure.

Mary AprahamianSchool of MathematicsThe University of Manchestermary.aprahamian@postgrad.manchester.ac.uk

Des HighamUniv. Strathclydedjh@maths.strath.ac.uk

Nicholas J. HighamUniversity of ManchesterSchool of MathematicsNicholas.J.Higham@manchester.ac.uk

MS30

Anticipating Behavior During Twitter Spikes

We propose and test a novel mathematical model for theactivity of microbloggers during an external, event-drivenspike. The model leads to a computable prediction of who

AN14 Abstracts 55

will become active during a spike. This information is of in-terest to commercial organisations, governments and char-ities, as it identifies key players who can be targeted withinformation in real time. The main expense is a large-scale,sparse linear system solve that is comparable with the costof computing Katz centrality. We will illustrate the newalgorithm on Twitter data around sporting events and TVshows, where spikes in social media activity are driven byexternal events such as referees’ decisions or dramatic plotdevelopments.

Desmond HighamUniversity of Strathclyde, UKd.j.higham@strath.ac.uk

Peter LaflinBloom Agency, UKpeter.laflin@bloomagency.co.uk

Peter GrindrodUniversity of Oxford, UKgrindrod@maths.ox.ac.uk

Alex MantzarisUniversity of Strathclyde, UKalexander.mantzaris@strath.ac.uk

Amanda OtleyBloom Agency, Leeds, UKamanda.otley@bloomagency.co.uk

MS30

A Matrix Analysis of Different Centrality Measures

Node centrality measures including degree, eigenvector,Katz and subgraph centralities are analyzed for both undi-rected and directed networks. We show how parameter-dependent measures, such as Katz and subgraph centrality,can be ”tuned” to interpolate between degree and eigenvec-tor centrality, which appear as limiting cases of the othermeasures. Our analysis gives some guidance for the choiceof parameters in Katz and subgraph centrality, and pro-vides an explanation for the observed correlations betweendifferent centrality measures.

Christine KlymkoEmory Universitycklymko@emory.edu

Michele BenziDepartmentofMathematics and Computer ScienceEmory Universitybenzi@mathcs.emory.edu

MS30

Low-rank Approximation Methods for Ranking theNodes of a Complex Network

Various network metrics have been introduced to identifythe most important nodes in a graph. Some of them aredefined as a function of the adjacency matrix associated tothe network. We propose a new method to compute suchmatrix functions, based on a low rank approximation of theadjacency matrix, which allows us to determine a subsetthat contains the most important nodes, followed by theapplication of Gauss quadrature to refine the result.

Giuseppe Rodriguez, Caterina Fenu

University of Cagliari, Italyrodriguez@unica.it, kate.fenu@gmail.com

Lothar ReichelKent State Universityreichel@math.kent.edu

MS31

A Family of Numerical Methods for Large ScaleDFN Flow Simulations avoiding Complex MeshGeneration

A novel optimization method for Discrete Fracture Net-work (DFN) simulations of subsurface flows is presented.Large scale DFN problems are iteratively split in quasi-independent smaller problems on the fractures that can beefficiently solved on parallel computers, applying severaldiscretization approaches on fractures, with independentmeshes. The approach leads to a flexible, efficient and re-liable method. The approach is also used for UncertaintyQuantification of flow properties in DFNs.

Matias Benedetto, Stefano Berrone, Caludio Canuto,Sandra Pieraccini, Stefano ScialoPolitecnico di TorinoDipartimento di Scienze Matematichematias.benedetto@polito.it, sberrone@calvino.polito.it,claudio.canuto@polito.it, pieraccini@calvino.polito.it,stefano.scialo@polito.it

MS31

Adaptive Mesh Refinement for Flow in FracturedPorous Media

Discrete fracture models are typically large due to the ex-plicit representation of fractures. For these systems, thefracture connectivity often has the largest impact on flow.In some cases fracture connectivity can restrict the flow toa limited area, leaving large parts of the reservoir essen-tially inactive. In this work we show how well-driven flowsolutions can be used to efficiently adapt the unstructuredgrid to resolve key flow regions.

Mohammad Karimi-FardStanfordkarimi@stanford.edu

Louis DurlofskyStanford Universitylou@stanford.edu

MS31

Meshing Strategies and the Impact of Finite El-ement Quality on the Velocity Field in FracturedMedia

For calculating flow in a fracture network, the mixed hybridfinite element (MHFE) method is a method of choice as ityields a symmetric, positive definite linear system. How-ever, a drawback to this method is its sensitivity to badaspect ratio elements. For poor-quality triangles, elemen-tary matrices are ill-conditioned, and inconsistent velocityvectors are obtained by inverting these local matrices. Herewe present different strategies for better reconstruction ofthe velocity field.

Geraldine PichotINRIA-Rennes, France

56 AN14 Abstracts

Campus de Beaulieugeraldine.pichot@inria.fr

Patrick LaugINRIA - RocquencourtFrancepatrick.laug@inria.fr

Jocelyne ErhelINRIA-Rennes, FranceCampus de BeaulieuJocelyne.Erhel@inria.fr

Jean E. RobertsINRIA Paris-RocquencourtFrancejean.roberts@inria.fr

Jerome JaffreINRIA-RocquencourtJerome.Jaffre@inria.fr

Jean-Raynald de DreuzyGeosciences Rennes, UMR6118 CNRSUniversite de Rennes 1jean-raynald.de-dreuzy@univ-rennes1.fr

MS31

XFEM for Flow in Fractured Porous Media

Simulations of flows in porous media in geological appli-cations are challenging due to geometric complexity andstrong variability of properties. To obtain a flexible nu-merical discretization we employ the XFEM. Grids can beset irrespectively of regions of different permeability sincewe can represent discontinuous coefficients within elementsaccurately. Fractures can cut grid elements thanks to suit-able enrichments of the pressure and velocity spaces. Fi-nally, n− 1 dimensional XFEM are employed to treat theintersections between fractures.

Anna ScottiMOX, Department of Mathematics, Politecnico di Milanoanna.scotti@mail.polimi.it

Luca FormaggiaDepartment of MathematicsPolitecnico di Milano, Italyluca.formaggia@polimi.it

MS32

Mathematical Models of Metabolic Dysfunction inType 2 Diabetes

Type 2 diabetes is a slowly progressing and complexmetabolic disease with a multitude of etiological factors.Although it is primarily caused by reduced cellular uptakeof glucose (insulin resistance) and insufficient insulin pro-duction (β-cell dysfunction), many of its underlying mech-anisms remain unknown. We develop a series of math-ematical models to describe cellular and molecular pro-cesses involved in the progression of insulin resistance andβ-cell dysfunction and discuss implications for metabolicirreversibility and disease onset time.

Erica J. GrahamNorth Carolina State UniversityDepartment of Mathematics

ejgraha2@ncsu.edu

MS32

Oscillation of Nabla Dynamic Equations on TimeScales

In this talk we discuss the oscillatory behavior of thesecond-order nonlinear nabla functional dynamic equation(

p(t)y∇(t))∇

+ q(t)f(y(τ (t))) = 0

on a time scale (a nonempty subset of the real numbers)T with supT = ∞. We establish a sufficient and neces-sary condition which ensures that every solution oscillates.Next we establish the oscillatory equivalence of the abovedynamic equation and the second-order nonlinear nabla dy-namic equation(

p(t)y∇(t))∇

+ q(t)f(yρ(t)) = 0

on time scales. We close with an example.

Raegan HigginsTexas Tech UniversityDepartment of Mathematics and Statisticsraegan.higgins@ttu.edu

MS32

Fetal Heart Rate and EEG Modeling: PredictingFetal Distress in Labor

During labor, fetal well-being is typically monitored bymeasuring fetal heart rate (FHR). It is known that morereliable monitoring modalities are needed. To address this,we present a mathematical model which explores the mon-itoring of two signals, FHR and EEG, as a way to predictfetal distress. Our modeling approach includes blood flowto the heart and brain and incorporates several key fea-tures such as, oxygen delivery, blood flow redistribution,blood pressure, chemo and baro-receptor mechanisms.

Aisha Najera CheslerClaremont Graduate Universityaisha.najera@cgu.edu

Ami RadunskayaPomona CollegeMathematics Departmentaer04747@pomona.edu

MS32

A Biological Application of the Oriented Skein Re-lation

The tangle model was developed in the 1980’s by profes-sors DeWitt Sumner and Claus Ernst. This model uses themathematics of tangles to model protein-DNA binding. Ann-string tangle is a pair (B, t) where B is a 3-dimensionalball and t is a collection of n non-intersecting curves prop-erly embedded in B. In the tangle model for DNA site-specific recombination, one is required to solve simultane-ous equations for unknown tangles which are summandsof observed DNA knots and links. This presentation willgive a review of the tangle model for site specific recombi-nation, discuss another tangle model that utilizes the ori-ented skein relation for knots and give an application forthese models to biological processes.

Candice Price

AN14 Abstracts 57

United States Military Academy, West PointDepartment of Mathematical Sciencescandice.price@usma.edu

MS33

Fast Sweeping Methods for Steady State Problemsfor Hyperbolic Conservation Laws

Fast sweeping methods are efficient interactive numer-ical schemes originally designed for solving stationaryHamilton-Jacobi equations. Their efficiency relies onGauss-Seidel type nonlinear iterations, and a finite num-ber of sweeping directions. We generalize it to hyperbolicconservation laws with source terms. The algorithm is ob-tained through finite difference discretization, with the nu-merical fluxes evaluated in WENO fashion, coupled withGauss-Seidel iterations. High order accuracy and the ca-pability of resolving shocks are achieved. In further study,we incorporate multigrid method to improve the efficiency.

Weitao ChenUniversity of California, Irvineweitaoc1@uci.edu

MS33

Nonlinear Traveling Waves for a Model of theMadden-Julian Oscillation

The Madden-Julian oscillation (MJO) is a planetary-scalewave envelope of cloud and storm activities in the trop-ics. MJO significantly affects other components of theatmosphere-ocean-earth system. Recently, a nonlinearmodel is presented for capturing MJO’s features. I willpresent the exact nonlinear traveling wave solutions basedon the model’s energy conservation. The solution allows forexplicit comparisons between features of linear and nonlin-ear waves, such as dispersion relations and eligible travelingwave speeds.

Shengqian ChenUniversity of Wisconsin, Madisonsqchen@math.wisc.edu

MS33

Nonlinear Neutral Inclusions: Assemblages ofSpheres and Ellipsoids

If a neutral inclusion is inserted in a matrix containinga uniform applied electric field, it does not disturb thefield outside the inclusion. The well known Hashin coatedsphere is an example of a neutral coated inclusion. In thistalk, we consider the problem of constructing neutral in-clusions from nonlinear materials. In particular, we discussassemblages of coated spheres and ellipsoids.

Silvia Jimenez BolanosDepartment of MathematicsColgate Universitysjimenez@colgate.edu

MS33

Energy-Conserving Discontinuous Galerkin Meth-ods for the Vlasov-Ampere System

In this talk, we propose energy-conserving numericalschemes for the Vlasov-Ampere (VA) systems. The VA

system is a model used to describe the evolution of proba-bility density function of charged particles under self con-sistent electric filed in plasmas. It conserves many physicalquantities, including the total energy which is comprisedof the kinetic and electric energy. Unlike the total particlenumber conservation, the total energy conservation is chal-lenging to achieve. For simulations in longer time ranges,negligence of this fact could cause unphysical results, suchas plasma self heating or cooling. In our work, we developthe first Eulerian solvers that can preserve fully discretetotal energy conservation. The main components of oursolvers include explicit or implicit energy-conserving tem-poral discretizations, an energy-conserving operator split-ting for the VA equation and discontinuous Galerkin finiteelement methods for the spatial discretizations. We vali-date our schemes by rigorous derivations and benchmarknumerical examples such as Landau damping, two-streaminstability and bump-on-tail instability.

Xinghui ZhongMichigan State Universityzhongxh@math.msu.edu

MS34

Bayesian Inference with Reduced-order Modelsand Statistical Error Estimates

Bayesian inversion for parameterized PDEs requires sam-pling from the posterior distribution, which can entailthousands of forward simulations; this is infeasible withlarge-scale models. To make this tractable, we 1) replacethe large-scale model with a reduced-order model (ROM),and 2) rigorously account for the ROM error using thenovel ROMES method. ROMES provides a statisticalmodel of this error by constructing a stochastic processmapping error indicators (e.g., residual norm) to a distri-bution over the ROM error.

Kevin T. CarlbergSandia National Laboratoriesktcarlb@sandia.gov

Martin DrohmannUniversity of MunsterInstitute for Computational and Applied Mathematicsmdrohma@sandia.gov

Matthias Morzfeld, Fei LuDepartment of MathematicsLawrence Berkeley National Laboratorymmo@math.lbl.gov, flu@lbl.gov

MS34

Partial Eigenvalue Assignment in Large-Scale Lin-ear Stochastic Dynamic Systems

The objective of the proposed work is to characterize feed-back matrices for large-scale linear dynamic systems withinthe framework of nonlinear eigenvalue problem and robustdesign optimization under uncertainty. The proposed for-mulation takes into account the effects of constraint vio-lations associated with certain risk assessment for the dy-namic system under consideration. It is based on the con-cept of quantiles and tail conditional expectations. Numer-ical examples will be presented to illustrate the proposedframework.

Sonjoy Das, Kundan GoswamiUniversity at Buffalo

58 AN14 Abstracts

sonjoy@buffalo.edu, kundango@buffalo.edu

Biswa N. DattaNorthern Illinois Universitydattab@math.niu.edu

MS34

Optimal Sampling of Polynomial Chaos Expansions

We investigate Monte Carlo sampling of random inputs forthe estimation of coefficients in a sparse polynomial chaosexpansion, with a particular focus on high-dimensionalrandom inputs. Sampling from the distribution of therandom variables is typically sub-optimal in a statisticalsense. Asymptotic properties of orthogonal polynomialsyield sampling schemes with reduced dependence on theorder and dimension of polynomial basis. We present alter-native sampling schemes including a Markov Chain MonteCarlo sampling with a statistical optimality.

Alireza DoostanDepartment of Aerospace Engineering SciencesUniversity of Colorado, BoulderAlireza.Doostan@Colorado.EDU

Jerrad HamptonUniversity of Colorado, Boulderjerrad.hampton@colorado.edu

MS34

High-Dimensional Approximation with DiscreteLeja Sequences

We investigate weighted Leja sequences for non-intrusiveinterpolatory/approximation schemes of differential equa-tions parameterized by a random variable. Leja sequencesare attractive for building surrogates of parametric depen-dence because of their asymptotically optimal properties inthe pdf-weighted norm. In this talk we discuss the applica-tion and construction of discrete approximations to thesesequences, the latter of which involves canonical numeri-cal linear algebra routines and maximum-volume subspaceselection.

Akil NarayanUniversity of Massachusetts Dartmouthakil.narayan@umassd.edu

MS35

Integration of Molecular Science and Engineering

Electrodeposition is a key process step in the fabricationof high-value products. Deposit formation involves a widevariety of physical phenomena that span multiple time-and length-scales. Although new scientific knowledge atthe atomic-scale is revolutionizing understanding, the de-sign of well-engineered products presents significant com-putational challenges. This presentation describes use ofkinetic Monte Carlo and First Passage Time algorithmsfrom an engineering perspective that requires massively it-erative optimization calculations based on incomplete fun-damental knowledge.

Richard C. AlkireUniversity of Illinois at Urbana-Champaign

r-alkire@uiuc.edu

MS35

Intrinsic and Extrinsic Fluctuations in a Spa-tiotemporal Oscillatory System

Appropriate modeling and simulation frameworks forstudying extrinsic noise in spatial settings will be increas-ingly important as cell biologists dissect the relative con-tributions of intrinsic and extrinsic fluctuations to totalstochasticity on ever finer scales. Here we present an ex-tension to URDME to incorporate extrinsic noise into aspatial, mesoscopic setting. As an example, the method isdemonstrated on a model of experimentally observed, spa-tiotemporal Min protein oscillations in E. Coli cells. Whenextrinsic fluctuations are modelled as a coloured noise pro-cess the sensitivity of a system may depend critically onthe typical lifetime of the noise. This phenomenon is ob-served here and illustrates the importance of taking thetimescale of interacting processes into account when ana-lyzing a models robustness to noise.

Andreas HellanderDepartment of Computer ScienceUniversity of California, Santa Barbaraandreash@cs.ucsb.edu

MS35

Multi-Physics Multiscale Simulations for DustyProto-Planetary Disks

We develop a numerical package to simulate the interactionbetween the protoplanetary disks and embedded proto-planets. The disk motion is described as PDEs(hyperbolic,parabolic, and elliptic type). The planet motion is de-scribed as ODEs. The coupled system contains multiplelength and time scales. Several numerical techniques in-cluding multiscale method have been developed to accel-erate the time integration. Adaptive mesh refinement andparallel-in-time methods are also used to speed up the cal-culation.

Shengtai LiLos Alamos National Laboratorysli@lanl.gov

MS35

Understanding the Network of Oscillators in theMammalian Circadian Clock

The mammalian circadian clock is comprised of thou-sands of heterogeneous intracellular oscillators synchroniz-ing their rhythms via intercellular communication. It is notwell understood how such a diverse set of cells synchronizes.Using a mechanistic ordinary differential equation model,we have identified an inverse relationship between intrinsicamplitude and phase response properties as a key factor insynchronization. Using a simple phase-amplitude model,we relate our earlier findings to the ability to synchronizeincreasingly heterogeneous populations.

Stephanie TaylorColby Collegesrtaylor@colby.edu

MS36

Inertial Particles in Turbulence, Caustics and Col-

AN14 Abstracts 59

lisions

Abstract not available at time of publication.

Gregory BewleyMax Planck Institute for Dynamics and Self-Organizationgregory.bewley@ds.mpg.de

MS36

Capillary Fracture

I will describe the initiation and growth of fractures in gelsclose to their solid-liquid transition. In experiments, chan-nel fractures form at the surface of the gel, driven by fluidpropagating away from a central droplet. Their initiationis governed by two processes. First, surface-tension forcesexerted by the droplet deform the gel substrate and breakazimuthal symmetry. We model the substrate as an incom-pressible, linear-elastic solid and characterize the elastic re-sponse to provide a prediction for the number of fracturearms as a function of material properties and geometric pa-rameters. Second, a thermally-activated process initiatesa starburst-shaped collection of fractures corresponding tothis strain-patterning. Once initiated, the fractures growwith a universal power law L = t3/4, with the speed limitedby the transport of an inviscid fluid into the fracture tip.

Karen DanielsNorth Carolina State Universitykdaniel@ncsu.edu

Joshua BostwickNorthwestern Universityjoshua.bostwick@northwestern.edu

MS36

Low Energy Cardiac Defibrillation

Abstract not available at time of publication.

Stefan LutherMax Planck Institute for Dynamics and Self-Organizationstefan.luther@ds.mpg.de

MS36

Nonlinear Waves and Wave Turbulence

Abstract not available at time of publication.

Nicolas MordantLaboratoire des Ecoulements Geophysiques et IndustrielsUniv. J. Fourier / CNRS / Grenoble INP / IUFnicolas.mordant@ujf-grenoble.fr

MS37

A Mathematical Model for the Sexual Selection ofExtravagant and Costly Mating Displays

The evolution of extravagant and costly ornaments on an-imals has intrigued biologists since Darwin suggested thatfemale preference for exaggerated courtship displays drivesthe sexual selection of these ornaments. We propose a min-imal mathematical model which incorporates two compo-nents of ornament evolution: an intrinsic cost of ornamen-tation to an individual, and a social benefit of relativelylarge ornaments within a population. Using bifurcationanalysis and perturbation theory, we show that animals

will split into two niches, one with large ornaments andone with small, a phenomenon observed in many species.

Sara CliftonNorthwestern University, USAsclifton@u.northwestern.edu

Danny AbramsNorthwestern Universitydmabrams@northwestern.edu

MS37

Qualitative and Asymptotic Theory of Detonations

We derive a multidimensional weakly non-linear asymp-totic model of detonation waves capable of reproducingthe rich nonlinear dynamics observed in solutions of thereactive Euler equations, both in one and multiple spacedimensions. Quantitative and qualitative comparison be-tween the asymptotic equations and the full system theyapproximate are also presented.

Luiz FariaKAUSTluiz.faria@kaust.edu.sa

Aslan R. KasimovApplied Mathematics and Computational ScienceKing Abdullah University of Science and Technologyaslan.kasimov@kaust.edu.sa

Rodolfo R. RosalesMassachusetts Inst of TechDepartment of Mathematicsrrr@math.mit.edu

MS37

A Linear Quadratic Programming Method for Non-linear Model Predictive Control

Nonlinear Model Predictive Control (NMPC) requires iter-ative approximative solution of optimal control problems.After discretization these are given as nonlinear programs.State-of-the-art solvers use Sequential Quadratic Program-ming to this end. Several industrial applications demandthe solution of Mixed-Integer NMPC Problems with com-binatorial constraints leading to Mathematical Programswith Equilibrium Constraints. We investigate an SLEQPmethod that uses LPs to determine active sets and stepsgiven by a combination of Linear and equality constrainedQuadratic Programs.

Felix LendersHeidelberg University, Germanyfelix.lenders@iwr.uni-heidelberg.de

Christian KirchesInterdisciplinary Center for Scientific ComputingUniversity of Heidelberg, Germanychristian.kirches@iwr.uni-heidelberg.de

MS37

Mathematical Model of Transplant Rejection:Roles of T cells, Antigen Presenting Cells, and Cy-tokines

A mathematical model of the immune-mediated rejectionof transplants predicts a 50% decrease in graft mass within

60 AN14 Abstracts

two weeks of transplantation. Effector T cells propagaterejection while regulatory T cells limit it; the model is usedto test graft tolerance-promoting interventions. Decreasingthe effector T cell translocation rate into the graft typicallydelays rejection, although this effect depends on relativecytokine concentrations. Doubling the initial number ofregulatory T cells delays rejection by two weeks.

Andrew MaturoIndiana University-Purdue University, Indianapolis, USAamaturo@umail.iu.edu

Giorgio RaimondiJohns Hopkins School of Medicine, Baltimore, MDg.raimondi@jhmi.edu

Julia ArcieroDepartment of Mathematical SciencesIndiana University-Purdue University Indianapolisjarciero@math.iupui.edu

MS37

Solving Differential Algebraic Equations UsingStructural Analysis Based Dummy Derivatives

Differential algebraic equations, DAEs, appear frequentlyin applications involving equation based modelling. A com-mon way of making a DAE amenable to numerical solutionis by reducing it to a corresponding (usually implicit) ODE.The signature matrix method instead solves the DAE di-rectly via Taylor series [1]. We draw comparisons betweenthese two different approaches and show the signature ma-trix method is in some sense equivalent to the dummyderivative index reduction method [2].

Ross McKenzieCardiff University, Wales, UKMcKenzieR1@cardiff.ac.uk

John PryceCardiff University, Wales, United Kingdomj.d.pryce@cantab.net

Guangning TanMcMaster University, Hamilton, Canadatgn3000@msn.com

Ned NedialkovMcMaster Universitynedialk@mcmaster.ca

MS37

A Mathematical Model of an Arterial Wall

Elastic arteries are significantly prestretched in axial direc-tion and this has great influence on the mechanical behav-ior during the pressure cycle. Our study presents results ofa simulation of the inflation-extension behavior and com-parisson of several different models of the wall. The con-stitutive parameters and geometries for 17 aortas adoptedfrom the literature were supplemented with initial axialprestretches obtained from the statistics of 365 autopsymeasurements.

Marek NetuilCharles University in Prague, Czech Republicmarek.netusil@gmail.com

Lukas HornyCzech Technical University in Praguelukas.horny@fs.cvut.cz

MS38

Hamilton-Jacobi Equations for the ContinuumLimits of Sorting and Percolation Problems

We show that two related combinatorial problems havecontinuum limits that correspond to solving Hamilton-Jacobi equations, and give convergent numerical schemes.The first problem is non-dominated sorting, which is fun-damental in multi-objective optimization, and the second isdirected last passage percolation (DLPP), which is an im-portant stochastic growth model closely related to directedpolymers and the totally asymmetric simple exclusion pro-cess (TASEP).

Jeff CalderDepartment of MathematicsUniversity of Michiganjcalder@umich.edu

MS38

Fast and Accurate Redistancing Via DirectionalOptimization

A fast and accurate algorithm for the reinitialization ofthe signed distance function in two and three spatial di-mensions is presented. The algorithm has computationalcomplexity O(N log N ) for the reinitialization of N gridpoints. The order of accuracy of the reinitialization isdemonstrated to depend primarily on the interpolation al-gorithm used. Bicubic interpolation is demonstrated toresult in fourth-order accuracy for smooth interfaces. Sim-ple numerical examples demonstrating the convergence andcomputational complexity of the reinitialization algorithmin two and three dimensions are presented as verificationof the algorithm.

Selim EsedogluUniversity of Michiganesedoglu@umich.edu

MS38

Numerical Solution of the Second Boundary ValueProblem for the Monge-Ampere Equation

The second boundary value problem for the Monge-Ampere equation consists of a fully nonlinear elliptic par-tial differential equation (PDE) with a global constrainton the image of the gradient map. The state constraint isreplaced by a more tractable local PDE on the boundary.Using wide-stencil finite difference schemes, we construct anumerical method that converges to the viscosity solutionof the underlying problem.

Brittany FroeseUniversity of Texas at Austinbfroese@math.utexas.edu

MS38

Convergent Filtered Schemes for the Eikonal Equa-tion

The approximation theory of Barles and Souganidis[Asymptotic Anal. 4 (1991), pp. 271-283] guarantees theconvergence of numerical schemes to the viscosity solution

AN14 Abstracts 61

provided they are monotone, stable and consistent. How-ever, theses schemes are in general only 1st order accu-rate. Froese and Oberman [Siam J. Numer. Anal. 51(2013), pp. 423-444] introduced recently convergent fil-tered schemes which achieve high order where the solu-tions are sufficiently smooth. In this talk, we constructfiltered schemes to the Eikonal equation, present results inone and two dimensions and compare them to the ENOschemes [Siam J. Numer. Anal. 28 (1991), pp. 907-922].

Tiago SalvadorMcGill Universitytiago.saldanhasalvador@mail.mcgill.ca

MS39

Using Krylov Subspace Method for the CanonicalPolyadic Decomposition

We propose method based on Krylov subspace methods infinding the minimum sum of rank one tensors. For rankdeficient least-squares problems, this iterative method isefficient with respect to the computational cost and mem-ory.

Christina GlennDepartment of MathematicsUniversity of Alabama at Birminghamtina7@uab.edu

Carmeliza NavascaUniversity of Alabama at Birminghamcnavasca@gmail.com

MS39

Source Apportionment of Time and Size ResolvedAmbient Particulate Matter

The proposed weighted alternating least squares methodwas used to analyze size- and time-resolved particle sam-ple compositional tensor data. The algorithm identi-fied five emission sources: soil, deicing road salt, air-craft landings, transported secondary sulfate, and local sul-fate/construction. The largest source associated with theairport operations was aircraft landing that had not beenpreviously considered as a significant source of particles.

Na LiMathWorksnalitensor@gmail.com

Carmeliza NavascaUniversity of Alabama at Birminghamcnavasca@gmail.com

MS39

Stochastic Approximation Algorithms for thePolyadic Decomposition

In a polyadic decomposition, a tensor is written as a sum ofrank-1 terms. The computation of this decomposition ofteninvolves the minimization of the distance between the ten-sor and the decomposition. Most iterative algorithms useevery known element in each iteration. By using stochasticapproximation techniques, only a few points are accessed ineach iteration. The number of data point accesses can thusbe reduced, which is important in big data applications.

Nico Vervliet

Department of Electrical Engineering (ESAT)KU Leuvennico.vervliet@esat.kuleuven.be

Lieven De LathauwerKatholieke Universiteit Leuvenlieven.delathauwer@kuleuven-kulak.be

MS40

Hydrodynamics and Control of Microbial Locomo-tion

Interactions between swimming cells, surfaces and fluidflow are essential to many microbiological processes, fromthe formation of biofilms to the fertilization of human eggcells. Yet, relatively little remains known quantitativelyabout the physical mechanisms that govern the responseof bacteria, algae and sperm cells to flow velocity gradi-ents and solid surfaces. A better understanding of cell-surface and cell-flow interactions promises new biologicalinsights and may advance microfluidic techniques for con-trolling microbial and sperm locomotion, with potentialapplications in diagnostics and therapeutic protein synthe-sis. Here, we report new experimental measurements thatquantify surface interactions of bacteria, unicellular greenalgae and mammalian spermatozoa. These experimentsshow that the subtle interplay of hydrodynamics and sur-face interactions can stabilize collective bacterial motion,that direct ciliary contact interactions dominate surfacescattering of eukaryotic biflagellate algae, and that rheo-taxis combined with steric surface interactions provides arobust long-range navigation mechanism for sperm cells.

Jorn DunkelMathematics, MITdunkel@math.mit.edu

Vasily KantslerUniversity of WarwickSkolkovo Institute of Technologyv.kantsler@warwick.ac.uk

Raymond E. GoldsteinDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of Cambridger.e.goldstein@damtp.cam.ac.uk

MS40

Orientational Order in Two-Dimensional ConfinedActive Suspensions

Geometric confinement in physical space is important forthe studies of the collective motion of suspensions of ac-tive swimmers. The reasons are two-fold: motile biolog-ical micro-organisms or active colloids are always subjectto different types of confinement in the swimming envi-ronment; The existence of confinement can have signifi-cant effects on the hydrodynamic interactions between theswimmers and thus changes the nature of the collectivemotion. We focus on the situation when the swimmers areconfined between two parallel plates (Hele-Shaw cell) suchthat the motion of the particles are restricted to two di-mensions. In this case, the far-field hydrodynamic effectof a swimmer is no longer given by a force-dipole, whichhas been used in numerous studies on discrete numericalsimulations and continuum theories. Instead, the far-fieldeffect of a confined swimmer is given by a potential-dipole.

62 AN14 Abstracts

Using a potential-dipole model in doubly-periodic domain,we perform numerical simulations to probe into the col-lective dynamics of confined active suspensions. We showthat, depending on whether the swimmers have head-and-tail symmetry, the isotropic suspensions of swimmers candevelop either long time polar orientation order, local align-ments and non-mobile clusters or combination of the above,which are novel collective behavior compared to swimmersuspensions in unconfined geometries.

Alan Cheng Hou Tsang, Eva KansoUniversity of Southern Californiaalanchet@usc.edu, kanso@usc.edu

MS40

Surface Interactions in Suspensions of SwimmingCells

Interactions between swimming cells and surfaces are es-sential to many microbiological processes, from bacterialbiofilm formation to human fertilization. However, despitetheir fundamental importance, relatively little is knownabout the physical mechanisms that govern the scatter-ing of flagellated or ciliated cells from solid surfaces. Inthe talk I will reveal recent advances in understanding offlagella interaction with surfaces, provide mechanisms forutilizing our knowledge about these interactions to controlswimming of flagellated cells. In addition, I will describeour very recent results on sperm rheotaxis near surfaces.The key focus will be on the experimental results, sup-ported by numerical simulation using minimal models.

Vasily KantslerUniversity of WarwickSkolkovo Institute of Technologyv.kantsler@warwick.ac.uk

Jorn DunkelMathematics, MITdunkel@math.mit.edu

Raymond E. GoldsteinDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of Cambridger.e.goldstein@damtp.cam.ac.uk

MS40

Modeling of Hydrodynamic Interactions of LargeGroups of Swimming Microorganisms in Viscoelas-tic Fluids

Hydrodynamic interactions of swimming microorganismscan lead to coordinated behaviors of large groups. Theimpact of viscoelasticity on the collective behavior of ac-tive particles driven by hydrodynamic interactions hasbeen quantified with the inclusion of rotational diffusion.Oldroyd-B, Maxwell, and generalized linear viscoelasticmodeled are considered as the constitutive equation of thesuspending fluid, inspired by some biological fluids. Amean field assumption is used to model the suspension dy-namics near an isotropic state. The onset of instabilityhas been quantified by a linear stability analysis in termsof wavenumber, diffusivities, and constitutive equation pa-rameters. Some key results are in contrast to suspensionsin Newtonian fluids. The maximal growth rate can occurat a particular wavelength, and diffusion can act to makethe system more unstable. Viscoelasticity can also affect

the long time dynamics of the continuum equations.

Patrick Underhill, Yaser BozorgiRensselaer Polytechnic InstituteDepartment of Chemical and Biological Engineeringunderhill@rpi.edu, bozorgi@rpi.edu

MS41

Low-Dimensional Dynamics Embedded in Echo-State Networks

Abstract not available at time of publication.

Andrea K. BarreiroDepartment of MathematicsSouthern Methodist Universityabarreiro@smu.edu

MS41

Metastability and Coherent Structures in LargeStochastic Neuronal Networks

We will consider stochastic dynamical systems defined onnetworks where the individual dynamics mimic standardneuronal models, and show that the systems can exhibitvarious types of coherent and metastable behavior. Wewill demonstrate that there is a naturally occurring, butnon-standard, spectral problem in problems of this type;analysis of this spectral problem will show that its salientfeatures are determined by a certain homology group.

Lee DeVilleUniversity of Illinois, Department of Mathrdeville@illinois.edu

MS41

Integrate-and-Fire Model of Insect Olfaction

When a locust detects an odor, the stimulus triggers aseries of synchronous oscillations of the neurons in the an-tenna lobe. These oscillations are followed by slow dy-namical modulation of the firing rates which continue afterthe stimulus has been turned off. I model this behaviorby using an Integrate-and-Fire neuronal network with ex-citatory and inhibitory neurons. The inhibitory responseof both types of neurons contains a fast and slow compo-nent. The fast component, together with the excitation,creates the initial oscillations while the slow componentsuppresses them and aids in the creation of the slow pat-ters that follow. During the initial oscillations the stimuluscan be identified by determining which excitatory neuronsparticipate consistently in every cycle of the oscillations.

Pamela B. FullerRensselaer Polytechnic InstituteFullep@rpi.edu

MS41

Generalized Linear Models for Networks of SpikingNeurons

Abstract not available at time of publication.

Sara A. SollaNorthwestern University

AN14 Abstracts 63

solla@northwestern.edu

MS42

Cytoplasm Rheology and Its Role Cellular Bleb-bing Dynamics

We present a computational model to describe the dynam-ics of blebbing, which occurs when the cytoskeleton de-taches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment andthe local expansion of the cell membrane. The model isused to explore the relative roles in bleb dynamics of cy-toplasmic rheology, permeability of the cytoskeleton, andelasticity of the membrane and cytoskeleton. We show thatthe multiphase poroelastic nature of cytoplasm is essentialto explain experimental observations.

Robert GuyDeptartment of Mathematics, U.C. Davisrdguy@ucdavis.edu

MS42

An Analytic Framework for Pairwise Correlationsin Active Swimming

In recent years there has been considerable interest inactive fluids, such as suspensions of swimming micro-organisms. A key observation for such suspensions is thetendency of ”pushing” swimmers (typically bacteria, e.g.E. coli) to develop long range orientational correlations; instark comparison to ”pulling” organisms (typically algae,e.g. C. reinhardtii) which tend to remain uncorrelated.This observation is consistent with analytical results inmean field theories for hydrodynamically interacting swim-mers, where the uniform isotropic state is stable for pullersbut unstable for pushers. However, a mean field theory cannot be used to actually predict correlation length scales, asit assumes independence of distinct swimmers. Being ableto predict such two-point statistics is an important step incharacterizing the macroscopic rheological properties of thesuspension as a whole. In this talk an analytical frameworkfor computing the correlations in a simplified phenomeno-logical model for swimming will be discussed.

Kajetan M. SikorskiUniversity of California Santa BarbaraDepartament of Mathematicssikork@math.ucsb.edu

MS42

Finite Length Undulatory Swimmers: Whether toKick Or to Burrow in a Viscoelastic Fluid

We explore finite length undulatory swimmers in viscoelas-tic fluids. The worm is modeled as an inextensible infinitelythin sheet in 2 dimensions and the swimming is driven us-ing a prescribed target curvature. We look at front-backasymmetries in the prescribed stroke pattern and considerthe effect on swimming speed and efficiency. The impor-tance of passive dynamics, where swimmers are given pre-scribed torques rather than prescribed shapes, is explored.We show that kickers can get a larger boost from viscoelas-ticity than burrowers.

Becca ThomasesUniversity of California at Davis

thomases@math.ucdavis.edu

MS42

Exploring the Effect of Glass-Forming Sugars onVesicle Membrane Dynamics During Drying

When immersed in a liquid, certain sugars have a ”glass-forming” effect on the liquid at large enough concentration.In particular, the viscosity of the liquid is found to be heav-ily dependent on the sugar concentration, reaching that ofa glass in optimal conditions. These sugars, and their affecton cellular structures, are of interest to the biological com-munity for various reasons, one of which is their use in thepreservation of biological material. Whereas cryopreserva-tion stores material using extremely low temperatures toreduce cellular mobility, a new technique named lyopreser-vation uses the aforementioned glass-forming effect to re-duce mobility. However, current attempts to achieve lyop-reservation have less than successful. The work discussedin this talk focuses on modeling a single cell undergoingdrying similar to that involved in current lyopreservationtechniques. This is done by considering a vesicle placed in afluid containing a spatially varying concentration of sugar.The model incorporates the bending resistance and inex-tensibility of the membrane, the viscosity dependence onthe sugar, the flow of liquid across the vesicle membrane, aswell as the surrounding concentration and velocity fields.It is solved using the level set, immersed boundary, and im-mersed interface methods. The results focus on identifyinghow the various material parameters affect the vesicle dy-namics and attempt to identify ideal regimes for achievinglyopreservation.

Chris VoglUniversity of WashingtonDepartment of Applied Mathematicschris.j.vogl@gmail.com

MS43

Qualitative Reasoning with Modelica Models

Qualitative reasoning allows us to reason about physicalsystems using simplified systems of qualitative differentialequations, in a way which preserves important behavioralaspects of those systems. However, a continuing challengein that work is the construction of appropriate qualita-tive models of those systems. Meanwhile, designers areincreasingly using the Modelica language to create simula-tion models of proposed designs for numerical simulation.Our group at PARC has addressed the model constructionbottleneck of qualitative reasoning by automatically trans-forming Modelica models into qualitative models. In thistalk, we describe that process, and discuss the challenges inabstracting equations into constraints, determining initialconditions and discrete events, and identifying appropriatecontinuous behavior. We identify places where additionalqualitative constraints can be derived from Modelica equa-tions, and describe how we bridge the gaps between Mod-elica and existing qualitative simulation work on discretebehavior. Our system has been integrated with existingModelica tools; we describe its potential applications tomechatronic engineering design.

Bill JanssenPARC

64 AN14 Abstracts

janssen@parc.com

MS43

Enabling Technologies for Web-Based EngineeringAnalysis

The web and cloud have become ubiquitous in our every-day lives. The societal impact of these technologies is sig-nificant. Everyday, new tools and technologies are intro-duced to facilitate the creation of web-based applications.But most of these applications are targeted at consumerlevel applications. Although these applications are drivenby very interesting mathematical principles (for machineintelligence, data correlation, etc), they are successful be-cause they use these principles to create a significant im-pact for non-technical users (i.e. consumers). In the engi-neering world, many interesting mathematical techniqueshave only a limited impact because there are fewer tech-nologies available to wrap these techniques up so they canimpact non-expert users. The first step in connecting en-gineering and software technologies is understanding therole of technology standards in streamlining the develop-ment and deployment process. The next step is identifyingapplications where these technologies can have a signifi-cant impact on the the customers of engineered products.Along the way, we need to consider how to educate engi-neers, mathematicians and scientists about the possibilitiesthat these technologies present and how to leverage them.This talk will discuss these issues and demonstrate exam-ples of how engineering standards combined with cuttingedge software technologies can help bridge the gap allow-ing engineers and mathematicians to have a greater impacton engineering product development and, ultimately, con-sumers. Specific topics will include mathematical modelsof products, cloud computing technologies and user expe-rience in web-based engineering applications.

Michael TillerXogenymichael.tiller@gmail.com

MS43

Introduction and Overview of Modelica

Modelica is a declarative, equation based, object orientedlanguage for the physics-based modeling of large scale en-gineering systems. Modelica is unique in being a vendor-neutral and widely accepted standard to describe suchcyber-physical systems as the composition of Differential-Algebraic Equations (DAE) to describe the system physicsand the software to control such systems. For the softwarepart, several models of computation can be expressed inModelica: signal oriented modeling, state machines, andsynchronous declarative descriptions can all be expressedwithin the scope of Modelica. This combination makesModelica useful through all phases of model based engi-neering, from the early phases of system design to the veri-fication of the control software, and even reaching into sys-tem operation, where Modelica based models are used fornon-linear model predictive control of complex and safety-critical plants. This talk will give an introduction to var-ious aspects of Modelica from the perspective of appliedmathematics and introduce how high-level Modelica codeis transformed in several of the Modelica compilers to arange of numerical algorithms that are then used to ana-lyze engineering design problems. In particular we will lookat the transformation of Modelica code into hybrid DAE

systems and to NLPs for solving optimal control problems.

Hubertus TummescheitModelon, Inc.tba

MS43

Modelica for Building and Community Energy Sys-tems

Building energy and control systems can be representedby systems of coupled stiff differential equations, algebraicequations and discrete equations. These equations couplemodels from multiple physical domains. We will presenthow these systems can be modeled using the equation-based, object-oriented Modelica language. We discuss nu-merical challenges and opportunities to use such modelsfor analysis that is outside the capabilities of conventionalbuilding simulation programs. The talk closes with anoverview of the international project ”new generation com-putational tools for building and community energy sys-tems based on the Modelica and Functional Mockup Inter-face standards”. This project is a collaboration among 16countries under the Energy in Buildings and CommunitiesProgramme of the International Energy Agency.

Michael WetterLBNLmwetter@lbl.gov

MS44

Dynamics Constrained Optimization of Power GridUsing Adjoint Sensitivity Analysis

We present a DAE-constrained optimization problem forthe electric power grid where the steady state operatingpoint has path constraints on the trajectory when thepower grid is subjected to severe disturbances. We useconstraint aggregration and adjoint sensitivity approachfor efficiently solving this optimal control problem. Thistalk discusses the problem formulation, solution approach,and the preliminary results obtained.

Shrirang AbhyankarArgonne National Laboratoryabhyshr@mcs.anl.gov

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov

Vishwas RaoDepartment of Computer ScienceVirginia Techvisrao@vt.edu

MS44

Global Error Estimation for Differential Equations

Global error represents the actual discretization error re-sulting after solving a system of differential equations. Iwill focus on time-stepping methods for ordinary and differ-ential algebraic equations. Calculating a posteriori errorsis generally viewed as an expensive process, and thereforein practice only the (local) error from one step to the nextis used to estimate the global errors. However, local er-ror estimation is not always suitable and may lead to error

AN14 Abstracts 65

underestimation. I will review several strategies for a pos-teriori error estimation and discuss new approaches thatgeneralizes the classical strategies.

Emil M. ConstantinescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov

MS44

Predicting the Future with Faster Than Real-TimePower System Dynamics Simulation

“Faster than real-time dynamics simulation” is a key goalof DOE’s Advanced Modeling Grid program. IIT is lead-ing a project to (eventually) predict complex, large-scalepower system behavior based on real-time measurements.The team is leveraging computational and hardware ad-vances (e.g., PETSc solvers, time-stepping algorithms, andmulti-core processors) to increase speed. Furthermore, theteam is integrating modeling advances (e.g., three-phaseunbalanced models, protection system models) to improveaccuracy. The ultimate goal is to avoid blackouts.

Alexander J. FlueckIllinois Institute of Technologyflueck@iit.edu

MS44

Dynamic-Feature Extraction, Attribution and Re-construction (dear) Method for Power SystemModel Redution

This paper presents a method of deriving the reduced dy-namic model of power systems based on dynamic responsemeasurements. The method consists of three steps, namelydynamic-feature extraction, attribution, and reconstruc-tion (DEAR), and results in a quasi-nonlinear reducedmodel of the original system. The network topology isunchanged. Tests on several IEEE standard systems showthat the proposed method yields better reduction ratio andresponse errors than the traditional coherency based reduc-tion methods.

Shuai Lu, Shaobu Wang, Ning Zhou, Marcelo Elizondo,Guang LinPacific Northwest National Laboratoryshuai.lu@pnnl.gov, shaobu.wang@pnnl.gov,ning.zhou@pnl.gov, marcelo.elizondo@pnnl.gov,guang.lin@pnnl.gov

M.A. PaiUniversity of Illinios, Championmapai@illinois.edu

MS45

Improved Multilevel Monte Carlo for High Perfor-mance Computing

Since models at extreme scales may have high dimensionalrandom space, it is important to continue the developmentof dimension-independent methods of uncertainty quantifi-cation. Here we accelerate MLMC for PDEs by using aFEM iterative solver that improves the initial guess duringsampling. By using previous samples to build an inter-polant that predicts the solution value at subsequent sam-ple points, we can greatly reduce the number of iterations

per MC sample. Implementation on GPU.

Zane Colgin, Abdul KhaliqMiddle Tennessee State Universityzac2g@mtmail.mtsu.edu, abdul.khaliq@mtsu.edu

Guannan Zhang, Clayton G. WebsterOak Ridge National Laboratoryzhangg@ornl.gov, webstercg@ornl.gov

Viktor ReshniakMiddle Tennessee State Universityvr2m@mtmail.mtsu.edu

MS45

A Multilevel Stochastic Collocation Methods forSPDEs

Multilevel methods for SPDEs seek to decrease computa-tional complexity by balancing spatial and stochastic dis-cretization errors. Multilevel techniques have been success-fully applied to Monte Carlo methods (MLMC), but can beextended to accelerate stochastic collocation (SC) approxi-mations. In this talk, we present convergence and complex-ity analysis of a multilevel SC (MLSC) method, demon-strating its advantages compared to standard single-levelapproximations, and highlighting conditions under whicha sparse grid MLSC approach is preferable to MLMC.

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesmgunzburger@fsu.edu

Aretha L. TeckentrupFlorida State Universityateckentrup@fsu.edu

Peter JantschUniversity of Tennesseejantsch@math.utk.edu

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

MS45

A Comparison of Algebraic Multigrid Precondi-tioning Approaches for Sampling-Based Uncer-tainty Propagation on Advanced Computing Ar-chitectures

Algebraic multigrid (AMG) methods are known to be ef-fective, scalable preconditioners for linear systems arisingin various application areas. Sampling-based uncertaintypropagation methods provide an opportunity to extendsuch techniques to what are essentially groups of closelycoupled systems. We compare AMG approaches in the con-text of ensemble propagation on advanced architectures,where sampling rearrangement has occurred in order toimprove access and parallelism. Examples will be givenusing the Trilinos solver framework.

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

66 AN14 Abstracts

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

MS45

Calibration of a Computer Model with FunctionalInputs

We investigate the use of specialized experimental datato find Bayesian estimates of a functional parameter ina model of the system. Ideas are illustrated using a casestudy on the action potential of ventricular myocytes.

Matthew PlumleeISYE, Georgia Techmplumlee@gatech.edu

MS46

Overview of High-Performance Algorithms forFunctions of Matrices

In this talk I will present an overview of recent develop-ments in high performance algorithms for matrix functions,with a focus on topics not covered by the subsequent talksin this minisymposium. I will discuss a selection of recentalgorithms and results on condition estimation, the actionof matrix functions on large, sparse matrices, and the im-plementation and testing of matrix function algorithms.I will also discuss some of the open problems and chal-lenges involved in developing high-performance algorithmsfor matrix functions.

Edvin DeadmanUniversity of Manchesteredvin.deadman@manchester.ac.uk

MS46

Efficient and Stable Arnoldi Restarts for MatrixFunctions Based on Quadrature

Arnoldi’s method is a popular tool for approximatingf(A)b, the action of a function f of a large sparse matrix Aonto a vector b. The practical applicability of this methodis limited by the storage requirements of the Arnoldi ba-sis. We will discuss a new restarting technique based onquadrature which removes this limitation and is more sta-ble and efficient than previously proposed restarting tech-niques. The new technique is applicable for a large classof functions f , including the so-called Stieltjes functionsand the exponential function, both of which have applica-tions in complex network analysis. Our method is applica-ble for functions of Hermitian and non-Hermitian matrices,requires no a-priori spectral information, and runs with es-sentially constant computational work per restart cycle.

Stefan GuettelThe University of Manchesterstefan.guettel@manchester.ac.uk

Andreas J. FrommerBergische Universitaet WuppertalFachbereich Mathematik und Naturwissenschaftenfrommer@math.uni-wuppertal.de

Marcel SchweitzerBergische Universitat Wuppertal

schweitzer@math.uni-wuppertal.de

MS46

Exponential Iterative Methods of Runge-Kutta-type (EPIRK): Construction, Analysis and Soft-ware

Exponential integrators have recently emerged as an ef-ficient alternative to the explicit and implicit methodsfor time integration of large stiff systems of differentialequations. A distinct feature of these techniques is thatthe approximation of the solution uses exponential andexponential-like functions of the Jacobian or the matri-ces corresponding to the stiff linear part of the problem.Exponential integrators possess better stability propertiescompared to explicit methods and can require fewer calcu-lations per time step then implicit schemes. We introduce anew class of Exponential Propagation Iterative methods ofRunge-Kutta type (EPIRK). These schemes are designedto offer computational savings and allow construction ofvery efficient schemes compared to other exponential andimplicit methods. We describe three different types ofEPIRK methods - the unsplit, the split and the hybridEPIRK schemes - as well as discuss a new type of implicit-exponential (IMEXP) methods. Both the classical and stifforder conditions for EPIRK integrators will be discussedand we will present a new software package EPIC (Expo-nential Propagation Integrators Collection) which imple-ments most efficient of these methods for serial and parallelcomputational platforms.

Mayya TokmanUniversity of California, MercedSchool of Natural Sciencesmtokman@ucmerced.edu

MS46

Blocked Algorithms for the Matrix Sign Function

The talk will describe two different blocked (partitioned)algorithms for the matrix sign functions. These algorithmsoffer improved performance over Higham’s adaptation ofthe Schur-Parlett method for this problem. The improvedperformance is a result of reduced communication (fewercache misses or less inter-processor communication). Onevariant uses existing efficient building blocks but requiresthe reordering of the Schur form, while the others has moreoverhead in the inner loop, but can utilize any ordering ofthe eigenvalues.

Sivan A. ToledoTel Aviv Universitystoledo@tau.ac.il

MS47

Gradient Discretization of Hybrid DimensionalTwo-Phase Darcy Flows in Fractured Porous Me-dia

We present a gradient discretization, including a large fam-ily of schemes, in a case of a two-phase Darcy flow in dis-crete fracture networks (DFN) . We consider the asymp-totic model for which the fractures are represented as inter-faces of codimension one immersed in the matrix domainwith continuous pressures at the matrix fracture interface.The convergence is proved under the assumption that therelative permeabilities are bounded from zero but coverthe discontinuous capillary pressures. The numerical tests

AN14 Abstracts 67

are performed on the 3D fracture networks using HybridFinite Volume and the novel Vertex Approximate Gradi-ent (VAG) discretizations. Compared with Control Vol-ume Finite Element (CVFE) approaches, the VAG schemehas the advantage to avoid the mixing of the fracture andmatrix rocktypes, while keeping the low cost of a nodal dis-cretization on unstructured meshes. The efficiency of VAGscheme is shown in the case of a high permeability contrastbetween fracture network and matrix.

Konstantin BrennerUniversity of Nice Sophia AntipolisLaboratoire de Mathematiques J.A. Dieudonnekonstantin.brenner@gmail.com

Cindy GuichardLJLL, University Paris 6guichard@ljll.math.upmc.fr

Mayya GrozaLJAD, University Nice Sophia AntipolisCOFFEE team, Inriamayya.groza@unice.fr

Gilles LebeauLJAD, University Nice Sophia Antipolisroland.masson@unice.fr

Roland MassonUniversity of Nice Sophia Antipolisroland.masson@unice.fr

MS47

A Double-Layer Reduced Model for Flow in FaultZones Using Hybrid Finite Volume Schemes

We consider single-phase flows for subsurface porous mediawith faults, the latter along which the surrounding domainon one side of the fault has slipped with respect to that onthe other. The fault width being smaller by several ordersof magnitude than other characteristic sizes, we proposea hybrid finite volume method based on a double-layer,reduced model. We allow non-matching grids along thefaults. Numerical and theoretical results are shown.

Isabelle FailleIFP Energies NouvellesFranceisabelle.faille@ifpenergiesnouvelles.fr

Alessio Fumagalli, Alessio Fumagalli

Institut Franais du Petrole Energies nouvellesalessio.fumagalli1984@gmail.com,alessio.fumagalli1984@gmail.com

Jerome JaffreINRIA-Roquencourt78153 Le Chesnay cedex FranceJerome.Jaffre@inria.fr

Jean E. RobertsINRIA Paris-RocquencourtFrancejean.roberts@inria.fr

MS47

Controlling Uncertainty in Fractured Porous Me-

dia Flow

We consider the dynamics of multiphase flow in heteroge-neous porous media with randomly located interfaces. Inthe deterministic case the modeling of such systems re-quires the usage of nonlinear discontinuous flow functions.Based on the capillarity-free fractional flow formulation fortwo-phase flow, a hybrid stochastic Galerkin finite volumemethod (HSG-FV) is presented. The method accounts forthe spatially random change of the mobilities and is par-ticularly well-suited for parallel computations.

Markus KoppelUniversity of StuttgartInstitute for Applied Analysis and Numerical Simulationmarkus.koeppel@mathematik.uni-stuttgart.de

MS47

A Fracture Indicator to Identify Fractures inPorous Media

We study the identification of fractures in porous media.The problem is formulated as a least squares minimiza-tion of a function evaluating the misfit between a mea-sured pressure and a pressure calculated using a particularreduced discrete model for flow in porous media with frac-tures. Inspired by the idea of refinement indicators, wedevelop fracture indicators to search for fractures as wellas their hydraulic conductivities through an iterative pro-cess.

Vincent MartinUTCvincent.martin@utc.fr

MS48

Learning Hierarchical Invariant Spatio-TemporalFeatures for Human Action and Activity Recog-nition

We propose a neural-network based learning scheme whichcomputes a manifold in a bag of spatio-temporal featuresthrough regression based modeling. The action class mod-els are designed to be independent of time without theneed for sequence length normalization and initialization ofstates. Using the bag of spatio-temporal features as a timeseries data, a time-independent orthogonal basis is com-puted where a low-dimensional manifold is learned. Ex-perimental results prove its efficiency on public data sets.

Binu Nair, Vijay AsariUniversity of Daytonbinuq8@gmail.com, vasari1@udayton.edu

MS48

An Inverse Kinematic Approach Using GroebnerBasis Theory Applied to Gait Analysis of the LowerExtremity Joint Angles

This research highlights the results obtained from an ex-perimental study of the lower limbs of a human gait cycle toextract and identify gait signatures. This biometric analy-sis was carried out by capturing the gait cycles in a normaland load bearing gait, using modalities such as passive in-frared and passive optical. The challenge of this study is todistinguish between normal and abnormal gait signaturesdue to a concealed load on the lower body.

Anum Barki

68 AN14 Abstracts

NASA Langley Research Centerbarkianum@gmail.com

Kimberly KendricksCentral State Universitykkendricks@centralstate.edu

Ronald Tuttle, David Bunker, Borel ChristophAir Force Institute of Technologyronald.tuttle@afit.edu, david.bunker@afit.edu,chris.borel@afit.edu

MS48

Game-Theoretic and Reliability Methods in Coun-terterrorism and Security

The routine application of reliability analysis is not ade-quate in the security domain. Protecting against inten-tional attacks is fundamentally different from protectingagainst accidents or acts of nature. In particular, an in-telligent and adaptable adversary may adopt a differentoffensive strategy to circumvent or disable protective secu-rity measures. Game theory provides a way of taking thisinto account. Thus, security and counter-terrorism requirea combination of reliability analysis and game theory.

Vicki BierUniversity of Wisconsin- Madisonbier@ie.engr.wisc.edu

MS48

Biomechanical Analysis of Pack Load Influence onGait Signatures Derived from Grobner Basis The-ory

This project examines kinematic gait patterns as predic-tors of the influence associated with individuals carryingconcealed weighted packs up to 20% of their body weight.An initial inverse dynamics approach combined with com-putational algebra provided lower limb joint angles duringthe stance phase of gait as measured from 12 human sub-jects during normal walking. This talk describes the ad-ditional biomechanical analysis of the joint angle data toproduce kinetic and kinematic parameters further charac-terizing human motion

Sean KohlesOregon Health and Science Universityssk@kohlesbioengineering.com

Anum BarkiNASA Langley Research Centerbarkianum@gmail.com

Kimberly KendricksCentral State Universitykkendricks@centralstate.edu

MS49

Numerical Optimization Method for SimulationBased Optimal Design Problems

The numerical optimization of simulation based problemis an interdisciplinary area of study that includes the op-timization with PDE constraints area in applied mathe-matics. The Finite Element Method to find the numericalsolution of a PDE subject to third-type boundary condi-tions as the ones that model electromagnetic phenomena,

adjoint and direct differentiation gradients, and proper or-thogonal decomposition are some of some of the topics ofinterest that continue to develop optimal design of devices.

Carmen CaisedaInter American University Bayamon, PRccaiseda@bayamon.inter.edu

MS49

A Characterization of the Reflected Quasipotential

Our purpose here is to characterize the reflected quasipo-tential in terms of a first-order Hamilton-Jacobi equa-tion. Because it is continuous but not differentiable ingeneral the characterization will be in terms of viscos-ity solutions. Using conventional dynamic programmingideas, along with a complementarity problem formulationof the effect of the Skorokhod map on absolutely continu-ous paths, we will derive necessary conditions in the formof viscosity-sense boundary conditions.

Kasie FarlowUnited States Military Academykasie.farlow@usma.edu

MS49

Analysis of Finite Difference Schemes for Diffusionin Spheres with Variable Diffusivity

Three finite difference schemes are compared for discretiz-ing the spatial derivatives of the diffusion equation inspherical coordinates for the general case of variable dif-fusivity, D. Five diffusivity cases are considered: 1) con-stant D, 2) time-dependent D, 3) spatially-dependent D,4) concentration-dependent D, and 5) implicitly time-dependent and spatially-dependent D. The results point toone of the schemes as the preferred finite difference methodfor numerically solving the diffusion equation in sphereswith variable diffusivity.

Ashlee Ford VersyptMassachusetts Institute of Technologyashleefv@mit.edu

MS49

Analysis of Si Models with Multiple InteractingPopulations Using Subpopulations with ForcingTerms

As a system of differential equations describing an epidemi-ological system becomes large with multiple connectionsbetween subpopulations, the expressions for reproductivenumbers and endemic equilibria become algebraically com-plicated, which makes drawing conclusions based on bi-ological parameters difficult. We present a new methodwhich deconstructs the larger system into smaller subsys-tems, captures the bridges between the smaller systems asexternal forces, and bounds the reproductive numbers ofthe full system in terms of reproductive numbers of thesmaller systems, which are algebraically tractable. Thismethod also allows us to analyze the size of the endemicequilibria.

Evelyn ThomasBennett College

AN14 Abstracts 69

evelyn.k.thomas@gmail.com

MS50

Krylov Subspace Methods for Solving Singular Lin-ear Systems or Least-Squares Problems

GMRES (Saad and Schultz 1986) is a famed generalizedminimal-residual method for solving nonsingular unsym-metric or non-Hermitian linear systems. It may suffernon-benign breakdown on nearly singular systems (Brownand Walker 1997). When working, the solver returns onlya least-squares solution for a singular problem (Reicheland Ye 2005). We present GMRES-QLP and GMRES-URV, both successful revamps of GMRES, for returningthe unique pseudoinverse solutions of (nearly) singular lin-ear systems or linear least-squares problems. On non-singular problems, they are numerically more stable thanGMRES. In any case, users do not need to know a pri-ori whether the systems are singular, ill-conditioned, orincompatible; the solvers constructively reveal such prop-erties. The solvers leverage the QLP and URV decom-positions (Stewart 1998 and 1999) to reveal the rank ofthe Hessenberg matrix from the Arnoldi process, incurringonly minor additional computational cost in comparison toGMRES. We present extensive numerical experiments todemonstrate the scalability and robustness of the solver,with or without preconditioners or restart.

Sou-Cheng T. ChoiUniversity of Chicago and Argonne National Laboratorysctchoi@uchicago.edu

MS50

Probabilistic Bounds for Randomized Precondi-tioner for a Krylov Least Squares Solver

The Blendenpik algorithm by Avron, Maymounkov andToledo solves least squares problems min ||Ax−b|| for m×nmatrices A with rank(A) = n, by computing a random-ized preconditioner and applying the Krylov method LSQRto the preconditioned matrix. The preconditioner is com-puted by randomly sampling rows from A. We presentprobabilistic bounds for the condition number of the pre-conditioned matrix, when rows are sampled with replace-ment, and the sampling probabilities are uniform or basedon leverage scores. Our bounds are derived from singularvalue bounds for a Monte Carlo matrix multiplication al-gorithm for computing the cross product AA′. For uniformsampling, the bounds imply that the number of sampledrows can be as much as 30 percent lower than existingbounds. For leverage-score based sampling, our boundsimply that the number of sampled rows must at least be amultiple of n ∗ ln(n). This is joint work with John Holod-nak.

Ilse IpsenNorth Carolina State UniversityDepartment of Mathematicsipsen@ncsu.edu

MS50

IDR-CGS-BiCGSTAB-IDR(s) - a Case ofSerendipity

In about 1976, the author was preparing a renovation ofan elementary course on numerical analysis in Delft Uni-versity. In relation to the problem of solving a single non-linear equation iteratively, he wondered whether the so-

called ‘secant method’ could be generalized to systems ofN nonlinear equations with N unknowns, just for show-ing the students that there is something behind the hori-zon. Before starting to read everything on the subject,the author always tries to think about it unbiased, andso he started with, probably, re-inventing the wheel. Hadhe seen the book by Ortega and Rheinboldt at that time,CGS, BiCGSTAB and IDR(s) probably wouldn’t exist to-day. Actually a new wheel was discovered, that appearedto be useful in the machinery of solving large sparse non-symmetric linear systems. The first application of the newwheel was called IDR − Induced Dimension Reduction.Afterwards, CGS − Conjugate Gradients Squared − wasdeveloped as an ‘improvement’ of IDR, and also for otherreasons. After CGS, in cooperation with Henk van derVorst, (Bi-)CGStab was constructed, followed by a lot ofother methods of this kind, developed by others. This wenton until about 10 years ago. In this short presentation areconstruction will be given of the strange history of theseso-called ‘Lanczos-type Product Methods’. It will be ex-plained why this ‘sleeping theory’ woke up just after theauthor’s retirement in 2006, resulting in a brand new familyof methods: IDR(s). History is a continuing story, there-fore some recently established features of IDR(s) will bementioned.

Peter SonneveldDelft Inst. of Appl. MathematicsDelft University of Technologyp.sonneveld@tudelft.nl

MS50

Multiple Preconditioners for GMRES

We propose a variant of GMRES which we call MPGM-RES, whereby multiple (two or more) preconditioners areapplied simultaneously, while maintaining minimal resid-ual optimality properties. To accomplish this, a block ver-sion of Flexible GMRES is used, but instead of consideringblocks starting with multiple right hand sides, we startwith the initial residual and grow the space by applyingeach of the preconditioners to all current search directionsand minimizing the residual norm over the resulting largersubspace. To alleviate the difficulty of rapidly increas-ing storage requirements and make the method practical,we further propose a selective algorithm that uses limitedmemory, and show theoretically and experimentally thatthis approach is highly effective. Convergence bounds for aspecial case are presented. Numerical results for problemsin domain decomposition, PDE-constrained optimization,and fluid flow problems are presented, illustrating the vi-ability and the potential of the proposed method. This isjoint work with Chen Greif and Tyrone Rees.

Daniel B. SzyldTemple UniversityDepartment of Mathematicsszyld@temple.edu

MS51

Title Not Available at Time of Publication

Abstract not available at time of publication.

Robert P. GilbertDepartment of Mathematical SciencesUniversity of Delaware

70 AN14 Abstracts

gilbert@math.udel.edu

MS51

Analysis of the Volume-Constrained PeridynamicNavier Equation of Linear Elasticity

Well-posedness results for the state-based peridynamicnonlocal continuum model of solid mechanics are estab-lished with the help of a nonlocal vector calculus. Theperidynamic strain energy density for an elastic constitu-tively linear anisotropic heterogeneous solid is expressed interms of the field operators of that calculus, after whicha variational principle for the equilibrium state is defined.The peridynamic Navier equilibrium equation is then de-rived as the first-order necessary conditions and are shownto reduce, for the case of homogeneous materials, to theclassical Navier equation as the extent of nonlocal inter-actions vanishes. Using standard results, well-posedness isalso established for the time-dependent peridynamic equa-tion of motion.

Richard B. LehoucqSandia National Laboratoriesrblehou@sandia.gov

MS51

Is Dynamic Fracture at the Macroscale a Distin-guished Limit of Unstable Nonlocal Bond Models?

We investigate a new class of models for solving problemsof free crack propagation described by the peridynamic for-mulation. In the peridynamic formulation material pointsinteract through short-range forces acting over a prescribedhorizon. The formulation allows for discontinuous defor-mations and free propagation of cracks. We upscale theperidynamic model, passing to a small horizon limit, tofind that the macroscopic evolution corresponds to the si-multaneous evolution of the fracture surface and the linearelastic displacement away from the crack set. This providesa new connection between the dynamics of nonlocal short-range forces acting at the microscale to a brittle fractureevolution at the macroscale.

Robert P. LiptonDepartment of MathematicsLouisiana State Universitylipton@math.lsu.edu

MS51

Peridynamics as a Multiscale Method

Abstract not available at time of publication.

Stewart SillingSandia National Laboratoriessasilli@sandia.gov

MS52

Rigorous Computations for Nonlinear PDEs: AnIntroduction

Abstract not available at time of publication.

Jean-Philippe LessardUniversite Laval

jean-philippe.lessard@mat.ulaval.ca

MS52

Computer-Assisted Existence and MultiplicityProofs for Semilinear Elliptic Boundary ValueProblems

Abstract not available at time of publication.

Michael PlumKarlsruhe University (KIT)Germanymichael.plum@kit.edu

MS52

Rigorous Computation of Connecting Orbits

Abstract not available at time of publication.

Jan Bouwe Van Den BergVU University AmsterdamDepartment of Mathematicsjanbouwe@few.vu.nl

MS52

Rigourous Computation of a Bifurcation Diagramfor the Ohta-Kawasaki Model

The Ohta-Kawasaki, or non-local Cahn-Hilliard, model is asimple description of energy-driven pattern formation withcompeting short- and long-range effects. One of the funda-mental problems in this area is to identify which patternshave lowest energy in which regions of parameter space.We address this problem by finding the curves along whichdifferent solutions have the same energy. We use methodsfrom rigourous computing to prove the existence of suchcurves and to get bounds between our discrete numericalapproximations and the true infinite-dimensional solutions.Results from both two and three dimensions will be pre-sented and discussed. This is joint work with JB van denBerg.

J.F. WilliamsSimon Fraser UniversityDept. of Mathematicsjfw@math.sfu.ca

MS54

The Exponential Formula for The WassersteinMetric

Many evolutionary partial differential equations may berewritten as the gradient flow of an energy functional, aperspective which can provide useful estimates concerningthe behavior of solutions. The notion of gradient flow re-quires both the specification of an energy functional anda metric with respect to which the gradient is taken. Inparticular, much recent work has considered gradient flowin the Wasserstein metric. Given the formal nature of thegradient in this setting, a useful technique for constructingsolutions to the gradient flow and studying their stability isto consider the ”discrete gradient flow”, a time discretiza-tion of the gradient flow problem analogous to the implicitEuler method in Euclidean space. In this talk, I will presenta new proof that the discrete gradient flow converges tothe continuous time gradient flow inspired by Crandall andLiggett’s result in the Banach space case. Along the way,

AN14 Abstracts 71

I will discuss theorems of independent interest concerningtransport metrics.

Katy CraigRutgers Universitykatycrow@mac.com

MS54

A Finite-Volume Method for Nonlinear NonlocalEquations with a Gradient Flow Structure

We consider a finite volume method for the general equa-tion

ρt = ∇ ·[ρ∇

(H ′(ρ) + V (x) +W ∗ ρ

)], x ∈ Rd

with the density of internal energy H(ρ), the confinementpotential V (x) and the interactional potentail W (x). Alarge variety of equations arises from physical or biologicalmodels can be written in this general form, and many im-portant theoretical advances like optimal transportationsare developed in certain special cases. The finite methodis carefully designed to preserve the non-negativity of thesolutions, and the total energy

E(ρ) =

∫Rd

H(ρ) dx+

∫Rd

V (x)ρ(x)dx+1

2

∫Rd

∫Rd

W (x−y)ρ(x)ρ(y)dx dy

is shown to be non-increasing in the semi-discrete form.We demostrate the effectiveness of this method with manyexamples, and show that it can be used to perform a nu-merical study of other unknown equations of similar types.

Yanghong HuangImperial College Londonyanghong.huang@imperial.ac.uk

Jose CarrilloDepartment of MathematicsImperial College Londoncarrillo@imperial.ac.uk

Alina ChertockNorth Carolina State UniversityDepartment of Mathematicschertock@math.ncsu.edu

MS54

Numerical Methods for the Fractional Laplacian

The fractional Laplacian is the seminal example of a nonlo-cal diffusion operator. Nonlocal diffusions are increasinglypopular, and the fractional Laplacian is the prototypicalmodel. Recent work by analysts including Caffarelli andSilvestre, among others, has studies nonlinear equationsinvolving this operator, starting with the obstacle prob-lem. But it solving even the one dimensional linear Frac-tional Laplacian equation on a bounded domain is a chal-lenge which has not yet been addressed. It might appearthat it should be quite simple to build schemes for thefractional Laplacian. For example the work of Valdinocisuggests that convolution kernels with the right decay willconverge. The difficulty turns out to be accuracy: build-ing even a first order accurate discretization is a challenge.The operator can be defined (and, in simple situations,approximated) using its Fourier symbol, which is multipli-cation by a power. However, when bounded domains areinvolved, the Fourier method is not as practical. The op-erator can also be represented as a singular integral: our

method comes from a careful discretization of the singularintegral. We apply rigorous numerical analysis methodol-ogy to the study of the fractional Laplacian. We derivea finite difference/quadrature method, and establish accu-racy, a proof of convergence, careful truncation of the oper-ator outside the computational domain, and numerical val-idation against exact solutions. Our method is comparedfavorably against existing methods, which do not have arigorous foundation. We also apply the method to solvethe obstacle problem.

Adam M. ObermanMcGill U.adam.oberman@mcgill.ca

Yanghong HuangImperial College Londonyanghong.huang@imperial.ac.uk

MS54

Error Estimates for Approximations to Fully Non-linear PDE

We discuss error estimates for finite difference approxima-tions to nonlinear elliptic and parabolic PDE. In particular,we highlight the relationship between error estimates andthe regularity of solutions of the original equation. Wepresent some recent progress and applications.

Olga TuranovaDepartment of MathematicsUniversity of Chicagoturanova@math.uchicago.edu

MS55

Active Nano-Rod Dispersions

Within the large space of fluids that behave nonlinearly, weconsider a niche fluid system between liquid crystals andactive micro scale swimmers: active nano scale rod disper-sions. We first highlight physical and biological systemsthat motivate our modeling, analysis, and simulations, andthen take liberty to explore the models for rich phenomenathat are reminiscent of behavior in either liquid crystals orbacterial suspensions.

M. Gregory ForestUniversity of North Carolina at Chapel HillDept of Math & Biomedical Engr.forest@unc.edu

Qi WangUniversity of South Carolinaqwang@math.sc.edu

Ruhai ZhouOld Dominion Universityrzhou@math.odu.edu

MS55

Physiological Boundary Conditions for Hemody-namics

A common goal in computational hemodynamics is the pre-diction of local blood flow downstream from stem arteriesin which measurements are available. Due to computa-tional complexity and uncertainties about the geometryand topology of the vasculature, such calculations are typ-

72 AN14 Abstracts

ically performed in a relatively small number of contigu-ous vessels. At the downstream edge of the computationaldomain, outflow boundary conditions have to be imposed.Choices of parameter values and type of conditions stronglyimpact the results, putting in question the significance ofthe entire modeling endeavor. We will discuss a new typeof outflow boundary conditions allowing for a reduced re-liance on calibration which is a major obstacle toward reli-able patient specific simulations. Our approach allows thecomputation of the impedance of tiered structured vascu-lar trees. It extends previous work from periodic to generictransient flows and relies on Laplace transforms and con-volution quadratures. Joint work with Will Cousins (MIT)and Daniel Tartakovsky (UCSD)

Pierre GremaudDepartment of Mathematics and Center for Research inScientific Computing, North Carolina State Universitygremaud@ncsu.edu

MS55

Two-Fluid Flow in a Capillary Tube

A phase field model for two-phase flow in a capillary tube,developed by Cueto-Felgueroso and Juanes, results in aPDE with higher-order terms. We find traveling wave so-lutions of the PDE and determine a bound on parametersto obtain physically relevant solutions. We observe that thetraveling wave height decreases monotonically with capil-lary number. Finite difference simulations of the injectionof a gas finger into water show a traveling wave advanc-ing ahead of a rarefaction, leaving a plateau region of fluidadjacent to the tube wall. The residual thickness of thisregion was measured in experiments by G.I. Taylor in hisfamous 1961 paper. We find agreement between the trav-eling wave heights and the plateaus seen in the PDE sim-ulations, and the results also compare favorably with theresidual fluid thickness observed in the experiments. Thisis joint work with Rachel Levy, Ruben Juanes, and LuisCueto-Felgueroso.

Michael ShearerMathematicsNC State Universityshearer@ncsu.edu

Melissa StraitNC State Universitymestrait@ncsu.edu

MS55

A Saddle-Point Formulation And Finite ElementMethod For The Stefan Problem With Surface Ten-sion

A dual formulation is proposed for the Stefan problem withsurface tension (Gibbs-Thomson law). The method uses amixed form of the heat equation in the solid and liquiddomains, and imposes the interface motion law (on thesolid-liquid interface) as a constraint. Well-posedness ofthe time semi-discrete and fully discrete (finite element)formulations is proved in 3-D, as well as an a priori bound,conservation law, and error estimates. Simulations are pre-sented in 2-D.

Christopher B. DavisLouisiana State UnivesityDepartment of Mathematicscdav135@lsu.edu

Shawn W. WalkerLouisiana State UniversityDepartment of Mathematics and CCTwalker@math.lsu.edu

MS56

Mechanics and Evolution in Bacterial Biofilms

Bacteria frequently occupy densely populated surface-bound communities, termed biofilms. Biofilms behave likeviscoelastic fluids at the macroscopic level. It is largely un-known how bacteria organize their behavior inside biofilms,and how biofilms behave in natural environments. In thistalk, I will focus on how biofilms solve a classical evolution-ary theory problem, the public goods dilemma, and howfluid physics shapes the dynamics of biofilms in complexenvironments.

Knut Drescher, Howard StonePrinceton Universityknutd@princeton.edu, hastone@princeton.edu

MS56

Hydrodynamics Affects Ordering and Organizationin Bacterial Suspensions

We explore the nature and causes of the spontaneous or-dering and organization that emerges in bacterial suspen-sions under confinement. Using simulations that captureoriented cell-cell and cell-fluid interactions, we show thathydrodynamics is crucial in reproducing and explaining thephenomena observed in recent experiments using bacteriaB. Subtilis. We give new insights into the microscopic ar-rangement of the bacteria, which are confirmed by newexperiments.

Enkeleida LushiImperial College Londonand Courant Institute NYUenkeleida lushi@brown.edu

MS56

Active Suspensions in Confinement

Active particle suspensions, of which a bath of swimmingbacteria is a paradigmatic example, are characterized bycomplex dynamics involving strong fluctuations and large-scale correlated motions. These motions, which result fromthe many-body interactions between particles, are biologi-cally relevant as they impact mean particle transport, mix-ing and diffusion, with possible consequences for nutrientuptake and the spreading of bacterial infections. In thiswork, we use a combination of kinetic theory and numer-ical simulations to analyze these effects, with particularfocus on confined suspensions. I will specifically discussthe transport and effective rheology of dilute to semi-dilutesuspensions in pressure-driven channel flows, as well as thepattern formation and complex dynamics arising in activesuspensions confined in a Hele-Shaw geometry.

David SaintillanDepartment of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaigndstn@illinois.edu

Barath EzhilanUniversity of Illinois at Urbana-ChampaignDepartment of Mechanical Science and Engineering

AN14 Abstracts 73

ezhilan2@illinois.edu

MS56

Effects of Micro-swimmer Locomotion in Peri-staltic Pumping

Peristaltic pumping is a form of fluid transport along thelength of a tube containing liquid when the tube undergoesa contraction wave. While much is known about the peri-stalsis of Newtonian liquids, complex ones have receivedlimited attention. If the fluid inside such a peristalticmicro-pump contains motile micro-particles (such as bac-teria), then the net transport and mixing are affected bythe micro-swimmer collective motion. We present a newnumerical method that couples the motion of many micro-swimmers, the pump and the fluid flow. We show that thetype of swimmer affects not only the net transport but canbe utilised for mixing passive material.

Adam StinchcombeUniversity of Michiganstinch@umich.edu

Enkeleida LushiImperial College Londonand Courant Institute NYUenkeleida lushi@brown.edu

Charles S. PeskinCourant Institute of Mathematical SciencesNew York Universitypeskin@cims.nyu.edu

MS57

Social Aggregation in Pea Aphids: ExperimentalMeasurement and Random Walk Modeling

Biological aggregations are found across the natural world.An ongoing challenge in the mathematical modeling of ag-gregations is to strengthen the connection between mod-els and biological data by quantifying the rules that in-dividuals follow. We model aggregation of the pea aphid,Acyrthosiphon pisum. Specifically, we conduct experimentsto track the motion of aphids walking in a featureless cir-cular arena in order to deduce individual-level rules. Weobserve that aphids follow a correlated random walk whoseparameters depend strongly on distance to an aphid’s near-est neighbor. We propose a random walk model anddemonstrate that it reproduces the salient features of theobserved macroscopic patterns of movement.

Chad M. TopazMacalester Collegectopaz@macalester.edu

Andrew J. BernoffHarvey Mudd CollegeDepartment of Mathematicsajb@hmc.edu

MS57

Trajectory Dynamics of Aquatic KleptoparasiticInteractions

Predation is among the most common pressures leadingto group formation in animals. Although predator-preysystems have been studied extensively at the populationlevel, relatively little work has been done to specify the

individual behavioral decisions in such interactions. Here,we study a rather unique instance of kleptoparasitic inter-actions, whereby seagulls attempt to ’rob’ flocks of aquaticseaducks of their food obtained from underwater dives. Byreconstructing individual trajectories of both kleptopara-site and prey, we analyze the evasion behavior of the sead-ucks.

Ryan LukemanDepartment of Mathematics, Statistics and ComputerScienceSt. Francis Xavier Universityrlukeman@stfx.ca

MS57

Collective Dynamics in Laboratory Insect Swarms

Aggregations of social animals, think bird flocks or swarmsof insects, are beautiful, natural examples of self-organizedbehavior far from equilibrium. Many models have beenproposed to describe these systems, including agent-basedmodels that specify social forces between individuals. Wediscuss measurements of laboratory midge swarms in thecontext of model assessment. In particular, we focus onthe question of the small-number limit: how large mustthe population be before collective properties emerge?

James PuckettSchool of Engineering and Applied ScienceYale Universityjames.puckett@yale.edu

MS57

Oscillatory Patch Formations from Social Foraging

Dynamics of resource patches and foragers have beenshown to exhibit pattern formations. Simple taxis of for-agers towards randomly moving prey cannot lead to spon-taneous formation of patchy environments. However, socialinteractions among foragers, specifically taxis in producer-scrounger group, can create novel spatiotemporal oscilla-tory patterns. I will also briefly discuss which of these be-havior is more beneficial and how switching between strate-gies affect the resulting spatiotemporal patterns.

Nessy TaniaSmith CollegeMathematics and Statistics Departmentntania@smith.edu

MS58

Elastic Swimmer in Viscous Fluid: How to SwimEfficiently?

We use fully-coupled computer simulations to examine thelow Re hydrodynamics of a self-propelling elastic swimmer.The swimmer is modelled as a thin elastic plate plungingat the root. The swimmer is free to move in the forwarddirection. We probe how swimming speed and efficiencydepend on swimmer parameters. Our simulations revealthat the efficiency is maximized when the swimmer centerof mass displacement is minimized. This regime reducesviscous losses, thereby enhancing the swimming efficiency.

Alexander Alexeev, Peter Derek YehGeorge W. Woodruff School of Mechanical EngineeringGeorgia Institute of Technology

74 AN14 Abstracts

alexander.alexeev@me.gatech.edu, pyeh3@gatech.edu

MS58

Mathematical Models for Microstructured OpticalFibre (MOF) Fabrication

We address various challenges arising in the fabricationof so-called microstructured optical fibres (MOFs) whichguide light by virtue of a specially designed geometricalarrangement of channels running along their length. Thefabrication involves placing a material (such as glass), heat-ing it in a draw tower, and pulling it into a fibre so that thematerial is essentially a highly viscous (Stokes) fluid underan axial strain. The simultaneous effects of surface ten-sion on the fibre/channel boundaries and the axial strainlead to deformations in the global fibre geometry that mustbe understood in order to arrive at the desired fibre state.This talk will describe recent progress in the mathemati-cal modelling of this process [joint with P. Buchak and Y.Stokes].

Darren G. CrowdyImperial College Londond.crowdy@imperial.ac.uk

MS58

Accelerated Boundary Integral Simulations for In-teractions of Drops and Solids in Micro-Fluidics

In micro-fluidic applications where the scales are small andviscous effects dominant, the Stokes equations are often ap-plicable. Simulation methods can be developed based onboundary integral equations, which leads to discretizationsof the boundaries of the domain only, reducing the numberof unknowns. Two main challenges associated with bound-ary integral methods are to construct accurate quadraturemethods for singular and nearly singular integrands, as wellas to accelerate the solution of the dense linear systemsthat arise. For drops and solids in 2D, including also ob-jects with sharp corners, we will discuss how to apply ageneral special quadrature approach to achieve highly ac-curate simulations also for very complicated settings. Thesimulations are accelerated with either the Fast Multipolemethod or a spectrally accurate FFT based Ewald method(for periodic problems). Simulation results for very chal-lenging problems are presented.

Anna-Karin TornbergKTHakto@kth.se

MS58

Self-Propulsion of An Inextensible Elastic Mem-brane in An Electric Field

In this work we illustrate a novel mechanism for self-propulsion of an inextensible elastic (lipid-bilayer) mem-brane subject to an electric field. In the lubrication frame-work, the dynamics of an inextensible elastic membraneis governed by a sixth order nonlinear partial differentialequation with an integral constraint. Through numericalsimulations we find (1) sloshing motion of the membrane,and (2) unit directional movement of the membrane, bothin the direction transverse to the imposed electric field. Wewill also demonstrate how such movements of an elasticmembrane can be further controlled by pattern electrodesand/or varying the temporal dependence of the externalelectric field. This work is a collaboration with Petia Vla-

hovska (Brown University). Y.-N. Young is partially sup-ported by NSF grants DMS 1222550.

Yuan-Nan YoungDepartment of Mathematical SciencesNJITyyoung@oak.njit.edu

Petia VlahovskaBrown Universitypetia vlahovska@brown.edu

MS59

Role of Network Topology in the ElectromechanicalDynamics of Cascading Power Grid Failure

Recent work in analysis of cascading failure of electricpower networks has sought to augment the quasi-steadystate representations of prior literature with faster timescale electromechanical dynamics, and with threshold-driven relay action that disconnects network links uponoverload. In these dynamic models, cascading failure ap-pears as a sequence of transitions between locally stableequilibria, each corresponding to a partially degraded net-work structure, and with the most vulnerable paths oftransition passing through saddle point unstable equilib-ria. This work will explore the role of network topologyin predicting the location of these saddle exits in the statespace, and the interplay of topology and relay thresholdvalues in determining the disturbance energy that must beinjected into the system to drive the state over such a sad-dle point.

Christopher DeMarcoUniversity fo Wisconsindemarco@engr.wisc.edu

Honghao ZhengUniversity of Wisconsin-Madisonhustfreedom.zheng@gmail.com

MS59

Centrality of Dynamical Graph Structures

We consider adapting well known graph centrality mea-sures to the case of dynamic graphs or static graphs withdynamic forcing functions. For instance, we present thePageRank method on a static graph with time-varying tele-portation and demonstrate a closed form analytical solu-tion that involves complex valued teleportation parame-ter. We consider how these could be deployed for studyingpower systems and contingency analysis.

David F. GleichPurdue Universitydgleich@purdue.edu

MS59

Stochastic Graph Modeling of Power Grids

Graph-theoretic approaches have long been used for char-acterizing the topological structure of power grids. Thecentral idea of such approaches is to use known algorithmsfor generating random graphs and then using graph-basedmetrics to match the characteristics with those from real-world power grid models, such as the Western and East-ern Interconnects. In our work, we are exploring severalvariants of the random geometric graph algorithm for the

AN14 Abstracts 75

purposes of generating synthetic models of the power grid.By exploiting the inherent hierarchical structure in voltagelevels, we show that random geometric graph models canbe used to generating synthetic power grids.

Mahantesh HalappanavarPacific Northwest National Laboratoryhala@pnnl.gov

Eduardo Cotilla-SanchezOregon State Universityecs@eecs.osu.edu

Emilie HoganPacific Nortwest National Labemilie.hogan@pnnl.gov

Paul HinesUniversity of Vermontpaul.hines@uvm.edu

MS59

Algorithms for Monitoring Oscillations in thePower Grid

Monitoring the oscillations in the power grid in real-timeis an increasingly difficult challenge due to the large num-ber of components. Additionally, large numbers of PhasorMeasurement Units (PMUs) are being deployed to gener-ate large-scale data on the state of the grid. Algorithms forcomputing a few singular values and vectors and updatingthese are critical components to monitor the oscillations.We describe efficient algorithms to compute and updatethe singular value decompositions in this context.

Alex PothenPurdue UniversityDepartment of Computer Scienceapothen@purdue.edu

Mani Venkatasubramanian, Tianying WuWashington State Universitymani@eecs.wsu.edu, tianying.wu@email.wsu.edu

Ananth KalyanaramanAssociate ProfessorSchool of EECS, Washington State Universityananth@eecs.wsu.edu

MS60

RBF-FD for Mesoscale Nonhydrostatic Atmo-spheric Modeling

In applications of radial basis functions (RBFs) for fluidmodeling, infinitely smooth RBFs have traditionally beenused due to the spectral convergence properties. However,fluid flows in nature can exhibit complex features such thatspectral accuracy cannot be realized on resolutions thatare observable or practical. A novel approach for model-ing with RBF-generated finite differences (RBF-FD) is pre-sented by using polyharmonic spline RBFs together withhigh-order polynomials. The approach is tested on nonhy-drostatic atmospheric flows.

Natasha FlyerNational Center for Atmospheric ResearchInstitute for Mathematics Applied to Geosciences

flyer@ucar.edu

MS60

RBF-FD for Elastic Wave Propagation in LayeredMedia

Seismic exploration is used to map out hydrocarbon de-posits. In forward modeling, substructures are assumed tobe known, and the task is to simulate elastic wave propaga-tion through the medium. Inversion programs then updatesubstructure assumptions to reconcile the model responsewith actual measurements. We have found that RBF-FDspatial discretization offers outstanding accuracy and al-gebraic simplicity for modeling elastic wave propagation,especially in layered media with large numbers of irregu-larly curved interfaces.

Bengt FornbergUniversity of ColoradoBoulderfornberg@colorado.edu

MS60

Application of the RBF-FD Method to LaminarFlame Propagation Problems

Premixed flame propagation is an important topic in com-bustion research with many applications in energy andsafety. In this paper we apply the RBF Finite differ-ence (RBF-FD) method to solve the equations describinglaminar fame propagation in two-dimensional and three-dimensional ducts. We use stencils with a relatively largenumber of nodes in order to achieve high order accuracy.Finally, we apply this methodology to solve a simplifiedmathematical model describing flame propagation in a ro-tary engine microcombustor.

Manuel KindelanUniversidad Carlos III de Madridkinde@ing.uc3m.es

MS60

Modeling Ocean Dynamics Using RBF-FD

RBFs have started to emerge as a powerful tool, not onlyfor interpolation, but also for discretizing differential oper-ators. Over the last few years, new approaches have beendeveloped to bypass the method’s well-known problems ofstability and of large computational complexity. Such anew approach resulted in the RBF-FD method which en-joys high accuracy, has an intrinsic ability to representcomplicated geometries in any dimension, still has a re-markable algorithmic simplicity, and leads to a sparse dif-ferentiation matrix. We will use this technique to solvethe Navier-Stokes equations and discuss its potential as ahigh-order method for the modeling of oceanic phenomena.

Cecile M. PiretUniversite catholique de Louvaincecile.piret@uclouvain.be

MS61

Electromagnetic Wave Propagation in RandomWaveguides

I will describe an analysis of electromagnetic wave propaga-tion in waveguides filled with heterogeneous media, mod-

76 AN14 Abstracts

eled by a random electric permeability. The waves aretrapped by perfectly conducting boundaries and the goal ofthe analysis is to quantify the long range net scattering ef-fects of the random medium. The result is a detailed char-acterization of the transport of energy, the loss of coher-ence and the depolarization of the waves due to scattering.I will give some numerical illustrations and will comparethe theory with that of scalar (acoustic) wave propagationin random waveguides.

Liliana BorceaUniversity of Michiganborcea@umich.edu

MS61

Homogenization of Interfaces Moving with Spatio-temporal Periodic Velocity

Abstract not available at time of publication.

Wenjia Jing, Panagiotis Souganidis, Hung V. TranUniversity of Chicagowjing@math.uchicago.edu, sougani-dis@math.uchicago.edu, hung@math.uchicago.edu

MS61

Imaging Multiply Scattering Point Targets UsingSparsity Promoting Optimization

We study active array imaging of small but strong scat-terers in homogeneous media when multiple scattering be-tween them is important. We discuss a non-iterative ap-proach that solves the imaging problem in two steps usingsparsity promoting optimization. We analize the unique-ness and stability of this imaging method using both singleand multiple illuminations. To improve its robustness andthe resolution of the images we also discuss the use of opti-mal illuminations. This is join work with Anwei Chai andGeorge Papanicolaou.

Miguel MoscosoUniversidad Carlos III de Madridmoscoso@math.uc3m.es

MS61

Correlation Based Imaging and Applications

Abstract not available at time of publication.

George C. PapanicolaouStanford UniversityDepartment of Mathematicspapanico@math.stanford.edu

MS62

Numerical Assessment of the Risk of Rock Damagein the Vicinity of Salt Caverns for the Storage ofGaseous Matter at Cyclic Operation Conditions

Abstract not available at time of publication.

Norbert BottcherHelmholtz-Centre for Environmental Research - UFZnorbert.boettcher@ufz.de

MS62

Numerical Simulation of Deformation and Flow in

Fractured, Poroelastic Materials

We introduce a coupled system of PDEs for the modelingof the fluid-fluid and fluid-solid interaction in a fractured,poroelastic material. The fluid flow in the fracture is mod-eled by a lower-dimensional equation, which interacts withthe surrounding rock matrix and the fluid it contains. Todetermine the mechanical and hydrological equilibrium ofthe system numerically, we combine an XFEM discretiza-tion for the rock matrix deformation and pore pressure witha lower-dimensional grid for the fracture. The resultingcoupled discrete problem is solved using a substructuringmethod.

Katja HanowskiIGPMRWTH Aachen Universityhanowski@igpm.rwth-aachen.de

Oliver SanderIGPM RWTH Aachen Universitysander@igpm.rwth-aachen.de

MS62

Fracture Propagation in Porous Media Using Iso-geometric Analysis

Abstract not available at time of publication.

Trond KvamsdalDepartment of Applied MathematicsSINTEF ICT, Trondheim, Norwaytrond.kvamsdal@sintef.no

MS62

Coupling Fluid Flow with Stresses Induced byFracture Deformation in Discrete Fracture Net-works

Fluid flow in fractures can cause deformation, but in-duced stresses can be challenging to implement in nu-merical models, especially in large DFNs. I will describeCFRAC, a simulator I developed that implicitly couplesfluid flow, fracture deformation, transmissivity evolution,friction evolution, and fracture propagation, and is efficientenough to simulate (2D) networks with thousands of frac-tures. I will describe model behaviors that emerge frominteractions between processes and which give insight intocomplex physical systems.

Mark McClureThe University of Texas at AustinPetroleum & Geosystems Engineeringmcclure@austin.utexas.edu

MS63

Learning the Association of Multiple Inputs in Re-current Networks

In spite of the many discoveries made in neuroscience,the mechanism by which memories are formed is still un-clear. To better understand how some disorders of thebrain arise, it is necessary to improve our knowledge ofmemory formation in the brain. With the aid of a biolog-ical experiment, an artificial neural network is developedto provide insight into how information is stored and re-called. In particular, the bi- conditional association of dis-tinct spatial and non-spatial information is examined using

AN14 Abstracts 77

computational model. This model is based on a combina-tion of feedforward and recurrent neural networks and abiologically-inspired spike time dependent plasticity learn-ing rule. The ability of the computational model to storeand recall the bi-conditional object-space association taskthrough reward-modulated plastic synapses is numericallyinvestigated.

Jeannine Abiva, Rodica CurtuUniversity of IowaDepartment of Mathematicsjeannine.abiva@gmail.com, rodica-curtu@uiowa.edu

MS63

Mechanistic Models of Retinitis Pigmentosa

In this talk we will give a brief overview of our work as itpertains to Retinitis Pigmentosa (RP). With mathematicsand computer (in silico) experiments, we explore the exper-imentally observed photoreceptor death and rescue in theprogression of RP. Using mechanistic mathematical mod-els of photoreceptor interactions in the presence of RP we(1) trace the evolution of RP from one stage to anotherin each main subtype, (2) capture the rod and cone wavedeaths, and (3) explore various treatment regiments viaRdCVF. Our work highlights the delicate balance betweenthe availability of nutrients and the rates of shedding andrenewal of photoreceptors needed for a normal functioningretina and to halt the progression of RP. This work pro-vides a framework for future physiological investigationspotentially leading to long-term targeted multi-faceted in-terventions and therapies dependent on the particular stageand subtype of RP under consideration.

Erika T. CamachoArizona State UniversityDivision of Mathematics and Natural Scienceserika.camacho@asu.edu

Stephen WirkusArizona State UniversitySchool of Mathematical and Natural SciencesStephen.Wirkus@asu.edu

MS63

Dynamics and Control of An Invasive Species: TheCase of the Rasberry Crazy Ant Colonies

This project is motivated by the costs related with the doc-umented risks of the introduction of non-native invasivespecies of plants, animals, or pathogens associated withtravel and international trade. Such invasive species of-ten have no natural enemies in their new regions. Thespatiotemporal dynamics related to the invasion/spread ofNylanderia fulva, commonly known as the Rasberry crazyant, are explored via the use of models that focus on thereproduction of ant colonies. A Cellular Automaton (CA)simulates the spatially explicit spread of ants on a grid.The impact of local spatial correlations on the dynamics ofinvasion is investigated numerically and analytically withthe aid of a Mean Field (MF) model and a Pair Approx-imation (PA) model, the latter of which accounts for ad-jacent cell level eects. The PA model approach considersthe limited mobility range of N. fulva, that is, the grid celldynamics are not strongly inuenced by non-adjacent cells.The model determines the rate of growth of colonies of N.fulva under distinct cell spatial architecture. Numerical re-sults and qualitative conclusions on the spread and control

of this invasive ant species are discussed.

Luis MelaraShippensburg Universitylamelara@ship.edu

Victor VidalSUNY Stony Brookna

Valerie CheathonASU Westna

Agustin FloresNoertheastern Illinois Universityna

Octavius TalbotMorehouse Collegena

Adrian SmithUniversity of Arizonatba@siam.org

Marta SarzynskaUniversity of Oxfordmarta.sarzynska@sjc.ox.ac.uk

Dustin PadillaASU Tempena

MS63

Qualitative Inverse Problems Using BifurcationAnalysis in the Recurrent Neural Network Model

We develop a framework for determining when there isbistability and multistability in the expression states ofsystems described by the recurrent neural network (RNN)model. Our results show that, although bistability can begenerated with autoregulation, it is also the case that bothautorepression or no autoregulation can yield bistability aslong as a sigmoidal behavior is present. Additionally, ourresults suggest that allowing only a single connection wheninferring a network may be a reason why parameter valuesin the inferred gene networks in the literature are not berealistic.

Stephen WirkusArizona State UniversitySchool of Mathematical and Natural SciencesStephen.Wirkus@asu.edu

Erika T. CamachoArizona State UniversityDivision of Mathematics and Natural Scienceserika.camacho@asu.edu

Pamela MarshallArizona State Universitypamela.marshall@asu.edu

MS64

Organism - Effects of Nonlinearities on Lamprey

78 AN14 Abstracts

Locomotion

The lamprey is a basal vertebrate and a model organismfor neurophysiology and locomotion studies. Here a 2D,integrative, multi-scale model of the lamprey’s anguilli-form (eel-like) swimming is driven by neural activation andmuscle kinematics coupled to body interactions with fluidsurroundings. The fluid-structure interaction problem issolved numerically using an adaptive version of the im-mersed boundary method (IBAMR). Effects on swimmingspeed and cost by nonlinear dependencies associated withmuscle force development are examined.

Christina HamletTulane UniversityNew Orleans LAchamlet@tulane.edu

Eric TytellTufts UniversityDepartment of Biologyeric.tytell@tufts.edu

Lisa J. FauciTulane UniversityDepartment of Mathematicsfauci@tulane.edu

MS64

The Breadth of Mathematical Modelling of Biolog-ical Systems: History and Opportunities

An overview of a number of established areas in mathe-matical biology, as well as more recent opportunities thathave emerged, will be presented as an introduction to thissession. In particular, the importance that nonlinearitiesoften pose, both in terms of reflecting realistic biologicaldynamics and the mathematical challenges that arise in an-alyzing the resulting models, will be emphasized. Recentillustrations of integrative research in this area in whichthe mathematical sciences guide biological studies and ex-perimental work and field data inform the modeling will bediscussed.

Mary Ann HornVanderbilt University & National Science Foundationmary.ann.horn@vanderbilt.edu

MS64

CellularNonlinear Models for Predicting ImmuneResponse Mechanisms

Johne’s disease, a persistent and slow progressing infectionin ruminants such as cows and sheep is caused by Mycobac-terium avium subspecies paratuberculosis (MAP) bacillus.Mycobacterial infections are associated with complex im-mune response mechanisms whose underlying biology is notclearly understood. Host immune response to MAP infec-tion is associated with predominance of a cell mediatedresponse in its early stages and a switch to the dominanceof antibody response with concomitant disease progression.How the switch in immune response predominance occurs isnot clearly known. In this study, we developed series non-linear models to predict the underlying immune responsemechanisms associated with MAP-bacteria shed in cattlefeces. Immune response mechanisms are identified by fit-ting these models to immune response data and longitudi-nal fecal shedding patterns of experimentally infected cat-tle. Using statistical model selection methods, we were able

to discriminate potential animal immune response mecha-nisms that can explain the variant shedding patterns foreach infected animal. Our results suggest that there arespecific variant immune response mechanisms that couldbe silent in other animals, however, these could be activein other animals, hence varying MAP shedding patternsand disease progression trends.

Gesham MagombedzeNIMBioSUniversity of Tennessee, Knoxvillegmagombedze@nimbios.org

MS64

Variability in Species Abundance Distributionsfrom Nonlinear Stochastic Competition Models

Species abundance distributions (SADs) are metrics forecological communities, or sets of similar species in anecosystem. Using a nonlinear stochastic competitionmodel, I will show that SADs of communities with neu-tral dynamics (demographic stochasticity and immigra-tion) differ from those of communities with niches (clustersof similar species) arising under trait-based competition,and quantify the likelihood of being able to use this metricto distinguish between these two community types basedon abundance data alone.

Rosalyn Rael, Rafael D’Andrea, Gyorgy Barabas,Annette OstlingDepartment of Ecology and Evolutionary BiologyUniversity of Michiganrosalyn.rael@gmail.com, rdandrea@umich.edu, dysor-dys@umich.edu, aostling@umich.edu

MS65

Block Preconditioners for Saddle-Point Linear Sys-tems

Symmetric indefinite 2×2 and 3×3 block matrices are fea-tured prominently in the solutions of constrained optimiza-tion problems and partial differential equations with con-straints. When the systems are large and sparse, moderniterative methods are often effective. For block-structuredmatrices it is often desirable to design block diagonal pre-conditioners. In this talk a few block preconditioning ap-proaches are discussed. We focus on the case of a maxi-mally rank deficient leading block, which gives rise to in-teresting algebraic properties that can be exploited in thedesign of preconditioners. The use of Schur complementsand null space matrices is illustrated.

Chen GreifDepartment of Computer ScienceThe University of British Columbiagreif@cs.ubc.ca

MS65

Krylov Subspace Methods for Large Scale MatrixEquations

Given the square large matrices A,B,D,E and the matrixC of conforming dimensions, we consider the numerical so-lution of the linear matrix equation AXE + DXB = Cin the unknown matrix X. These matrix equations arebecoming a reliable tool in the numerical treatment of ad-vanced mathematical models in engineering and scientificcomputing. Our aim is to provide an overview of the majoralgorithmic developments in projection methods based on

AN14 Abstracts 79

Krylov-type subspaces, that have taken place in the pastfew years.

Valeria SimonciniUniversita’ di Bolognavaleria.simoncini@unibo.it

MS65

Krylov Subspaces and Dense Eigenvalue Problems

When we think of Krylov subspace methods, we normallythink of large, sparse problems. It is not widely appreciatedthat Krylov subspace ideas are also applicable to denselinear algebra. In this talk, which is more pedagogy thanresearch, we show how thinking about Krylov subspacesleads to a powerful algorithm for solving dense eigenvalueproblems. Unfortunately the algorithm is not new; it wasinvented over 50 years ago by John Francis.

David S. WatkinsWashington State UniversityDepartment of Mathematicswatkins@math.wsu.edu

MS65

Computing Singular Values of Large Matrices withan Inverse Free Preconditioned Krylov SubspaceMethod

We present an efficient algorithm for computing a fewextreme (largest and smallest) singular values and corre-sponding singular vectors of a large sparse m × n matrixC. Our algorithm is based on reformulation of the singularvalue problem as an eigenvalue problem for CTC and, toaddress the clustering of singular values, we use an inverse-free preconditioned Krylov subspace method to accelerateconvergence. We consider preconditioning that is basedon robust incomplete factorizations and we discuss variousimplementation issues. Extensive numerical tests are pre-sented to demonstrate efficiency and robustness of the newalgorithm.

Qiao LiangUniversity of Kentuckyqiao.liang@uky.edu

Qiang YeDept of MathUniv of Kentuckyqye@ms.uky.edu

MS66

Closure-based Algorithms for Simulation ofMesoscale Evolution of Large ODE Systems

We study a problem of designing efficient methods basedon space-time averaging for simulation of mesoscale dy-namics of large particle systems. Averaging produces exactmesoscale partial differential equations but they cannot besimulated without solving the underlying microscale sys-tem. To simulate these mesoscale equations independently,we consider several closure methods including regularizeddeconvolution closure and kinetic closure. We investigatethe relationship between their accuracy and computationalcost.

Lyudmyla BarannykUniversity of IdahoDepartment of Mathematics

barannyk@uidaho.edu

MS66

Forward and Inverse Homogenization of Maxwell’sEquations in Time Domain

The talk discusses a time domain problem for Maxwell’sequations for a multiscale dispersive medium. Homoge-nization results in time-convolution equations with a mem-ory kernel. We relate this kernel to the spectral measureof the local problem and use it to derive information aboutthe microgeometry of the finely structured medium.

Elena CherkaevUniversity of UtahDepartment of Mathematicselena@math.utah.edu

Niklas WellanderSwedish Defence Research Agencyniklas.wellander@foi.se

Dali ZhangUniversity of CalgaryDepartment of Mathematicsdlzhang@math.ucalgary.ca

MS66

On Reconstruction of Dynamic Permeability andTortuosity of Poroelastic Materials

Dynamic permeability refers to the permeability of poroe-lastic media subjecting to oscillatory pressure gradient. Itdepends on both the frequency and the pore space geom-etry. The dynamic tortuosity is inversely related to thedynamic permeability and plays an important role in themechanism of energy dissipation of waves through poroe-lastic materials. Numerically, dynamic tortuosity is thekernel in the memory term in the dissipation term for timedomain wave equations; it is known to be associated withfractional derivative of order 1/2. In this talk, we willpresent our results on reconstructing the dynamic perme-ability as a function of frequency from partial data by uti-lizing its analytical properties when extending to the com-plex frequency plane. Using the relation between tortuosityand permeability, a set of quadratures are constructed forhandling the memory term in the poroelastic wave equa-tions.

Miao-Jung Y. OuUniversity of Delaware, USADepartment of Mathematical Sciencesmou@math.udel.edu

MS66

Kinetic Equation for Spatial Averages of ParticleDynamics

Abstract not available at time of publication.

Alexander PanchenkoWashington State Universitypanchenko@math.wsu.edu

MS67

Symmetry and Bifurcations in First-order PDEswith Nonlocal Terms Modelling Animal Aggrega-

80 AN14 Abstracts

tion

Pattern formation in self-organised biological aggregationis a phenomenon that has been studied intensively over thepast twenty years. I will present a class of models of an-imal aggregation in the form of two first-order hyperbolicpartial differential equations on a one-dimensional domainwith periodic boundary conditions, describing the motionof left and right moving individuals. The nonlinear termsappear using nonlocal social interaction terms for attrac-tion, repulsion and alignment. This class of models hasbeen introduced in the Ph.D thesis of R. Eftimie. In thistalk, I will show that the equations are O(2) equivariantwhere the group O(2) is generated by space-translationsand a reflection which interchanges left-moving individualswith right-moving individuals across the middle of the in-terval. I will discuss steady-states and their symmetry witha focus on homogeneous O(2) symmetric states and theexistence of codimension two steady-state/steady-state,steady-state/Hopf and Hopf/Hopf bifurcation points. Iwill discuss how using existing symmetry-breaking bifur-cation theory and new theoretical results, one can studythe neighborhood of those bifurcation points and classifythe patterns obtained. This is joint work with R. Eftimie(U. Dundee, Scotland).

Pietro-Luciano BuonoUniversity of Ontario Institute of TechnologyOshawa, Ontario CanadaPietro-Luciano.Buono@uoit.ca

Raluca EftimieUniversity of Alberta, Edmonton, Canadareftimie@maths.dundee.ac.uk

MS67

Network Symmetry and Binocular Rivalry Exper-iments

Hugh Wilson has proposed a class of models that treathigher-level decision making as a competition between pat-terns coded as levels of a set of attributes in an appropri-ately defined network. In this talk, I will propose thatsymmetry-breaking Hopf bifurcation from fusion states insuitably modified Wilson networks can be used in an algo-rithmic way to explain the surprising percepts that havebeen observed in a number of binocular rivalry experi-ments.

Casey DiekmanDepartment of Mathematical SciencesNew Jersey Institute of Technologycasey.o.diekman@njit.edu

Martin GolubitskyOhio State UniversityMathematical Biosciences Institutemg@mbi.osu.edu

MS67

Spontaneous Symmetry-Breaking in Neural Mor-phology

A developing neuron initially extends several protrusionswhich are similar in length, but selects a single one whichelongates much longer than the others and becomes anaxon. This morphological symmetry breaking is impor-tant for the neuron to form its input (dendrite) and out-put (axon) devices. In this talk, we introduce quantitative

mathematical model of the neuronal symmetry breakingas a nonlinear dynamical system, and show how symmetrybreaks by phase plane analysis.

Yuichi SakumuraSchool of Information Science and TechnologyAichi Prefectural Universitysakumura@ist.aichi-pu.ac.jp

Naoyuki InagakiGraduate School of Biological SciencesNara Institute of Science and Technologyninagaki@bs.naist.jp

MS68

Mathematical Modelling of Wind Turbines

America is home to one of the largest and fastest growingwind markets in the world. In 2012 the United States windpower installations were more than 90% higher than in2011. With the growing demand for installations, the needfor mathematical modelling has become critical. In thistalk, I will describe a simple model of a wind turbine andsome of it’s applications. Future lines of research will alsobe discussed.

Andre CandidoState University of New York at New Paltz, USAn02284572@hawkmail.newpaltz.edu

MS68

Well-Balanced Positivity Preserving Central-Upwind Scheme for the Shallow Water Systemwith Friction Terms

Shallow water models are widely used to describe and studyfree-surface water flow. The friction terms will play a sig-nificant role when the depth of the water is very small. Inthis talk, we introduce shallow water equations with fric-tion terms and a well-balanced central-upwind scheme thatis capable of exactly preserving physically relevant steadystates. The data in the numerical example correspond tothe laboratory experiments designed to mimic the rain wa-ter drainage in urban areas.

Shumo CuiTulane University, USAscui2@tulane.edu

Alina ChertockNorth Carolina State UniversityDepartment of Mathematicschertock@math.ncsu.edu

Alexander KurganovTulane UniversityDepartment of Mathematicskurganov@math.tulane.edu

Tong WuTulane Universitytwu2@tulane.edu

MS68

Membrane Deformation by Protein Inclusions

I will explore various models for the deformation ofbiomembranes by protein molecules which are embedded

AN14 Abstracts 81

in or attached to the membrane, termed protein inclusions.Mathematically we focus on minimisation problems involv-ing the Helfrich energy functional. Inclusions will be mod-elled by enforcing pointwise constraints on the membranedisplacement or curvature. I will present results detailingthe existence and behaviour of minimal energy states forsome of these models.

Graham HobbsUniversity of Warwick, UKg.hobbs@warwick.ac.uk

MS68

Modeling Feral Hogs in the Great Smoky Moun-tains National Park

Feral Hogs (Sus Scrofa) are an invasive species that haveoccupied the Great Smoky Mountains National Park sincethe early 1900s. Recent studies have revitalized interestin the pest and have produced useful data on vegetation,mast and harvest history. Using these data, a model withdiscrete time and space was formulated to represent thehog dynamics in the park. Management strategies andestimation of actual total population was investigated.

Benjamin LevyUniversity of Tennesse, USAlevy@math.utk.edu

Bill StiverGreat Smoky Mountains National Parkbill stiver@nps.gov

Rene SalinasAppalachian State Universitysalinasra@appstate.edu

Joseph Corn, Marguerite MaddenUniversity of Georgiajcorn@uga.edu, mmadden@uga.edu

Charles CollinsUniversity of TennesseeKnoxville, Tennesseeccollins@math.utk.edu

Suzanne M. LenhartUniversity of TennesseeDepartment of Mathematicslenhart@math.utk.edu

MS68

Stochastic Diffusion Processes in Systems Biology

In cell biology many species are only present at very lowcopy numbers, therefore a deterministic description by par-tial differential equations often doesnt reproduce experi-mental results and a stochastic model is needed. We use acontinuous-time discrete-space Markov process to simulatediffusion stochastically. To represent complex geometriesaccurately we discretize the cell into an unstructured meshand compare the jump coefficients resulting from a finiteelement method and a first exit time approach.

Lina MeineckeUppsala University, Swedenlina.meinecke@it.uu.se

Per LotstedtUppsala Universityper.lotstedt@it.uu.se

MS68

A Smoothing Trust Region Filter Algorithm forNonsmooth Nonconvex Least Squares Problems

We propose a smoothing trust region filter algorithm fornonsmooth and nonconvex least squares problems withzero residual. We present convergence theorems of the pro-posed algorithm to a Clarke stationary point or a globalminimizer of the objective function under certain condi-tions. Preliminary numerical experiments show the effi-ciency of the proposed algorithm for finding zeros of asystem of polynomial equations with high degrees on thesphere and solving differential variational inequalities.

Yang ZhouThe Hong Kong Polytechnic University, Chinazhyg1212@163.com

Xiaojun ChenDepartment of Applied MathematicsThe Hong Kong Polytechnic Universitymaxjchen@polyu.edu.hk

Shouqiang DuQingdao University, Chinaqddsq1@163.com

MS69

Filtered Spectral Methods for Transport Problems

We analyze the behavior of filtered spectral approxima-tions that are used in the angular discretization of radia-tive transport equations. Recently the filtering approachhas been recast as a transport equation with modified scat-tering cross-section. We examine this modified equation,prove some basic convergence properties, and show somesupporting numerical results.

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

Martin Frank, Kerstin KuepperRWTH Aachen UniversityCenter for Computational Engineering Sciencefrank@mathcces.rwth-aachen.de,kuepper@mathcces.rwth-aachen.de

MS69

Hybrid Algorithms for Hybrid Computers:Kinetic-Continuum Models of Transport Phenom-ena

Recent developments in high-performance computing haveled to a hybrid architecture composed of multicore CPUsand GPU coprocessors (e.g. ORNL Titan machine). Insuch architectures, a premium is placed on algorithmsthat require minimal communication between CPU/GPUnodes. We introduce a set of algorithms in this spiritbased upon stochastic differential equation solvers for ki-netic level models of transport phenomena, coupled withhigh-order finite element models of the continuum (homog-

82 AN14 Abstracts

enized) scale.

Michael Malahe, Sorin MitranUniversity of North Carolina Chapel Hillmmalahe@email.unc.edu, mitran@unc.edu

MS69

Hydraulic Modeling for Quantum Absorption Cal-culation in Plasmonics Based on High-Order Spec-tral Element Discontinuous Galerkin Approach

I will discuss about recent development of spectral elementdiscontinuous Galerkin (SEDG) schemes for solving localinteractions between electrons and the light in plasmonicsystems. The dispersive material properties of the sys-tem are described by a hydraulic model. This approachis formulated by coupling the macroscopic Maxwell equa-tions with the equations of motion of the electron gas. Thenonlocal polarization current induced by an external elec-tromagnetic field is represented by a system of the first-order partial differential equations with an auxiliary ordi-nary differential equation. I will present efficient and stableSEDG algorithms with properly designed numerical fluxes,provided with stability analysis. We validate our compu-tational results for nano sized metallic cylinders for theabsorption cross sections and field distributions.

MiSun MinArgonne National LaboratoryMathematics and Computer Science Divisionmmin@mcs.anl.gov

MS69

Semi-Lagrangian Discontinuous Galerkin Schemesfor the Relativistic Vlasov-Maxwell System

The Vlasov-Maxwell system describes the evolution of acollisionless plasma, represented through a probability den-sity function (PDF) that self-interacts via the electromag-netic force. One of the main difficulties in numerically solv-ing this system is the severe time-step restriction that arisesfrom parts of the PDF associated with moderate-to-largevelocities. The dominant approach in the plasma physicscommunity is the so-called particle-in-cell method. Thefocus of the current work is on semi-Lagrangian methods.In particular, we develop a method based on high-orderdiscontinuous Galerkin (DG) scheme in phase space, andan operator split, semi-Lagrangian method in time. Themethod is designed to be (1) high-order accurate, (2) massconservative, and (3) positivity-preserving. The resultingscheme is applied to laser-plasma acceleration problems.

James A. RossmanithDeparment of MathematicsIowa State Universityrossmani@iastate.edu

MS70

Optimal Control of Free Boundary Problems withSurface Tension Effects

We will give a novel proof for the second order order suffi-cient conditions for an optimal control problem where thestate system is composed of Laplace equation in the bulkand Young-Laplace on the free boundary. Next, we will dis-cuss a novel analysis for a Stokes free boundary problemwith surface tension effect. We will conclude with some re-cent results for the Navier-Stokes problem with slip bound-

ary conditions.

Harbir AntilGeorge Mason UniversityFairfax, VAhantil@gmu.edu

MS70

Numerical Investigations of Bouncing Jets

The Kaye effect is a fascinating phenomenon of a leapingshampoo stream which was first described by Alan Kayein 1963 as a property of non-Newtonian fluid. It manifestitself when a thin stream of non-Newtonian fluid is pouredinto a dish of fluid. As pouring proceeds, a small stream ofliquid occasionally leaps upward from the heap. We inves-tigate numerically the impact of the experimental settingas well as the fluid rheology on the apparition of bouncingjets. In particular, we observe the importance of the cre-ation of a thin lubricating layer of air between the jet andthe rest of the liquid. The numerical method consists of aprojection method coupled with a level-set formulation forthe interface representation. Adaptive finite element meth-ods are advocated to capture the different length scalesinherent to this context.

Andrea BonitoTexas A&M UniversityDepartment of Mathematicsbonito@math.tamu.edu

Jean-Luc GuermondDepartment of MathematicsTexas A&M, USAguermond@math.tamu.edu

Sanghyun LeeTexas A&M UniversityDepartment of Mathematicsshlee@math.tamu.edu

MS70

Splitting for Variable Density Flows

We show the equivalence between the so-called gaugeUzawa method and the pressure correction schemes in ro-tational form. Using this equivalence we show simpler sta-bility proofs for known schemes and devise a new stablescheme for the approximation of incompressible flows withvariable density. The main feature of the new method isthat only involves constant, in time, matrices.

Abner J. SalgadoDepartment of MathematicsUniversity of Marylandasalgad1@utk.edu

MS70

Modeling Viscoelastic Networks in Stokes Flow

We present a simple method for modeling heterogeneousviscoelastic media at zero Reynolds number. The methodcan be extended to capture viscoelastic features as wellas some other models. Linking rules for the network arebased on linear viscoelastic models, then varying complex-ity allows the model to exhibit different kinds of behavior.A few rheology tests are used to analyze the mechanicalproperties of the model networks and the effects of input

AN14 Abstracts 83

parameters on these properties.

Jacek K. WrobelDepartment of Mathematics, Tulane UniversityCenter for Computational Sciencejwrobel@tulane.edu

Ricardo Cortez, Ricardo CortezTulane UniversityMathematics Departmentrcortez@tulane.edu, rcortez@tulane.edu

Lisa J. FauciTulane UniversityDepartment of Mathematicsfauci@tulane.edu

MS71

Interferometric Waveform Inversion: GeophysicsMeets Spectral Graph Theory

In seismic and SAR imaging, fitting cross-correlations ofwavefields rather than the wavefields themselves can resultin improved robustness vis-a-vis model uncertainties. Thisapproach however raises two challenges: (i) new spuriouslocal minima may complicate the inversion, and (ii) onemust find a good subset of cross-correlations to make theproblem well-posed. I will explain how to address thesetwo problems with lifting, semidefinite relaxation, and ex-pander graphs. This mix of ideas has recently proved tobe the right approach in other contexts as well, such asangular synchronization (Singer et al.) and phase retrieval(Candes et al.). Joint work with Vincent Jugnon.

Laurent DemanetProfessor of Mathematics, MITlaurent@math.mit.edu

MS71

Inverse Born Series for the Radiative TransportEquation

We propose a direct reconstruction method for the inverseradiative transport problem that is based on inversion ofthe Born series. We characterize the convergence and ap-proximation error of the method and illustrate its use innumerical simulations.

Manabu MachidaDepartment of MathematicsUniversity of Michiganmmachida@umich.edu

John SchotlandUniversity of Michiganschotland@umich.edu

MS71

Layered Media Scattering: Fokas Integral Equa-tions and Boundary Perturbation Methods

In this talk we describe a class of Integral Equations tocompute Dirichlet-Neumann operators for the Helmholtzequation on periodic domains inspired by the recent workof Fokas and collaborators on novel solution formulas forboundary value problems. These Integral Equations havea number of advantages over standard alternatives includ-ing: (i.) ease of implementation (high-order spectral ac-

curacy is realized without sophisticated quadrature rules),(ii.) seamless enforcement of the quasiperiodic boundaryconditions (no periodization of the fundamental solution,e.g. via Ewald summation, is required), and (iii.) reducedregularity requirements on the interface proles (derivativesof the deformations do not appear explicitly in the formu-lation). We show how these can be efficiently discretizedand utilized in the simulation of scattering of linear acous-tic waves by families of periodic layered media which arisein geoscience applications.

David P. NichollsUniversity of Illinois at Chicagonicholls@math.uic.edu

MS71

Numerical Algorithms for Simultaneous Determi-nation of Acoustic and Optical Coefficients in Pho-toacoustic Tomography

Photoacoustic tomography (PAT) aims at reconstructingphysical properties of optically heterogeneous media frommeasured acoustic signals generated by the photoacousticeffect. Image reconstructions in PAT are usually done ina two-step process. In the first step, one solves an inversewave propagation problem to recover the initial pressurefield inside the media. In the second step, one solves an in-verse diffusion/transport problem to recover optical prop-erties, using the result of the first step as the data. Thistwo-step procedure breaks down when the acoustic wavespeed is also assumed unknown and to be reconstructed.We present here some numerical algorithms that solve theinverse wave and inverse diffusion problems simultaneouslyto image both optical and acoustic properties.

Kui RenUniversity of Texas at Austinren@math.utexas.edu

MS72

Hydrodynamic Interaction of Swimming Microor-ganisms in Complex Fluids

The interaction of motile microorganisms, surrounding flu-ids and boundaries is of paramount importance in a va-riety of physical and environmental phenomena includingthe development of biofilms, colonization of microbes inviscoelastic mucus of human and animal bodies, bacterialaggregating in oceanic gels, and swimming of spermatozoain female reproductive tract. In this study, we scrutinizethe role of rheological properties of background fluids onthe interaction of microorganisms with rigid surfaces.

Gaojin LiUniversity of Notre Damegli5@nd.edu

Arezoo ArdekaniNotre Dame UniversityDepartment of Aerospace and Mechanical Engineeringarezoo.ardekani.1@nd.edu

MS72

Swimming Through Heterogeneous Networks

I will present results for swimmers moving near similar-sizemicrostructural heterogeneities. Spherical obstructions areused to deduce physical principles linking the swimmer flow

84 AN14 Abstracts

field, forces on obstructions, and changes in swimming ve-locities. Then single rod-like obstructions are studied todeduce the effect of a network of filaments. The averageand variance of the swimming speed reflect the density andorientation correlations of the microstructure, and henceswimming properties can be used as probes of microstruc-ture.

Henry FuUniversity of Nevada, RenoDept. Mechanical Engineeringhfu@unr.edu

MS72

Mechanism of Microorganism Propulsion in Vis-coelastic Fluids

Abstract not available at time of publication.

Alexander MorozovUniversity of EdinburghSchool of Physics & Astronomyalexander.morozov@ph.ed.ac.uk

MS72

Flagellar Locomotion in Viscoelastic andAnisotropic Environments

We will discuss recent investigations of helical andundulatory locomotion in viscoelastic (Oldroyd-B) andanisotropic (liquid crystal) fluids. Elastic and anisotropiceffects can either enhance or retard a microorganism’sswimming speed, and can even change the direction ofswimming, depending on the body geometry and the fluidproperties. Our findings connect studies showing situation-ally dependent enhancement or retardation of swimmingspeeds, and may help to clarify phenomena observed in anumber of biological systems.

Saverio E. SpagnolieUniversity of WisconsinDepartment of MathematicsSpagnolie@math.wisc.edu

MS73

The Response of the Lyapunov Exponent to Exter-nal Perturbations

We present a new approach to predict the response of thelargest Lyapunov exponent of a dynamical system to smallexternal perturbations of different types. The connectionbetween the external perturbation and the change in thelargest Lyapunov exponent is approximately representedthrough the corresponding response operator, computedfor the original unperturbed system. The theory for the re-sponse operator of the largest Lyapunov exponent is basedon the well-known Fluctuation-Dissipation theorem. Wealso compute the response prediction for a simple model ofchaotic nonlinear dynamics, and compare it against the ac-tual response of the largest Lyapunov exponent computedby directly perturbing the system, for a simple constantforcing perturbation.

Rafail AbramovDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at Chicago

abramov@math.uic.edu

MS73

Stochastic Mode-Reduction in Models with Con-servative Fast Sub-Systems

We will consider application of the stochastic mode re-duction to multi-scale models with deterministic energy-conserving fast sub-system. In particular, we consider thesituation when the slow variables are driven stochasticallyand interact with the fast subsystem in an energy conserv-ing fashion. Since there is energy exchange between thefast conservative sub-system and the slow variables, it isnecessary to explicitly keep track of the energy of the fastsub-system. Therefore, we develop a new stochastic modereduction process in this case by introducing energy of thefast subsystem as an additional hidden slow variable. Weuse several prototype models to illustrate the approach.

Ankita JainDept of Applied and Computational Mathematics andStatisticsUniversity of Notre Dameankita.jain@nd.edu

MS73

Stochasticity in An Integrable System: Pulse Po-larization Switching in An Active Optical Medium

Propagation of optical pulses through an active opticalmedium with two working levels, known as the Lambda-configuration, is described by an initial-boundary valueproblem for a set of completely integrable partial differ-ential equations. If the initial conditions are preparedrandomly, the resulting soliton solutions exhibit stochas-tic behavior, which can be described exactly in terms ofprobability-density functions and first- and last-passagetime problems. The talk will present these soliton statis-tics.

Gregor KovacicRensselaer Polytechnic InstDept of Mathematical Scienceskovacg@rpi.edu

MS73

Dynamics of Ferromagnets

Driving nanomagnets by spin-polarized currents offers ex-citing prospects in magnetoelectronics, but the response ofthe magnets to such currents remains poorly understood,even more so with the addition of thermal noise. For asingle domain ferromagnet, I will show that an averagedequation describing the diffusion of energy on a graph cap-tures the low-damping dynamics of these systems. I willthen present the problem of extending the analysis to spa-tially non-unifrom magnets, modeled by an infinite dimen-sional Hamiltonian systems, equivalently a non-linear waveequation with stochastic in space initial conditions.

Katherine NewhallCourant Institute of Mathematical ScienceNew York Universitynewhall@cims.nyu.edu

MS74

Data Analytics Throughout Undergraduate Math-

AN14 Abstracts 85

ematics

DATUM is an education/research program which trainsfreshman and sophomore students in the philosophy andtools of data analysis and modeling. The course, Intro-duction to Data Mathematics, introduces high-dimensionalmodeling, data analytics, and their use in applications. Re-quiring only basic calculus, it prepares students for summerresearch on real-world data analytics problems. It teachesdata analytics methods along with a targeted examinationof underlying high-dimensional mathematics including Eu-clidean geometry, matrix algebra, eigenvalues, and spectraldecomposition.

Kristin BennettMathematical SciencesRensselaer Polytechnic Institutebennek@rpi.edu

Bruce PiperRensselaer Polytechnic InstituteDept of Mathematical Sciencespiperb@rpi.edu

MS74

Research and Training in Computational and Data-Enabled Science and Engineering for Undergradu-ates in the Mathematical Sciences at NJIT

The NJIT EXTREEMS-QED program is designed toimmerse undergraduates in courses and group researchprojects in the computational analysis of data and themodeling and simulation of complex systems in multidisci-plinary contexts. In this talk, we will describe the researchactivities of our first cohort of undergraduates and the cur-ricular enhancements in computational and data enabledscience and engineering that have already been made. Thisproject is supported by the NSF.

David J. HorntropDept of Mathematical Sciences, Center for Applied MathNew Jersey Institute of Technologydavid.horntrop@njit.edu

MS74

Data-Enabled Science and Computational Analy-sis Research, Training, and Education for Students(descartes) Program at UC Merced

The Data-Enabled Science and Computational Anal-ysis Research, Training, and Education for Students(DESCARTES) Program at UC Merced trains AppliedMathematical Sciences majors in the computational toolsneeded to study modeling and simulation of complex sys-tems and analysis of large data sets. This program hasthree specific aims: (1) Provide exceptional undergraduatestudents unique research opportunities and state-of-the-arteducation and training in computational and data-enabledscience; (2) Develop the Computational and Data-EnabledScience emphasis track within the Applied MathematicalSciences Major; and (3) Provide high school math teach-ers from the region the opportunity to learn the tools andmethods of computational and data-enabled science. Inthis talk, we will describe current developments within theDESCARTES program and discuss new initiatives that wehave undertaken since the inception of the program.

Arnold D. KimUniversity of California, Merced

adkim@ucmerced.edu

MS74

Computational and Data-Enabled Training inWilliam & Mary

In this talk, I will talk about how EXTREEMS-QED isorganized at W&M, how we recruit students, and how torun our summer research programs. I will also talk abouthow we develop Data-related courses.

Gexin YuDepartment of MathematicsThe College of William and Marygyu@wm.edu

MS75

A Stochastic-Oriented NLP Relaxation for IntegerProgramming

We introduce a nonlinear, nonconvex relaxation of integerconstraints in certain linear programs. The relaxation ismotivated by the interpretation of relaxed integer variablesas probability of units to be on in energy systems applica-tions. The relaxation depends on a complexity parameterthat controls its strength that is derived from a quantileinterpretation of a stochastic formulation. We analyze thedependence of the solution on this complexity parameterand provide numerical examples to support our claims.

John BirgeUniversity of ChicagoBooth School of Businessjohn.birge@chicagobooth.edu

Mihai Anitescu, Cosmin G. PetraArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov, petra@mcs.anl.gov

MS75

Uncertainty Analysis of Wind Power Plant Dy-namic Model

In transient stability studies, large wind power plants(WPP) are usually represented by reduced model consist-ing on one, or few, equivalent machines. However individ-ual wind turbine generators (WTG), within a WPP, canproduce diverse power outputs, because of terrain topog-raphy and/or wake effect. Under these conditions, the ac-curacy of the reduced WPP model has not been studiedyet. In this paper, we present an uncertainty analysis toinvestigate the model accuracy of a WPP model under di-verse power outputs of its individual WTGs. Wake effectis considered as the reason for diverse power outputs. Theimpact of wake effect in dynamic WPP model uncertaintyis investigated. The importance of diverse WTG poweroutput is evaluated in full and reduced models of a large168-machine test WPP connected to the IEEE-39-bus sys-tem. The results show that diverse WTG output due towake effect can affect the transient stability outcome anal-ysis. The reduced WPP model misrepresents the dynamicresponse observed with the full WPP representation. Engi-neers should be aware of this difference when using reducedWPP models.

Guang Lin, Marcelo Elizondo, Shuai Lu, Shaobu WangPacific Northwest National Laboratory

86 AN14 Abstracts

guang.lin@pnnl.gov, marcelo.elizondo@pnnl.gov,shuai.lu@pnnl.gov, shaobu.wang@pnnl.gov

MS75

Global Optimization of Large Optimal Power FlowProblems

We propose a global optimization algorithm based onbranch and bound for the Optimal Power Flow (OPF)problem in power grids. The algorithm uses Semidefi-nite Programming (SDP) relaxations of the OPF to pro-vide strong lower bounds on the optimal objective functionvalue. The algorithm is able to guarantee global optimalityto a small tolerance for several IEEE benchmark instancesand modified instances, orders of magnitude faster thangeneral purpose global optimization solvers. We also ex-tend the algorithm to the smart grid problem, which is amulti period extension of the OPF to address integrationof renewable energy sources and storage devices into thepower grid. Results illustrate the effectiveness of storagein lowering costs and absorbing fluctuations due to inter-mittent power sources in the grid.

Lorenz T. BieglerCarnegie Mellon UniversityPittsburgh, USAbiegler@cmu.edu

Bethany NicholsonCarnegie Mellon Universityblnichol@andrew.cmu.edu

MS75

Exploiting Large-Scale Natural Gas Storage to Mit-igate Power Grid Uncertainty

We present a stochastic optimal control model to optimizegas network inventories in the face of system uncertainties.We demonstrate that gas network inventories can be usedto mitigate volatility observed in power grid operations.

Victor ZavalaArgonne National Laboratoryvzavala@mcs.anl.gov

MS76

Mathematical Models and Computational Soft-ware for Hazardous Earth-Surface Flows: fromTsunamis to Landslides

There is a large class of geophysical flows that can be cate-gorized as hazardous, free-surface, gravity-driven inundat-ing flows. These problems include tsunami propagationand inundation; overland flooding; hurricane-generatedstorm surges; and a range of granular-fluid flows includ-ing landslides, debris flows and lahars. These problemsare often modeled with depth-averaged PDEs sharing com-mon mathematical features and presenting similar compu-tational challenges. I will describe these models and showsimulations of tsunamis, floods and landslides using thesemethods.

David GeorgeU.S. Geological SurveyCascades Volcano Observatory

dave.jorge@gmail.com

MS76

Dynamically and Kinematically Consistent GlobalOcean State Estimation for Climate Research

The sparsity of observations for oceanographic (andcryospheric) research directed at climate requires the de-velopment and application of mathematical and computa-tional tools, variously known as inverse methods, or stateand parameter estimation, to infer poorly known or notdirectly measurable quantities, and to provide useful un-certainty estimates. Data assimilation commonly used innumerical weather prediction applies filtering methods thatare optimal for forecasting. However, to the extent that thefocus is on understanding the dynamics of the ocean’s pastevolution such methods have limitations; they do not pre-serve known conservation laws and evolution equations. In-stead, climate reconstruction is best solved using smoothermethods such that optimal use is made of the sparse obser-vations while preserving known physical laws encapsulatedin the model used for data interpolation. Two examplesfrom global ocean state estimation and ice sheet modelingwill be discussed.

Patrick HeimbachMassachusetts Institute of Technologyheimbach@mit.edu

MS76

Computational Challenges in High-Resolution,Experimentally-Constrained Non-Newtonian Sub-duction Modeling

Results from high-resolution, massively parallel, three-dimensional numerical models of subduction zone deforma-tion are presented. The models are observationally based,contain multiple plates, and use a non-Newtonian viscosity,making them among the highest fidelity convergent mar-gin models to date. A scalable solver is used to solve thedifficult variable viscosity stokes flow. Large viscosity gra-dients emerge due to the strain-rate dependent viscosity,allowing for local decoupling and complex circulation semi-independent from the larger scale mantle circulation.

Margarete A. JadamecBrown UniversityDepartment of Geological SciencesMargarete Jadamec@Brown.edu

MS76

Promoting the Development and Application ofMathematics, Statistics and Computational Sci-ence in the Geosciences

I will begin by describing recent efforts of the Consortiumfor Mathematics in the Geosciences (CMG++) formed bymembers of the mathematical, statistical, computationaland geoscience communities. The goal of the consortium isto accelerate traditional interactions between these groupsof scientists. Then I will discuss a computational inversemethod developed by myself and colleagues that was mo-tivated by specific challenges in oceanographic data assim-ilation and geophysics.

Jodi MeadBoise State UniversityDepartment of Mathematics

AN14 Abstracts 87

jmead@boisestate.edu

MS77

Imaging of Extended Reflectors in Two-Dimensional Waveguides

We consider the problem of imaging extended reflectors inwaveguides using the response matrix of the scattered fieldobtained with an active array. We employ selective imag-ing techniques to focus onto the edges of a reflector whichtypically give raise to weaker echoes than those comingfrom its main body. A selective imaging functional basedon Kirchhoff migration and the SVD of a weighted modalprojection of the response matrix is proposed and analyzed.

Chrysoula TsogkaUniversity of Crete and FORTH-IACMtsogka@tem.uoc.gr

Dimitrios MitsoudisInstitute of Applied and Computational MathHeraklion, Cretedmits@tem.uoc.gr

Symeon PapadimitropoulosDepartment of Applied Mathematics, University of Cretespapadem@tem.uoc.gr

MS77

Imaging of Sparse Scatterers

Abstract not available at time of publication.

Alexei NovikovPenn State UniversityMathematicsanovikov@math.psu.edu

MS77

Connecting the Dots: from Homogenization to Ra-diative Transport

Abstract not available at time of publication.

Lenya RyzhikStanford Universityryzhik@math.stanford.edu

MS77

Signal to Noise Ratio Analysis in Virtual SourceArray Imaging

We consider imaging a reflector located on one side of a pas-sive array where the propagation medium is homogeneous.The reflector is illuminated by remote impulsive sourcessituated on the other side of the passive array where themedium is complex and strongly scattering. We transformthe passive array to an active virtual array by migratingthe cross correlations of the field recorded on the passivearray. We will present an analysis of the signal to noiseratio of the obtained image.

Chrysoula TsogkaUniversity of Crete and FORTH-IACM

tsogka@tem.uoc.gr

MS78

Flagellar Kinematics of Algal Cells in ViscoelasticFluids

The motility behavior of microorganisms can be signifi-cantly affected by the rheology of their fluidic environment.In this talk, we experimentally investigate the effects offluid elasticity on both the flagella kinematics and swim-ming dynamics of the microscopic alga Chlamydomonasreinhardtii. We find that the flagellar beating frequencyand wave speed are both enhanced by fluid elasticity. In-terestingly, the swimming speeds during the alga powerand recovery strokes are enhanced by fluid elasticity forDe 1. Despite such enhancements, however, the alga netforward speed is hindered by fluid elasticity by as much as30% compared to Newtonian fluids of similar shear viscosi-ties. The motility enhancements could be explained by themechanism of stress accumulation in the viscoelastic fluid.

Paulo E. ArratiaMechanical Engineering and Applied MechanicsUniversity of Pennsylvania, Philadelphia.parratia@seas.upenn.edu

MS78

The Dynamics of Sperm Detachment from Epithe-lium in a Coupled Fluid-Biochemical Model of Hy-peractivated Motility

Amechanical advantage of the spermatozoa hyperactivatedwaveform has been hypothesized to be the promotion ofdetachment from oviductal epithelium. Using a Stokesfluid model that incorporates forces due to dynamic elas-tic bonds between the flagellar head and a surface, we findthat hyperactive waveforms do result in the frequent de-taching and binding dynamics that are observed in recentlab experiments.

Lisa J. FauciTulane UniversityDepartment of Mathematicsfauci@tulane.edu

Julie SimonsTulane Universityjsimons@tulane.edu

Sarah D. OlsonWorcester Polytechnic Institutesdolson@wpi.edu

Ricardo Cortez, Ricardo CortezTulane UniversityMathematics Departmentrcortez@tulane.edu, rcortez@tulane.edu

MS78

The Phylogeny of Sperm Swimming Kinematics

Phylogenetic analyses have dominated the study of ecologyand evolution. However, physical interactions between or-ganisms and their environment are mediated by organismform and function, highlighting the importance of mechan-ics to understanding evolutionary trajectories. We com-bined high-speed video microscopy and singular value de-composition analysis to quantitatively compare the flagel-

88 AN14 Abstracts

lar waveforms of sperm from eight diverse species. Theemergence of dominant flagellar waveforms is suggestive ofbiological optimization, driven by environmental cues.

Jeffrey GuastoMassachusetts Institute of TechnologyJeffrey.Guasto@tufts.edu

Lisa Burton, Filippo MenolascinaMITlisab@mit.edu, filipm@mit.edu

Richard ZimmerUCLAz@biology.ucla.edu

Anette HosoiMassachusetts Institute of Technology77 Massachusetts Avenue, Room 3-173, Cambridge MA02139peko@mit.edu

Roman StockerMITCivil and Environmental Engineeringromans@mit.edu

MS78

Flagellar Bundling and Unbundling in E. Coli

Flagellar bundling and unbundling are important aspectsof locomotion in bacteria such as Escherichia coli. To studythe hydrodynamic behavior of helical flagella, we present acomputational model that describes the motion of bacterialflagellar filament at the micrometer scale. Bundling occurswhen all flagella are left-handed helices turning counter-clockwise or when all flagella are right-handed helices turn-ing clockwise. Helical flagella of the other combinations ofhandedness and rotation direction do not bundle.

Sookkyung LimUniversity of Cincinnatisookkyung.lim@uc.edu

MS79

Unifying the Equations of Life: Time Scale Calcu-lus and Evolutionary Dynamics

Evolutionary dynamics is concerned with the evolutionof populations. In a general framework, each populationhas its own geometry, method of adaptation (incentive),and time-scale (discrete, continuous, and others). Usingan information-theoretic measure of distance, a widely-applicable stability result will be given for all of these sce-narios. A wealth of examples leading up to and beyond themain results is included. No prior knowledge of evolution-ary dynamics, information theory, Riemannian geometry,or game theory is required.

Dashiell FryerPomona CollegeDashiell.Fryer@Pomona.edu

Marc HarperUCLA

marc.harper@gmail.com

MS79

Flight Stability of Mosquitoes using a ReducedModel

We employ a reduced model that represents a mosquito asa rigid body with two rigid wings to explore mosquito sta-bility. Wing motions derived from analysis of high speedmovies are used as inputs to a dynamical model of themosquito body. We study uniform flight where flight tra-jectories are periodic orbits in a suitable translating refer-ence frame. We analyze the stability of body motions inthis frame by computing a linearized return map of the pe-riodic orbit along with its eigenvalues and singular values.Long time stability corresponds to eigenvalues all smallerthan one in magnitude and depends upon model param-eters. For our mosquito geometry, we find that hoveringflight is unstable but locate parameter ranges in which for-ward flight is stable. We also investigate the effect of vary-ing the location of the joint between wings and body onstability of hovering flight. All cases are close to marginalstability.

Sarah IamsNorthwestern UniversityEvanston, ILsmi6@cornell.edu

MS79

On a Non-Linear Investigation of An Electrospin-ning Model under Combined Space and TimeEvolving Instabilities

We study the nonlinear problem of axisymmetric electri-cally driven jets with applications to the electrospinningprocess. We consider classical stability point of view inthe early stage and then weakly nonlinear wave theory ofcertain dyad resonance modes that later involve the use ofNewton’s Method to solve a dispersion relation. Finally wepresent the Method of Lines (MOL) to solve a system ofPDEs that governs the combined time and space evolvingamplitude instability functions.

Saulo OrizagaDepartment of MathematicsIowa State Universitysorizaga@iastate.edu

MS79

Analyzing Coherent Structure in Signals and FluidFlows

We consider a dynamical systems based method for mea-suring the complexity of particle trajectories in fluid flows.This complexity is measured in terms of ergodicity whichrelates to how a trajectory samples a space and how it sam-ples provides insight about the structure in the phenomenaor region of interest. We discuss how this insight is used tovisualize the 2D and 3D Lagrangian coherent structures inocean flows and how this information can in turn be usedto better understand the transport in the flow - e.g., trans-port barriers and transport facilitators. As time permits,other related diagnostics will also be presented.

Sherry ScottMarquette University

AN14 Abstracts 89

sherry.scott@marquette.edu

MS80

Asymptotically Compatible Schemes for RobustDiscretization of Nonlocal Models

We present an abstract framework of asymptotically com-patiable (AC) schemes for robust discretizations of a familyof parametrized problems. The AC schemes provide con-vergent approximations to problems associated with fixedparameter values as well as their limiting values. Thisframework is then applied to study approximations of non-local models such as peridynamic models of nonlocal elas-ticity parametrzed by the horizon parameter and their localPDE limits (Navier equations) when the horizon parame-ter approaches zero. In particular, by combining with thetheory of nonlocal calculus of variations, a precise char-acterization of AC schemes can be obtained for popularconforming finite element discretizations.

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

Xiaochuan TianPennsylvania State Universitytian x@math.psu.edu

MS80

Analysis and Approximation of Finite-Range JumpProcesses

The classical Brownian motion model for diffusion isnot well-suited for applications with discontinuous samplepaths. For instance, the mean square displacement of adiffusing particle undergoing a jump process often growsfaster than that for the case of Brownian motion, or growsat the same rate but is of finite variation or finite activ-ity. Such jump processes are viable models for anomaloussuper-diffusion or nonstandard normal diffusion. In par-ticular, such jump diffusions are expedient models whenthe process sample-path is discontinuous because nearly in-stantaneous price volatility, species migration or heat con-duction is suggested by the length and time scales overwhich the data is collected. My presentation is on recentwork for the associated deterministic equation on boundeddomains where the jump process is of finite-range, i.e, thejump-rate is positive over a region of compact support. Werefer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume con-straint is the nonlocal analogue of a boundary conditionnecessary to demonstrate that the nonlocal diffusion equa-tion is well-posed and be consistent with the jump process.

Marta D’EliaDepartment of Scientific ComputingFlorida State University, Tallahassee, FLmdelia@fsu.edu

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

Max GunzburgerFlorida State UniversitySchool for Computational Sciences

mgunzburger@fsu.edu

Richard B. LehoucqSandia National Laboratoriesrblehou@sandia.gov

MS80

Modeling Anomalous Diffusion Using the Frac-tional Bloch-Torrey Equation

Contrast in magnetic resonance imaging (MRI) can bemanipulated to display the apparent diffusion coefficientfor water. In complex, heterogeneous materials, such asbiological tissue, diffusion is anisotropic and often non-Gaussian. Such anomalous diffusion can be succinctly de-scribed via the fractional order Bloch-Torrey equation - aFPDE that captures both deterministic and stochastic pro-cesses. Using this model, MRI can display spatial maps oftissue properties in terms of sub- and super-diffusion.

Richard MaginDepartment of BioengineeringUniversity of Illinois at Chicagormagin@uic.edu

MS80

Fractional PDEs: Numerical Methods and Mathe-matical Analysis

We present a faithful and efficient numerical methods fortime-dependent space-fractional PDEs in three space di-mensions, without resorting to any lossy compression, butrather by exploring the structure of the coefficient matrices.The method reduces computational cost from O(N3) toO(N log2 N) per time step and memory requirement fromO(N2) to O(N). We also address some mathematical is-sues that are characteristic for fractional PDEs and reportour recent progress in this direction.

Hong WangUniversity of South CarolinaDepartment of Mathematicshwang@math.sc.edu

MS81

BANDITS: A Matlab Package of Band Krylov Sub-space Iterations

Band Krylov subspace iterations are extensions of Krylovsubspace methods such as the Arnoldi process and theLanczos algorithm, which can handle only single startingvectors, to the case of multiple starting vectors. Bandmethods have a number of advantages over the more tra-ditional block Krylov subspace methods. We describe theMatlab package BANDITS that provides implementationsof band versions of the Arnoldi process, the general Lanc-zos method, and the symmetric and Hermitian Lanczosalgorithms.

Roland W. FreundUniversity of California, DavisDepartment of Mathematicsfreund@math.ucdavis.edu

MS81

Newton-Krylov Method for Problems with Embed-

90 AN14 Abstracts

ded Monte Carlo Simulations

We analyze the behavior of inexact Newton methods forproblems where the nonlinear residual, Jacobian, andJacobian-vector products are the outputs of Monte Carlosimulations. We propose algorithms which account for therandomness in the iteration, develop theory for the behav-ior of these algorithms, and illustrate the results with anexample from neutronics.

Carl T. KelleyNorth Carolina State Universitytim kelley@ncsu.edu

Jeffrey WillertLos Alamos National Laboratoryjaw@lanl.gov

Xiaojun ChenHong Kong Polytechnic Universityxiaojun.chen@inet.polyu.edu.hk

MS81

The Lanczos Algorithm and Extensions for Quater-nionic Matrices

Let A be an associative algebra containing one and A asquare matrix with entries from A. Let there be a vectorx = 0 with entries from A and λ ∈ A such that

Ax = xλ, (1)

where the multiplication on the right is carried out com-ponentwise. Then, λ will be called an eigenvalue of Aassociated with an eigenvector x of A. If we multiply (1)from the right by an invertible element h ∈ A we obtain

A[xh] = xλh = [xh] [h−1λh], (2)

which shows that the set of eigenvalues of quaternionic ma-trices can always be reduced to complex numbers. Thisis not necessarily so in other algebras. The Lanczos al-gorithm produces a series of tridiagonal j × j matricesTj , j = 1, 2, . . . from a symmetric matrix A, and the eigen-values of Tj (called Ritz values) approximate the eigenval-ues of A (usually very quickly). We report on the resultsfor quaternionic matrices and on extensions to other non-commutative algebras. Algebraic operations with quater-nions are in general more effective than the correspondingoperations with their matrix counterpart. This researchwas supported by the DFG, GZ OP 33/19-1

Gerhard OpferUniversitat Hamburggerhard.opfer@uni-hamburg.de

MS81

Hierarchical Krylov and Nested Krylov MethodsUsing PETSc for Extreme-Scale Computing

We develop hierarchical Krylov methods and nested Krylovmethods to overcome the scaling difficulties for extreme-scale computing. We demonstrate the impact at high corecounts on the PFLOTRAN subsurface flow application.Because these algorithms can be activated at runtime viathe PETSc library, application codes that employ PETSccan easily experiment with such techniques. The principlesof hierarchal Krylov methods and nested Krylov methodscan be applied to complementary advances in synchroniza-tion and communication-avoiding Krylov methods, thereby

offering potentially multiplicative benefits of combined ap-proaches.

Hong ZhangArgonne National Labhzhang@mcs.anl.gov

MS82

Information Theoretic Projection of CytoskeletonDynamics onto Surrogate Cellular Motility Models

Lattice Boltzmann and lattice Fokker-Planck methods canreadily handle the geometric and physical complexity ofthe reactions underlying cytoskeleton formation and dy-namics from actin polymerization and myosin motor mo-tion. The computational cost, even for such simplifieddiscretizations of the flow velocity and cytoskeleton con-figuration, is still prohibitive for study of cellular motionover many cell diameters. This talk presents a non-linearprojection approach to the construction of surrogate mod-els of cellular motility, as extracted from lattice compu-tations. A mesoscale state is represented by a set of pa-rameters from a family of probability density functions.The non-linear projection is induced by geodesic transportin the non-Euclidean geometry of the space of probabil-ity functions, guided by information theoretic functionalsthat quantify the fidelity of a reduced model. Several in-teresting links between microscopic parameters governingcytoskeleton formation and overall cell motion are broughtout by this approach.

Sorin MitranUniversity of North Carolina Chapel Hillmitran@unc.edu

MS82

Hybrid Models and Interfaces

In various applications the traditional mathematical mod-els based on PDEs, with their empirically determined co-efficients, and associated traditional numerical approxima-tions, are not sufficient to describe all the relevant dynam-ics and complexity. In the talk we describe our progresson hybrid computational models which combine tradi-tional numerical PDEs with other computational methodsfrom, e.g., statistical mechanics, and more broadly com-putational physics. We focus on a model which accountsfor complicated physics occuring at a fixed interface insemiconductors, which involves a Density Function The-ory model at microscale and a Domain Decomposition ap-proach involving a traditional drift-diffusion equation atmacroscale.

Timothy CostaOregon State Universitycostat@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

MS82

Lagrangian Particle Methods for Multiphase Flows

Here we present a novel formulation of the so-called mul-tiphase Pairwise Force Smoothed Particle HydrodynamicsMethod originally proposed by Tartakovsky and Meakin.

AN14 Abstracts 91

We derive a relationship between parameters in the pair-wise forces and the surface tension and static contact an-gle, validate the model and demonstrate its applicabilityfor studying complex processes such as multiphase flow inporous media with variable wettability.

Alexandre TartakovskyUniversity of South Floridatartakovsky@usf.edu

Alexander PanchenkoWashington State Universitypanchenko@math.wsu.edu

MS82

Modeling Nanoscale Fluid-Solid Interfaces

Structure and dynamics of soft matter are governed bymolecular interactions and hydrodynamic fluctuations. Asthe molecular and hydrodynamic aspects are coupled, com-puter simulations of soft matter must confront this multi-scale challenge. I will present a new scale-consistent simu-lation framework that combines molecular dynamics (MD)and fluctuating hydrodynamics (FHD) to enable multiscalemodeling of complex systems. This method allows resolu-tion of solute-solvent interfaces and realization of excludedvolumes of particles in the presence of hydrodynamic cou-pling. Simulation results show that the hybrid FHD/MDmethod can reproduce the solvation free energies and scal-ing laws of particles dynamics for hydrophobes of differencesizes. Simulations of self-assembly of hydrophobic particleswill also be presented.

Nikolaos VoulgarakisWashington State Universitynvoul@tricity.wsu.edu

MS83

Persistence Modules and their Applications to Ma-terial Sciences

In this talk, we present several applications of persistencemodules to material sciences such as proteins and glasses.The types of persistence modules are given by represen-tations on An-quiver (i.e., standard persistent homology)and on commutative triple ladder quivers. Furthermore,we give a generalized notion of persistence diagrams whichis defined as a graph on Auslander-Reiten quivers. Some ofthe computational results applied to proteins and glassesare also shown.

Yasuaki HiraokaKyushu Universityhiraoka@imi.kyushu-u.ac.jp

MS83

Analyzing the Dynamics of Pattern Formation inthe Space of Persistence Diagrams

Persistence diagrams are a relatively new topological toolfor describing and quantifying complicated patterns in asimple but meaningful way. We will demonstrate thistechnique on patterns appearing inRayleigh-Benard con-vection. This procedure allows us to transform experimen-tal or numerical data from experiment or simulation intoa point cloud in the space of persistence diagrams. Thereare a variety of metrics that can be imposed on the spaceof persistence diagrams. By choosing different metrics one

can interrogate the pattern locally or globally, which pro-vides deeper insight into the dynamics of the process of pat-tern formation. Because the quantification is being donein the space of persistence diagrams this technique allowsus to compare directly numerical simulations with experi-mental data.

Miroslav KramarRutgers UniversityDepartment of mathematicsmiroslav@math.rutgers.edu

Konstantin MischaikowDepartment of MathematicsRutgers, The State University of New Jerseymischaik@math.rutgers.edu

Mark PaulDepartment of Mechanical EngineeringVirginia Techmrp@vt.edu

Michael F. SchatzCenter for Nonlinear Science and School of PhysicsGeorgia Institute of Technologymichael.schatz@physics.gatech.edu

Jeffrey TithofCenter for Nonlinear Science and School of PhysicsGeorgia Ijtithof3@gatech.edu

Mu XuDepartment of Mechanical EngineeringVirginia Techxumu8621@vt.edu

MS83

Reconstructing Manifolds and Functions fromPoint Samples

We will survey some fantastic work of Niyogi, Smale andWeinberger which provides explicit bounds on the num-ber of sample points required to reconstruct an underly-ing manifold up to homotopy type with high confidence.Next, we imagine the situation where an unknown func-tion between two such manifolds must be inferred frompoint samples along with the ability to evaluate the func-tion at the domain-samples. Not only can such functionsbe reconstructed up to homotopy from finite point sampleswith high confidence, but also that the entire process of re-construction is robust to certain models of sampling andevaluation noise.

Vidit NandaDepartment of MathematicsUniversity of Pennsylvaniavnanda@sas.upenn.edu

MS83

Word Representations of Structurally StableHamiltonian Flows in Multiply Connected Do-mains and its Applications

We consider Hamiltonian vector fields with a dipole sin-gularity that satisfy the slip boundary condition in two-dimensional multiply connected domains. One exampleof such a Hamiltonian vector field is the incompressible

92 AN14 Abstracts

and inviscid flow in an exterior multiply connected domainin the presence of a uniform flow whose Hamiltonian iscalled the stream function. They are regarded as mathe-matical models of biofluids, rivers and coastal flows. Here,we are interested in structurally stable Hamiltonian vectorfields and their topological structures of contour lines ofthe Hamiltonian, i.e. streamline patterns. We develop anencoding procedure to assign a unique sequence of words toevery streamline pattern. Owing to this word representa-tion, we not only determine all possible streamline patternsin a combinatorial manner, but also describe the complexevolution of fluid flows as a change of words. Moreover,we can determine possible transitions between two differ-ent structurally stable streamline patterns. In the presenttalk, we introduce the theory of word representations forstructurally stable Hamiltonian vector fields and demon-strate how it is applicable to fluid flow problems with vor-tex structures.

Takashi SakajoKyoto Universitysakajo@math.kyoto-u.ac.jp

Tomoo YokoyamaKyoto University of Educationtomoo@kyokyo-u.ac.jp

MS85

High-Order Algorithms for Compressible ReactingFlow with Complex Chemistry

We describe a numerical algorithm for integrating the mul-ticomponent, reacting, compressible Navier-Stokes equa-tions, targeted for direct numerical simulation of combus-tion phenomena. The algorithm addresses two shortcom-ings of previous methods. First, it incorporates an eighth-order narrow stencil approximation of diffusive terms thatreduces the communication compared to existing methodsand removes the need to use a filtering algorithm to removeNyquist frequency oscillations that are not damped withtraditional approaches. The methodology also incorporatesa multirate temporal integration strategy that provides anefficient mechanism for treating chemical mechanisms thatare stiff relative to fluid dynamical time scales. The over-all methodology is eighth order in space with option forfourth order to eighth order in time. The implementationuses a hybrid programming model designed for effective uti-lization of many-core architectures. We present numericalresults demonstrating the convergence properties of the al-gorithm with realistic chemical kinetics and illustrating itsperformance characteristics. We also present a validationexample showing that the algorithm matches detailed re-sults obtained with an established low Mach number solver.

Matthew Emmett, Weiqun ZhangLawrence Berkeley National LaboratoryCenter for Computational Sciences and Engineeringmwemmett@lbl.gov, weiqunzhang@lbl.gov

John B. BellCCSELawrence Berkeley Laboratoryjbbell@lbl.gov

MS85

High-Order Numerical Methods for Fractional

PDEs in Water Wave Propagation

We consider numerical solutions for a fractional PDE aris-ing as a nonreflecting boundary condition in water wavepropagation. The fractional derivative is expressed as di-vergence of a singular integrable convolution. The equationis viewed as a linear conservation law with a nonlocal sin-gular flux. A semi-discrete finite volume scheme uses localpolynomial approximation of order p from solution cell av-erages, followed by exact integration of the singular flux,and yields a surprising convergence rate of p+ 3/2. Timeintegration uses Runge-Kutta methods of matching order.We discuss stability and convergence, and show numericalresults for uniform and nonuniform grids.

David PriggeUniversity of MichiganDepartment of Mathematicsdkprigge@umich.edu

Sean CarneyUniversity of Michigancarneys@umich.edu

Smadar KarniUniversity of MichiganDepartment of Mathematicskarni@umich.edu

Remi AbgrallINRIA Bordeaux Sud-OuestUniversite de Bordeauxremi.abgrall@inria.fr

MS85

Semi-Lagrangian Discontinuous Galerkin Schemesfor the 2+2 Vlasov-Poisson System on Unstruc-tured Meshes

The Vlasov-Poisson system is a set of equations that de-scribe collisionless plasma far from thermodynamic equilib-rium. Numerical difficulties in solving the Vlasov-Poissonsystem include the high-dimensionality and severe timestep restrictions attributed to moderate to large veloci-ties in the system. Explicit Eulerian methods require ex-cessively small time steps, and implicit Eulerian methodshave matrices with large condition numbers. Particle inCell methods together with their Lagrangian and semi-Lagrangian counterparts relax this time step restrictionby solving for the characteristics in the system. We pro-pose a high-order operator split DG method for solving theVlasov-Poisson system. Our hybrid method incorporateslarge time steps using semi-Lagrangian methods, and com-plicated geometries in configuration space with unstruc-tured grids. We present 2D-2V results including the for-mation of a plasma sheath in the proximity of a cylindri-cal Langmuir probe, as well as the simulation of a single-species charged particle beam in an accelerator.

James A. RossmanithDeparment of MathematicsIowa State Universityrossmani@iastate.edu

David C. SealDepartment of MathematicsMichigan State Universityseal@math.msu.edu

AN14 Abstracts 93

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

MS85

Evaluation of Discrete and Continuous Adjoint Ap-proaches for Sensitivity Analysis and Error Estima-tions for Numerical Approximations of HyperbolicPdes with Shocks

The literature on adjoint methods for shock-hydrodynamicapplications is actually rather sparse and recent. Early in-vestigations with continuous adjoint problems required ac-curate knowledge of the discontinuities. Recent work hasshown that this issue may be mitigated by considering analternative dual problem based on the concept of limitingviscocity. We compare and evaluate this approach usingeither a discontinuous Galerkin approximation or a contin-uous Galerkin approximation with flux-corrected transportfor shock-hydrodynamic applications.

Tim WildeyOptimization and Uncertainty Quantification Dept.Sandia National Laboratoriestmwilde@sandia.gov

John N. ShadidSandia National Laboratoriesjnshadi@sandia.gov

Eric C. CyrScalable Algorithms DepartmentSandia National Laboratotorieseccyr@sandia.gov

MS86

Energetic Variational Approaches in Ion Transport

Almost all biological activities involve transport of chargedions in specific biological environments. In this talk, Iwill discuss a unified energetic variational approach de-veloped specifically for these multiscale-multiphysics prob-lems. I will discuss the relevant classical theories and rel-evant physical approaches and methods. I will focus onthe mathematics, in particular the analytical issues arisingfrom these studies.

Chun LiuDepartment of Mathematics, Penn State UniversityUniversity Park, PA 16802liu@math.psu.edu

MS86

From Micropolar Navier Stokes to Ferrofluids,Analysis and Numerics

The Micropolar Navier-Stokes Equations (MNSE), is a sys-tem of nonlinear parabolic partial differential equationscoupling linear velocity, pressure and angular velocity, i.e.:material particles have both translational and rotationaldegrees of freedom. The MNSE is a central component ofthe Rosensweig model for ferrofluids, describing the linearvelocity, angular velocity, and magnetization inside the fer-rofluids, while subject to distributed magnetic forces andtorques. We present the basic PDE results for the MNSE(energy estimates and existence theorems), together with afirst order semi-implicit fully-discrete scheme which decou-

ples the computation of the linear and angular velocities.Similarly, for the Rosensweig model we present the basicPDE results, together with an fully-discrete scheme com-bining Continuous Galerkin and Discontinuous Galerkintechniques in order to guarantee discrete energy stability.Finally, we demonstrate the capabilities of the Rosensweigmodel and its numerical implementation with some numer-ical simulations in the context of ferrofluid pumping bymeans of external magnetic fields.

Ignacio TomasUniversity of Maryland, College Parkignaciotomas@math.umd.edu

MS86

Optimal Energy Norm Error Estimates for a MixedFEM for a Cahn-Hilliard-Stokes System

In this I talk describe a mixed finite element method fora modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation andcoupled fluid flow in immiscible binary fluids and diblockcopolymer melts. The time discretization is based on a con-vex splitting of the energy of the equation. I show that thescheme is unconditionally energy stable and uncondition-ally uniquely solvable and that the discrete phase variableis bounded in L∞ (0, T ;L∞) and the discrete chemical po-tential is bounded in L∞ (

0, T ;L2), for any time and space

step sizes, in two and three dimensions, and for any fi-nite final time T . With this in hand I show that thesevariables converge with optimal rates in the appropriateenergy norms in both two and three dimensions. I willdescribe how this analysis can be extended to two-phasediffuse interface models with large density mismatch. Thisis joint work with Amanda Diegel and Xiaobing Feng.

Steven M. WiseMathematics DepartmentUniversity of Tennesseeswise@math.utk.edu

MS87

Generalized Multiscale Finite ElementMethods forWave Propagation in Heterogeneous Media

Numerical modeling of wave propagation in heterogeneousmedia is important in many applications. Due to the com-plex nature, direct numerical simulations on the fine gridare prohibitively expensive. It is therefore important todevelop efficient and accurate methods that allow the useof coarse grids. In this talk, we present a multiscale finiteelement method for wave propagation on a coarse grid.To construct multiscale basis functions, we start with twosnapshot spaces in each coarse-grid block where one rep-resents the degrees of freedom on the boundary and theother represents the degrees of freedom in the interior. Weuse local spectral problems to identify important modesin each snapshot space. To our best knowledge, this isthe first time where multiple snapshot spaces and multiplespectral problems are used and necessary for efficient com-putations. These multiscale basis functions are coupled viathe symmetric IPDG method which provides a block diag-onal mass matrix, and, consequently, results in fast com-putations in an explicit time discretization. Our methods’stability and spectral convergence are rigorously analyzed.Numerical examples are presented to show our methods’performance. The research is supported by Hong Kong

94 AN14 Abstracts

RGC General Research Fund (Project number: 400411).

Eric ChungThe Chinese University of Hong KongDepartment of Mathematicstschung@math.cuhk.edu.hk

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

Wing Tat LeungTexas A&M Universitysidnet123@yahoo.com.hk

MS87

Maximal Laplace-Beltrami Eigenvalues on Com-pact Riemannian Surfaces

Let (M, g) be a connected, compact Riemannian sur-face and denote by λk(M, g) the k-th eigenvalue of theLaplace-Beltrami eigenproblem. We consider the mapping(M, g) �→ λk(M, g). We propose computational methodsfor solving the eigenvalue optimization problem of maxi-mizing λk(M, g) as g varies within a conformal class [g0]of fixed volume and for the problem where M is addition-ally allowed to vary over surfaces with fixed genus. Sev-eral properties are also studied computationally, includinguniqueness, symmetry, and eigenvalue multiplicity.

Chiu-Yen KaoClaremont McKenna Collegeckao@cmc.edu

Rongjie LaiUniversity of Southern Californiarongjielai@gmail.com

Braxton OstingUniversity of California, Los Angelesbraxton@math.ucla.edu

MS87

A Level Set-Adjoint State Method for the JointTransmission-Reflection First Arrival TraveltimeTomography

We propose an efficient partial differential equation (PDE)based approach to the joint transmission-reflection trav-eltime tomography using first arrivals. In particular, weconsider only the first arrivals from the transmission andreflection measurements at a series of receiver-source pairs.Unlike typical reflection tomography where the locationof the reflector is assumed to be known by some migra-tion techniques, we propose an efficient numerical approachbased on the adjoint state method and the PDE based lo-cal level set method to invert both the piecewise smoothvelocity within the computational domain and the locationof a codimension-one reflector. Since we are using only firstarrivals for tomography, we might not be able to obtain aperfect illumination of the reflector because the relevantinformation might be carried by the later arrivals. In thiswork, we propose an easily computed quantity which canquantify the reliability of our reconstruction. Numericalexamples in both two- and three-dimensions will be givento demonstrate the efficiency of the proposed approach.The work is supported in part by the Hong Kong RGC

under Grant GRF603011.

Wenbin LiDepartment of Mathematics,Hong Kong University of Science and Technologylwb@ust.hk

Shingyu LeungHong Kong University of Science and Technologymasyleung@ust.hk

Jianliang QianDepartment of MathematicsMichigan State Universityqian@math.msu.edu

MS87

Fast Matrix-free Direct Solution and Selected In-version for Seismic Imaging Problems

Fast direct solvers have been shown very useful for mod-eling large inverse problems. In this talk, we show ourrecent development of matrix-free direct solvers for largedense or spare matrices based on rank structures and ran-domized sampling. Unlike existing direct or iterative meth-ods, these new solvers can quickly provide direct solutionswith controllable accuracies, using only a small number ofmatrix-vector multiplications. This is especially attractivefor problems which are ill-conditioned, where it is too ex-pensive to form the matrix, or where there are too manyright-hand sides. The solvers are also useful for problemswith varying parameters (e.g., frequency). We then dis-cuss the application of the methods to the extraction ofselected entries of the inverse of large sparse matrices. Fordiscretized Helmholtz equations, we can quickly computethe diagonal blocks or any off-diagonal entries of the in-verse. Such information is useful for the preconditioning ofthe problem. These methods can significantly improve theefficiency of the solution/inversion of the Hessian matrixin Gauss-Newton iterations for FWI.

Jianlin XiaDepartment of MathematicsPurdue Universityxiaj@math.purdue.edu

Maarten de HoopCenter for Computational & Applied MathematicsPurdue Universitymdehoop@math.purdue.edu

Xiao LiuDepartment of MathematicsPurdue Universityliu867@math.purdue.edu

Yuanzhe XiPurdue Universityyxi@math.purdue.edu

MS88

The Scholarly Work of Reliable and Well-DesignedMathematical Software

Well-designed mathematical software has long been con-sidered a cornerstone of scholarly contributions in compu-tational science. Forsythe, founder of Computer Science atStanford and regarded by Knuth as the ”Martin Luther of

AN14 Abstracts 95

the Computer Reformation,” is credited with inauguratingthe refereeing and editing of algorithms not just for theirtheoretical content, but also for design, robustness, and us-ability. His vision extends to the current day, and this talkpresents a modern perspective of academic software. Thespeaker’s academic software constitutes much of x=A\b inMATLAB when A is sparse, and is widely used in manyother academic, government, and commercial applications,because of its performance and its reliability.

Timothy A. DavisUniversity of FloridaComputer and Information Science and EngineeringDrTimothyAldenDavis@gmail.com

MS88

A Deterministic Guaranteed Automatic Algorithmfor Univariate Function Approximation

Function recovery is a fundamental computational prob-lem. It is desirable to have automatic algorithms for solv-ing such problems, i.e., the algorithms decide adaptivelyhow many and which pieces of function data are neededand then use those data to construct an approximate func-tion. The error of this approximation should be guaranteednot to exceed the prescribed tolerance. We provide a de-terministic guaranteed automatic algorithm for univariatefunction approximation on a given finite interval and proveits reliability.

Yuhan Ding, Fred J. HickernellIllinois Institute of Technologyyding2@hawk.iit.edu, hickernell@iit.edu

MS88

A Survey of Issues in Reliable Computational Sci-ence

Continuing developments in computing software and hard-ware allow us to solve more complex problems than everbefore. However, there remains the nagging question ofhow we can be sure that the answers are correct. This talksurveys the efforts that have been made to ensure that com-putational science is reliable and the work that still needsto be done.

Fred J. HickernellIllinois Institute of TechnologyDepartment of Applied Mathematicshickernell@iit.edu

MS88

Generation of Appropriate Publication Citationsby Numerical Software Libraries

Properly citing academic publications that describe soft-ware libraries and algorithms is the way that open sourcescientific library users “pay” to use the free software. Withlarge multifaceted libraries and applications that use sev-eral such libraries, even the conscientious user may end upciting publications in error or missing relevant publications.Based on a feature recently added to the PETSc numericalsoftware libraries, we suggest an alternative model wherethe library itself generates the bibtex items based on ex-actly what algorithms and portions of the code are used inthe application.

Barry F. SmithArgonne National Lab

MCS Divisionbsmith@mcs.anl.gov

MS89

The Inverse Fast Multipole Method

We present a fast direct solver for dense linear systems aris-ing out of wide range of applications, integral equations,multivariate statistics, radial basis interpolation, etc., toname a few. The highlight of this new fast direct solver isthat the solver scales linearly in the number of unknownsin all dimensions. The solver, termed as the Inverse FastMultipole Method, works on the same data-structure asthe Fast Multipole Method. More generally, the solver ex-tends to the class of hierarchical matrices, denoted as H2

matrices with strong admissibility criteria, i.e., only the in-teraction between particles corresponding to well-separatedclusters is represented as a low-rank matrix, and therebythe algorithm departs from the existing (HSS/ HODLR)approaches. We also present numerical benchmarks in 1Dand 2D validating the linear scaling of the algorithm.

Sivaram AmbikasaranDepartment of MathematicsCourant Institute of Mathematical Sciencessivaram@cims.nyu.edu

Eric F. DarveStanford UniversityMechanical Engineering Departmentdarve@stanford.edu

MS89

Hierarchical Interpolative Factorization

We present some recent results on the efficient factoriza-tion of matrices associated with non-oscillatory integral op-erators in 2D and 3D. In contrast to the 1D case, suchmatrices exhibit considerable rank growth in their off-diagonal blocks when compressed using standard hierar-chical schemes. We combat this with explicit dimensionalreductions via geometric reclustering and additional com-pression. The resulting ranks are much better behaved,yielding essentially linear costs to construct, apply, and in-vert the factorization. Our method is fully adaptive andcan handle both boundary and volume problems.

Kenneth L. HoDepartment of MathematicsStanford Universityklho@stanford.edu

MS89

Randomized Methods for Accelerating StructuredMatrix Computations

Randomized methods have over the last several yearsproven to be powerful tools for computing low-rank approx-imations to matrices whose singular values exhibit appro-priate decay. In this talk, we describe how such techniquescan be extended to certain ”rank-structured” matrices, forwhich only certain off-diagonal blocks (not the matrix it-self) admit accurate low-rank approximations. Matricesof this type often arise in the construction of O(N) directsolvers for elliptic PDEs.

Gunnar MartinssonUniv. of Colorado at Boulder

96 AN14 Abstracts

martinss@colorado.edu

MS89

Parallel Structured Direct Solvers for Nonsymmet-ric and Indefinite Sparse Matrices

Fast structured direct solvers have been extensively studiedfor matrices with a low-rank property. Most existing workconcentrates on symmetric and/or positive definite prob-lems. Here, we exploit this structure in the direct solutionof nonsymmetric and indefinite matrices. Graph orderingand pivoting are performed. The pivoting strategy is de-signed in a way so as to preserve both the sparsity and therank structure. A structured multifrontal LU factorizationis then performed. To implement the method in parallel,we use static mapping to preallocate tasks to processes.Under a certain switching level in the tree, factorizationsare done locally in each process. Beyond the switchinglevel, processes of child nodes form a process grid on parentnodes where structured operations are performed amongthe processes. In such a way, both idling and communi-cations are reduced. All the frontal and update matricesare structured and their factorizations are done in parallel.In the numerical experiments, we show the applications ofthis method to seismic imaging and more general problems.This is joint work with Jianlin Xia.

Zixing XinDepartment of MathematicsPurdue Universityzxin@purdue.edu

MS91

A Fully Implicit Approach for the Solution ofTemporal Multiscale Problems with Application toPower Grid

In this talk, we present a fully implicit approach for tem-poral multiscale problems and discuss a power grid appli-cation that involves two time-scales. At each step of theslow time-scale, our approach involves solving equations forone step of the slow time-scale along with several coupled-in-time equations for the fast time-scale. We will discussthe formulation, preconditioning techniques, and parallelimplementation of our approach.

Shrirang AbhyankarArgonne National Laboratoryabhyshr@mcs.anl.gov

Alexander J. Flueck, Xu ZhangIllinois Institute of Technologyflueck@iit.edu, xu zhang ¡xzhang70@hawk.iit.edu¿

MS91

Gridpack Toolkit for Developing Power Grid Simu-lations on High Performance Computing Platforms

This presentation describes the GridPACK framework,which is designed to help power grid engineers developmodeling software capable of running on todays high per-formance computers. The framework contains modules formanaging power grid networks, distributed matrices andvectors, parallel linear and non-linear solvers, and map-ping functionality to create matrices and vectors based onproperties of the network. Examples of applications builtwith GridPACK will be presented and performance results

will be discussed.

Bruce PalmerPacific Northwest National Labbruce.palmer@pnl.gov

William PerkinsPacific Northwest National Laboratorywilliam.perkins@pnnl.gov

Kevin GlassPacific Northwest National LaboratoryRichland WAkevin.glass@pnnl.gov

Yousu ChenPacific Northwest National Labyousu.chen@pnnl.gov

Shuangshuang Jin, Ruisheng DiaoPacific Northwest National Laboratoryshuangshuang.jin@pnnl.gov, ruisheng.diao@pnnl.gov

Mark RicePacific Northwest National Labmark.rice@pnnl.gov

David Callahan, Steve ElbertPacific Northwest National Laboratorydavid.callahan@pnnl.gov, steve.elbert@pnnl.gov

Zenyu HuangPacific Northwest National Labzenyu.huang@pnnl.gov

MS91

Power Grid Simulation: Needs, State of the Art,Challenges

The complexity of Power Grid is increasing, due to the mas-sive integration of intermittent generation far away fromload centers or dispersed in the distribution grids. ThePower Grid is operated nearest to its limits; more and moreclosed loop controls are installed in the system. Thereis an urgent need to base decisions on a more accuratedescription of the system including its dynamic behavior.The Power Grid simulation must now include time domainsimulation and not only static Power Flow. Most of thePower Grid Simulation tools use fixed time step methodsand hard coded modeling of the components even if onlyvariable time step implicit method can offer a certain levelof confidence for the accuracy of the results in particularat the design stage when the dynamic behavior could befar away from a realistic and expected behavior. A toughrequirement is that physical unstable Power Grid must besimulated as unstable. The ”over damping” intrinsically in-duces by numerical methods which guarantees the dampingof numerical errors, must be minimized as much as possi-ble.

Patrick PanciaticiRTE Francepatrick.panciatici@rte-france.com

MS91

Experiences with Time Integration Algorithms in

AN14 Abstracts 97

a Time Domain Simulation Code

Commercial power grid simulators often employ a stan-dard Trapezoid time integration scheme along with con-stant time steps for their time evolution. In this talk we willdiscuss our experiences in incorporating a variable step in-tegrator within a commercial time domain simulation code.The method used includes a second order predictor anda time step selector based on controlling local truncationerror. Preliminary results show potential for significantspeedup in simulation runs.

Carol S. WoodwardLawrence Livermore Nat’l Labwoodward6@llnl.gov

Chaoyang JingeMITc.jing@myemit.com

Liang MinLawrence Livermore National Laboratorymin2@llnl.gov

Steve G. SmithLawrence Livermore National Labsmith84@llnl.gov

MS92

Mathematics Research: Support, Stakeholders,Accountability

The papers we publish and read are crucial to us as re-searchers. However, there are many other stakeholders ofmathematical publishing as well: our employers, organi-zations like SIAM, corporate publishers, funding agencies,and society, which ultimately pays for and benefits fromthe research. The diverse requirements of stakeholders,together with rapidly advancing technology and economicand social factors have created turmoil and sometimes con-flict in publishing, placing us in a time of both peril andopportunity.

Douglas N. ArnoldSchool of MathematicsUniversity of Minnesotaarnold@umn.edu

MS92

Mathematics and Science Policy: Some Perspec-tives from SIAM’s President

Mathematical sciences are a common denominator behindkey scientific and technological advance, from robotics andgenetics to Big Data, reminding us all of the vital impor-tance of a well-trained STEM community to the future.Accordingly, SIAM plays a pivotal role promoting the visi-bility of mathematics in the halls of government, contribut-ing to science policy discussions, all the while advocatingfor much-needed research dollars and resources to improveSTEM education.

Irene FonsecaCarnegie Mellon UniversityCenter for Nonlinear Analysis

fonseca@andrew.cmu.edu

MS92

Building Support, Building Budgets for the Math-ematical Sciences

I will provide some perspectives on how federal science bud-get requests are built; what kinds of arguments seem tobe effective for increasing requests; and what actions themathematical sciences community can take to justify andsupport such requests.

Peter MarchOhio State UniversityDepartment of Mathematicsmarch.2@osu.edu

MS92

SIAM’s Initiatives and Activities in STEM Educa-tion

In this talk SIAM’s initiatives in STEM education, andtheir relations to science policy will be discussed. Impor-tant aspects of this are the Modeling across the Curricu-lum, MaC, initiative. The two MaC workshops (August2012 and January 2014) and their outcomes will be pre-sented. Other important recent activities include the IN-GenIOuS project which exemplified the way various math-ematical sciences professional societies can work togetherto enhance understanding of the issues and affect policy.

Peter R. TurnerClarkson UniversitySchool of Arts & Sciencespturner@clarkson.edu

MS93

Crop Rotation Modeling and Optimization for Sus-tainable Water Use

We use a simulation-based optimization framework toguide planting decisions with a constraint to account forsustainable water usage. The motivation is the berryfarming region of the Pajaro Valley, CA, which is over-drawing from the aquifer, resulting in seawater intrusion.MODFLOW-FMP is treated as a black-box with optimiza-tion tools from DAKOTA. We compare modeling formula-tions and optimization algorithms to understand trade-offsand identify challenges.

Kathleen FowlerClarkson UniversityDepartment of Mathematicskfowler@clarkson.edu

MS93

Estimating Uncertainty in Annual Energy Produc-tion

A primary quantity in the evaluation of a proposed solarpower plant is the annual energy production (AEP). Un-certainty in the AEP is often quantified by estimating the50th and 10th percentiles by means of a model. The ratiobetween these quantiles significantly affects the financialrisk associated with the proposed power plant, and thus,uncertainty in AEP significantly impacts a proposals suc-cess. We outline a method for estimating uncertainty in

98 AN14 Abstracts

annual energy accounting for the three primary contribu-tions to this uncertainty: inter-annual variability in theweather; uncertainty in measurements of irradiance; andmodeling error in the translation from irradiance to power.We describe how this can be used to improve AEP uncer-tainty estimates in Arizona and Georgia.

Genetha GraySandia National Laboratoriesgagray@sandia.gov

MS93

Analysis of a Managed Aquifer Recharge System

Over the last few decades, groundwater resources have beendepleted at a faster rate than the underlying aquifers havebeen replenished. This imbalance has led water manage-ment agencies to consider managed aquifer recharge net-works, where infiltration basins are used to replenish theaquifers using previously uncaptured storm water runoff.In this work, we utilize optimization to evaluate the costsassociated with constructing such a network while simul-taneously meeting demands placed on the aquifer. Wepresent results for a realistic subwatershed in the PajaroValley region of California. We utilize existing computa-tional tools to determine limits for the constraint equa-tions, to compute subwatershed drainage areas, and tocompute the corresponding storm water runoff over a pre-determined time period consisting of several rain events.We present results that may be used to suggest best prac-tices with regards to regional recharge basin design.

Lea JenkinsDepartment of Mathematical SciencesClemson Universitylea@clemson.edu

MS93

Modeling Impacts of Water Level Control Proce-dures on Water Quality of the St Lawrence River

The St Lawrence River is the 13th largest river on the earthand the greatest single fluvial point source of freshwater tothe North Atlantic. This river is faced with importantecosystem management issues related to the interdepen-dence of environmental issues, e.g., the effect of climatechange on invasive species, nutrient processing, and wa-ter budgets. Our work focus on development of integratedmodeling techniques to explore the interplay of nutrientloading and population dynamics as modulated by the wa-ter control procedures implement to maintain nearly neu-tral levels. Our work seeks to understand the impact ofmore natural level excursions in the river that might beconsidered as a way to maintain the nearshore ecosystem.

Joseph SkufcaClarkson Universityjskufca@clarkson.edu

MS94

Discovery of Principles of Nature from Matrix andTensor Modeling of Large-Scale Molecular Biolog-ical Data

We will describe the use of matrix and tensor decomposi-tions in comparing and integrating different types of large-scale molecular biological data, from different studies ofcell division and cancer and from different organisms, to

computationally predict previously unknown physical, cel-lular and evolutionary mechanisms that govern the activityof DNA and RNA. We will present novel generalizations ofthe singular value decomposition as well as experimentalverification and validation of some of the computationalpredictions.

Orly Alter

Sci Comp & Imaging (SCI) Inst, Bioeng & HumanGenetics DeptsUniversity of Utahorly@sci.utah.edu

MS94

Deconvolution of the Mammalian Cell CycleMetabolome

We have completed a comprehensive mass spectrometryanalysis quantifying hundreds of small molecule metabo-lites throughout the phases of the mammalian cell cy-cle. Using singular value decomposition of the matrix ofmetabolite abundance from a synchronized culture of HeLacells, we have produced a map of metabolic changes byphase of cycle, allowing the characterization of the coor-dinated metabolic changes occurring in the proliferatinghuman tumor cell.

Anneleen Daemen, Christopher Delnagro, Jonathan Choi,Peter Jackson, Thomas O’Brien, Matthew BrauerBioinformatics & Computational BiologyGenentech, Inc.daemena@gene.com, chrisjde@gene.com,choi.jonathan@gene.com, pjackson@stanford.edu, to-mob@gene.com, brauer.matthew@gene.com

MS94

Tensor Completion Methods in Seismology: Re-construction, Denoising and Un-Mixing SeismicSources

Seismic data can be stored in 5D tensors that depend ontime (or frequency), x-y position of receivers, and x-y po-sition of sources. This talk will discuss the developmentof algorithms, inspired by tensor algebra and recent workon nuclear norm minimization, to de-noise and reconstructlarge 5D volumes of seismic data. I will also discuss theapplication of tensor algebra techniques to the problem ofseismic source separation. The latter arises when seismicdata are acquired with sources that are triggered almostsimultaneously in order to save acquisition time.

Mauricio D. SacchiDeparment of PhysicsUniversity of Albertamsacchi@ualberta.ca

MS94

Coherent Pattern Detection in Tensor Data

In real-world applications, multidimensional data may con-tain coherent patterns and we need to perform clusteringsimultaneously along all dimensions of the data to detectthese patterns. In this talk, we will discuss how column-pair based strategies we have developed for biclustering 2Ddata can be extended to higher dimensions. We can usetensor decomposition algorithms to convert a complicatedcoherent pattern detection problem in a high dimensional

AN14 Abstracts 99

data space to simpler 2D data analysis problems.

Hongya Zhao, Hong YanDepartment of Electronic EngineeringCity University of Hong Konghyzhao@cityu.edu.hk, h.yan@cityu.edu.hk

MS95

A Spectral Analysis for Regularization and ImageProcessing Applications

Regularization incorporates prior information into math-ematical models to favor desired solutions. When com-puting piecewise polynomial solutions whose derivatives ofcertain order are sparse, a common regularizer is the L1-norm of the derivatives. Our interest evolved from the factthat approximations to the desired solution are often moreaccurate, up to orders of magnitude, than approximationsto the derivatives. We explain such a phenomenon by aspectral analysis of discrete derivatives and propose alter-native regularizers.

Jorge A. CastanonRice Universityjorge.a.castanon@rice.edu

MS95

Exploiting Nonlinear Structure for Nonconvex Op-timization

Many important design and operational planning problemsgive rise to nonconvex optimization problems. We reviewthe reformulation-linearization technique (RLT) for solvingcertain polynomial optimization problems to global opti-mality. We show how to exploit nonlinear structure inRLT, such as partial separability, and present numerical re-sults that show that the resulting relaxation can be solvedorders of magnitude faster.

Sven LeyfferArgonne National Laboratoryleyffer@mcs.anl.gov

MS95

Topology Control for Load Shed Recovery

We introduce the dc optimal load shed recovery with trans-mission switching model (DCOLSR-TS), which seeks toreduce potential post-contingency load shedding by mod-ifying the system topology. Since solving DCOLSR-TS iscomputationally difficult, we develop a heuristic (MIP-H),which improves the system topology while specifying thesequence of switching operations. We argue the use of aparallelized version of MIP-H for on-line load shed recoveryand recurring contingency-response analysis.

Erick Moreno-CentenoTexas A&M University-College Statione.moreno@tamu.edu

MS95

A Coxian-Phased Approximation for Border Cross-ing Service Times of Commercial Trucks

Since 2011, yearly combined trade exceeds $1 trillion withinNorth American nations, with 80% transported by com-mercial trucks. Previous analytical models assume Marko-vian distributions for service time. Yet, field data lacks

fit, and security procedures such as canine detection createdependencies. This research presents an analytical modelof the border crossing process with an implementation ofMixture of Generalized Erlang (MGE) distributions, alsoknown as Coxian k-phased distributions, as an improvedinspection service time approximation.

Hiram MoyaUniversity of Texas-Pan Americanmoyah@utpa.edu

MS96

A Fast Finite-Volume Eulerian-Lagrangian Lo-calized Adjoint Method for Space-FractionalAdvection-Diffusion Equations

Fractional advection-diffusion PDEs provide an adequateand accurate description of subsurface flow and trans-port processes in porous media that exhibit anomalousdiffusion, which can not be modeled properly by second-order advection-diffusion equations. However, fractionaladvection-diffusion PDEs raise mathematical and numeri-cal difficulties that have not been encountered in the con-text of second-order advection-diffusion PDEs. In thistalk we present a faithful and fast finite-volume Eulerian-Lagrangian localized adjoint method for space-fractionaladvection-diffusion equations, without resorting to anylossy compression, but rather by exploring the structureof the coefficient matrices. These methods have computa-tional cost of O(N log2 N) per time step and memory ofO(N), while retaining the same accuracy and approxima-tion property of the underlying numerical methods.

Mohamed Al-LawatiDepartment of Mathematics and StatisticsSultan Qaboos Universityallawati@squ.edu.om

MS96

Variational Formulation of Problems InvolvingFractional Order Differential Operators

In this talk, we consider boundary value problems involv-ing either Caputo or Riemann-Liouville fractional deriva-tives of order α ∈ (1, 2) on the unit interval (0, 1). Thevariational problem for the Riemann-Liouville case is co-

ercive on the space Hα/20 (0, 1) but the solutions are less

regular, whereas that for the Caputo case involves differ-ent test and trial spaces. We establish the regularity pickupof the solutions of the variational problem, which enablesone to establish convergence rates of the finite element ap-proximations. The analytical theory is then applied to theSturm-Liouville problem involving a fractional derivativein the leading term. Finally, extensive numerical resultsare presented to illustrate the error estimates.

Bangti JinDepartment of MathematicsUniversity of California, Riversidebangti@math.ucr.edu

MS96

High Order Scheme for Caputo Derivative and ItsApplication to Caputo Type Advection-DispersionEquation

In this paper, we derive a high order numerical scheme forα(∈ (0, 1))-th order Caputo derivative of a given function

100 AN14 Abstracts

f(t), where the convergence order is 4−α, which is higherthan any reference available. Then we apply this schemeto Caputo type advection-dispersion equation. The con-vergence, stability, and error estimate for the Caputo typeadvection-dispersion equation are also given.

Jianxiong CaoShanghai Universitycaojianxiong2007@126.com

Changpin LiCollege of SciencesShanghai University, Shanghai, Chinalcp@shu.edu.cn

YangQuan ChenUniversity of California, Mercedychen53@ucmerced.edu

MS96

Fractional Sturm-Liouville Theory for Spectral andSpectral Element Methods

We first introduce a new theory on fractional Sturm-Liouville problems, leading to the development ofexponentially-accurate spectral and spectral element meth-ods for time- and space-fractional PDEs. We introducea new Discontinuous Petrov-Galerkin (DPG) method forfractional hyperbolic problems. Next, we present a uni-fied Petrov-Galerkin (PG) spectral method for low-to-high dimensional fractional advection, diffusion, and Pois-son/Helmholtz problems. We conclude the talk with a frac-tional collocation spectral method for efficient treatment ofnonlinear/multi-term FPDEs.

Mohsen Zayernouri, George E. KarniadakisDivision of Applied MathematicsBrown Universitymohsen zayernouri@brown.edu,george karniadakis@brown.edu

MS97

z-Pares: A Complex Moment Based HierarchicalParallel Eigensolver Package

We have developed a parallel software package for solvinggeneralized eigenvalue problems which is named z-Pares.This software enables users to utilize a large amount ofcomputational resources because of its hierarchical par-allel structure. z-Pares implements the Sakurai-Sugiuramethod proposed in 2003. This method computes an eigen-subspace using complex moments that are obtained bycontour integral. Numerical experiments and performanceevaluations using matrices from some practical applicationsare shown.

Yasunori Futamura, Tetsuya SakuraiDepartment of Computer ScienceUniversity of Tsukubafutamura@mma.cs.tsukuba.ac.jp, saku-rai@cs.tsukuba.ac.jp

MS97

Improved Convergence and Parallel Performancesfor the FEAST Eigensolver

A new numerical scheme is introduced for the symmetricFEAST algorithm. The approach combines the FEAST

subspace iteration technique using the approximate spec-tral projector with a truncated series of expanding gener-ated subspaces. This approach significantly improves thecurrent performance capabilities and convergence efficiencyof the solver. In particular, the approach allows to re-duce considerably the number of linear systems to solve bycontour integration and then optimize the need in parallelcomputing power.

Eric PolizziUniversity of Massachusetts, Amherst, USApolizzi@ecs.umass.edu

MS97

Compact Rational Krylov Methods for SolvingNonlinear Eigenvalue Problems

We present a new framework of Compact Rational Krylov(CORK) methods for solving the nonlinear eigenvalueproblem (NLEP):

A(λ)x = 0.

In this framework, we generalize the linearization basedmethods for solving NLEPs by writing the different linearpencils in a similar form and exploiting the correspondingstructure. The CORK family of rational Krylov methodsalso uses a generalization of the compact Arnoldi decom-position. In this way, the extra memory cost due to thelinearization of the original NLEP is negligible.

Roel Van BeeumenKU Leuvenroel.vanbeeumen@cs.kuleuven.be

Karl MeerbergenK. U. Leuvenkarl.meerbergen@cs.kuleuven.be

Wim MichielsKU Leuvenwim.michiels@cs.kuleuven.be

MS97

Preconditioning Subspace Iteration for LargeEigenvalue Problems with Automated Multi-LevelSub-Structuring

The subspace iteration method (SIM) is a numerical pro-cedure for normal mode analysis which has shown to berobust and reliable for solving very large general eigen-value problems. Although its classical form as introducedby Bathe in the seventies of the last century is less effi-cient than the Lanczos iteration method in terms of CPUtime, it is beneficial in terms of storage use if a very largenumber (say hundreds) of eigenmodes are needed and goodapproximations to the wanted eigenvectors are at hand. Inthis paper we take advantage of the automated multi-levelsub-structuring (AMLS) to construct an accurate initialsubspace for SIM. Along with the AMLS reduction we de-rive a very efficient preconditioning method for SIM whichsolves the linear systems for a transformed system withblock diagonal system matrix whereas the multiplicationwith the mass matrix is executed in the original variables.The presentation is based on a joint paper with Pu Chenand Jiacong Yin, Peking University.

Heinrich VossHamburg Univ of TechnologyInstitute of Numerical Simulation

AN14 Abstracts 101

voss@tu-harburg.de

MS98

Transport Properties of Periodic Metamaterials

Periodic microstructures such as metamaterials may con-tain arrays of nanowires, holes or metallic nanoparticles,whose material properties are complex-valued. Evaluationof their overall properties requires challenging computa-tions. In this talk I will present a new approach based onthe construction of periodic harmonic functions, and derivea formula for the effective tensor that excellently agreeswith numerical calculations. Results of the talk has ap-peared in the Journal of Mathematical Physics 54, 053505(2013).

Yuri GodinUniversity of North Carolina at Charlotteygodin@uncc.edu

MS98

Homogenization for Sea Ice

Sea ice is a leading indicator of climate change, and akey component of Earth’s climate system. As a material,sea ice is a porous composite of pure ice with submillime-ter scale brine inclusions whose volume fraction and con-nectedness vary significantly with temperature. Fluid flowthrough the brine microstructure mediates a broad range ofgeophysical and biological processes. Sea ice also displayscomposite structures over much larger scales. For exam-ple, the sea ice pack itself is a fractal composite of ice floesand ocean, while surface ponds on melting Arctic sea iceexhibit complex dynamics and self-similar geometrical con-figurations. I will discuss how methods of homogenizationand statistical physics are being used to study the effectiveproperties of such systems. This work helps improve ourunderstanding of the role of sea ice in the climate system,and the representation of sea ice in climate models.

Kenneth M. GoldenUniversity of UtahDepartment of Mathematicsgolden@math.utah.edu

MS98

Review of Network Methods for Study of SingularPhenomena in Heterogeneous Media

This talk will provide a comprehensive overview of discretenetwork approximation techniques that have been demon-strated to be an elegant and powerful approach for derivingand justifying asymptotic formulas for (1) effective proper-ties, (2) electric field, and (3) Dirichlet to Neumann map ofhigh contrast disordered composites with inhomogeneitiesclose to touching.

Yuliya GorbDepartment of MathematicsUniversity of Houstongorb@math.uh.edu

MS98

On Global Microchannel Configurations for Liquid-Cooled Electronics Applications with Large PowerDensities

We are interested in extending classical asymptotic ap-

proaches to allow for the spatial pattern wavenumber tovary on the macroscale variables and to find how changesin microstructure geometry affect macroscopic propertiesand transport. To this end, we consider the thermal trans-port of a fluid through nonuniformly spaced laminates, asa simple model for heat sinks in electronics. We find a cou-pled system of partial differential equations that describethe local microscale temperature and deviations from theDarcy pressure. Microscale values of all of these quantitiesare known in terms of the solutions to these effective eqau-tions. Examples of optimal channel geometries are found,which depend on the ability to transfer heat from the de-vice to the enviornment, the orientation of the device withrespect to gravity, and the available power needed to drivethe fluid motion.

Burt S. TilleyWorcester Polytechnic InstituteMathematical Sciences Departmenttilley@wpi.edu

MS99

Deterministic Quantities for UnderstandingStochastic Dynamics

To understand dynamics under uncertainty, it is desirableto examine the quantities that carry dynamical informa-tion. A quantity called escape probability is investigatedin order to describe transitions between dynamical regimes.This leads to consideration of a deterministic nonlocal par-tial differential equation. The speaker will focus on under-standing stochastic dynamics by examining escape proba-bility, in the context of prototypical examples in biophysi-cal and physical settings. Relevant theoretical results willalso be highlighted.

Jinqiao DuanIllinois Institute of Technologyduan@iit.edu

MS99

A Multi-Time-Scale Analysis of Stochastic Chemi-cal Reaction Network

We consider stochastic descriptions of reaction networksin which there are both fast and slow reactions, and thetime scales are widely separated. We obtain a reducedequation on a slow time scale by applying a state spacedecomposition method to the full governing equation anddescribe our reduction method on the reaction simplex. Weillustrate the numerical accuracy of the approximation bysimulating several motivating examples.

Xingye KanUniversity of Minnesotaxykan@ima.umn.edu

MS99

Fokker-Planck Equations for Stochastic DynamicalSystems with Symmetric Levy Motions

The Fokker-Planck equations for stochastic dynamical sys-tems, with non-Gaussian α−stable symmetric Levy mo-tions, have a nonlocal or fractional Laplacian term. Tak-ing advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algo-rithm is proposed to simulate the nonlocal Fokker-Planckequations, under either absorbing or natural conditions.

102 AN14 Abstracts

The scheme is shown to satisfy a discrete maximum prin-ciple and to be convergent. It is validated against a knownexact solution and the numerical solutions obtained by us-ing other methods. The numerical results for two proto-typical stochastic systems, the Ornstein-Uhlenbeck systemand the double-well system are shown.

Xiaofan LiIllinois Institute of Technologylix@iit.edu

MS99

DiPaola-Falsone Formula and Marcus Integral forStochastic Dynamical Systems under non-GaussianWhite Noise

DiPaola-Falsone formula is widely used in engineering andscience. The equivalence between DiPaola-Falsone formulaand Marcus integral was first proved by Sun, Duan and Li( arXiv:1202.2565 , Feb. 2012, the published final versionappeared on Probabilistic Engineering Mechanics, Vol 32,pp:1-4, Jan. 2013). This talk further explores the rela-tionship between DiPaola-Falsone formula and Marcus in-tegral to solve some challenging problems associated withstochastic dyanamcial systems such as deriving Fokker-Planck equations and moment equations .

Xu SunHuazhong University of Science and Technologyxsun@mail.hust.edu.cn

MS100

Stable, Accurate, and Efficient Schemes forParabolic Problems using the Method of LinesTranspose

We present a numerical scheme suitable for solvingparabolic partial differential equations using the Methodof Lines Transpose (MOLT ), and dimensional splitting. Asa result, several one-dimensional boundary value problemscan be solved in O(N) work, to high precision; and a multi-dimensional solution is formed by dimensional sweeps. Weprove that the scheme converges to prescribed orders inboth time and space, and is L-stable. We demonstrate oursolver on the Allen-Cahn equation, and discuss.

Matthew F. CausleyMichigan State Universitycausleym@math.msu.edu

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

MS100

Spectral Deferred Correction Methods for VesicleSuspensions

Many fluid structure interaction problems have changingcharacteristic time scales throughout a simulation. Forsuch problems, an adaptive high-order time integrator isimportant. Adaptive time stepping methods often requireforming multiple numerical solutions to estimate the lo-cal truncation error. However, for vesicle suspensions, bytaking advantage of the underlying physics, we are able toestimate the local truncation error with a single numericalsolution. I will also show how we couple vesicle suspen-

sions with spectral deferred correction methods in order toachieve high-order accuracy.

Bryan D. QuaifeInstitute for Computational Engineering and SciencesUniversity of Texas at Austinquaife@ices.utexas.edu

MS100

Boundary Integral Methods for General EllipticProblems

Elliptic problems such as Poisson, Yukawa, Helmholtz,Maxwell, Stokes and elasticity equations are converted toa consistent overdetermined first-order form. We derivesimple well-conditioned integral equations for this form,analyze their solvability in Sobolev spaces, and build fasthigh-order solution methods with Ewald summation andthe nonuniform fast Fourier transform.

John A. StrainDepartment of MathematicsUniversity of California at Berkeleystrain@math.berkeley.edu

MS100

Volume Integral Equation Approaches for FastField Analysis in Inhomogeneous Media, with ap-plications to MR Imaging and Induction PowerCouplers

Volume integral methods are an appealing choice for com-puting electromagnetic fields in inhomogeneous media,such as a human head or an induction power coupler.These methods generates second-kind integral equations,so matrix-implicit iterative methods should convergencerapidly, though convergence is often slow in practice. Inthis talk we show that the observed slow convergence canbe an artifact of mismatching the material and basis func-tion boundaries, and resolve the mismatch to generatea fast FFT-accelerated iterative method suitable for MRimaging field computation. We also show an approach ef-fective for induction power couplers, where proper bound-aries allow the use of a numerically computed Toeplitz-Hankel decomposition.

Athanasios Polimeridis, Richard ZhangMITthanos p@mit.edu, ryz@mit.edu

Jacob WhiteDept. of Elec. Eng. and Comp. Sci and Res. Lab. Elec.MITwhite@mit.edu

MS101

Computing Singular and Nearly Singular Integrals

We will describe recent progress with J. Wilson and W.Ying in computing a singular or nearly singular integral,such as a harmonic function given by a single or doublelayer potential on a smooth, closed curve surface in 3D. Thepresent approach is suited for use with moving interfacessince the representation of the interface is simple and thevalue of the integral can be found at nearby points as wellas on the surface. The value of the integral is found usinga standard quadrature, with the singularity replaced by aregularized version. Correction terms are then added for

AN14 Abstracts 103

the errors due to regularization and discretization. Theyare needed at points near the surface, since the integralsare nearly singular. Surface integrals can be computedin overlapping coordinate grids; however, in recent work,we improve this method and make it more practical. Weuse a technique of J. Wilson for surface integration whichallows accurate representation without explicit reference tothe coordinate charts. For efficient summation, we use atreecode developed by Duan and Krasny for the Gaussianregularization of the fundamental solution of Laplacian.

J. Thomas BealeDuke Universitybeale@math.duke.edu

Wenjun YingDepartment of Mathematics and Institute of NaturalSciencesShanghai Jiao Tong Universitywying@sjtu.edu.cn

MS101

An Interface Problem for Biomolecules

A biomolecule placed in solvent can be viewed as gener-ating an interface separating the biomolecule and vacuumfrom the surrounding solvent. The size and configuration ofthis interface plays an important role in biomolecule func-tions such as protein folding and docking. We develop thesetup and algorithms to capture such interfaces, using avariational framework and gradient descent flow for en-ergy minimization; the level-set method to handle interfa-cial motion and topological changes; and a new finite dif-ference compact stencil approach to compute electrostaticcontributions.

Li-Tien ChengUniversity of California, San DiegoDepartment of Mathematicslcheng@math.ucsd.edu

Bo LiDepartment of Mathematics, UC San Diegobli@math.ucsd.edu

MS101

An Overlapping Patch Boundary Integral Methodfor Dynamic Interface Problems

A nonstiff boundary integral method for 3D interfacial flowwith surface tension or elastic membrane stress is pre-sented. The stiffness is removed by developing a small-scaledecomposition, based on a generalized isothermal parame-terization of the interface. New applications of the methodto water waves and hydroelastic waves will be discussed.We will also present preliminary work on a new version ofthe method which uses domain decomposition or overlap-ping coordinate patches to describe the interface. This isnecessary to treat problems for which generalized isother-mal coordinates do not provide a global parameterization.It also provides a framework for significant spatial adaptiv-ity of the method. This is joint work with David Ambroseand Carlo Fazioli.

Michael SiegelNew Jersey Institute of Technology

misieg@njit.edu

MS101

A Kernel-Free Boundary Integral Method for Mov-ing Interface and Free Boundary Problems

The kernel-free boundary integral method is a Cartesiangrid-based boundary integral method for elliptic partialdifferential equations. The method avoids direct evalua-tion of boundary integrals and does not need to know ananalytical expression for kernels of boundary integrals orthe fundamental solution of the associated elliptic partialdifferential equation. To evaluate a boundary integral, thekernel-free boundary integral method first solves an equiv-alent interface problem on a Cartesian grid and then inter-polates the grid solution to get values of the correspondingboundary integral at discretization points of the boundaryor interface of the problem. The method is efficient as wellas accurate. Numerical experiments for some moving in-terface and free boundary problems such as the Hele-Shawflow will be presented in this talk.

Wenjun YingDepartment of Mathematics and Institute of NaturalSciencesShanghai Jiao Tong Universitywying@sjtu.edu.cn

MS102

Elastic Structure Coupled with the Air/water In-terface, Inspired by Diving Birds

We investigate how a soft elastic body responds to water-entry impact analogous to a bird diving into water to catchprey. Experimentally, dumbbell shaped objects made oftwo acrylic spheres connected by an elastic rod are droppedinto water. A buckling threshold was calculated using alinear Euler beam theory, which is expressed in terms ofbody geometry, impact force, and elastic rod stiffness. Thisthreshold may have implication as to how birds are able tosafely dive into water at high speeds and avoid any neck-injury.

Sunghwan JungEngineering Science and MechanicsVirginia Techsunnyjsh@vt.edu

MS102

Simulations of Pulsating Sessile Coral and the Re-sulting Fluid Flow

Soft coral of the family Xeniidae have a pulsating motion,a behavior not observed in other immobile marine organ-isms. These pulsations consume a large amount of energy,and determining the benefits of this behavior is vital to un-derstanding the evolution of such animals. We will presentdirect numerical simulations of the pulsations of the coraland the resulting fluid flow by solving the Navier-Stokesequations coupled with the immersed boundary method tomodel individual and interacting polyps.

Shilpa KhatriDepartment of MathematicsUniversity of North Carolina at Chapel Hill

104 AN14 Abstracts

khatri@email.unc.edu

MS102

Performance of Vortex-Based Propulsion on aJellyfish-Like Swimmer

This study develops a computational approach to inves-tigate the vortex wakes generated by an axisymmetricjellyfish-like swimmer. The parameter space of swimmerbody kinematics is explored. The effects of these parame-ters on thrust, input power and circulation are quantified.Two metrics, cruising speed and energy cost of locomo-tion, are used to evaluate the propulsion performance. Theknowledge from this study can be used for the design ofrobotic swimmers that use vortex rings for propulsion.

Jifeng PengDepartment of Mechanical EngineeringUniversity of Alaskajpeng@alaska.edu

MS102

Simulation of a 3D Viscous Flow Past a DeformableThin-Walled Circular Disk Tethered at Its Centerby An IB Method

Motived by animal locomotion in a fluid, we model andsimulate the interaction of a viscous incompressible flowpast a deformable circular thin-walled disk tethered at itscenter. The thin-walled structure is modelled by a classicapproach (shell as an assembly of plate elements) and aspecial finite element method (the corotational scheme) isused to solve numerically the partial differential equations(PDE) governing the motion of the thin-walled structure.The flow is modelled by the classic viscous incompress-ible Navier-Stokes equations and are solved numerically bya popular lattice Boltzmann model (D3Q19). The inter-action between the structure and flow is handled by theimmersed boundary (IB) method. Our simulations haveidentified three distinct deformation modes of the thindisk: circular, folding, and triple-petalled, depending onthe parameters of the flow and the structure. Our resultsare in very good agreement with laboratory experimentspublished very recently (L Schouveiler and C Eloy, Flow-induced drapping, Phys Rev Lett 111: 064301, 2013).

RuNan HuaUniv of Science and Technology of Chinarnhua@ustc.edu.cn

Xiyun LuUniv of Science and Technology of ChinaPR Chinaxlu@ustc.edu.cn

Luoding ZhuIndiana Univ-Purdue Univ Indianapolislzhu@math.iupui.edu

MS103

Multiple Scattering Using the Generalized Foldy-Lax Formulation

Consider the scattering of a time-harmonic plane wave inci-dent on a two-scale heterogeneous medium, which consistsof scatterers that are much smaller than the wavelengthand extended scatterers that are comparable to the wave-length. This talk will present the computational study for

the wave propagation. The imaging functions are designedto visualize the location of the point scatterers and theshape of the extended obstacle scatterers.

Kai HuangDepartment of MathematicsFlorida International Universitykhuang@fiu.edu

Peijun LiDepartment of MathematicsPurdue Universitylipeijun@math.purdue.edu

Hongkai ZhaoUniversity of California, IrvineDepartment of Mathematicszhao@math.uci.edu

MS103

Fast Solver for Multi-Particle Scattering in a Lay-ered Medium

This talk is devoted to the scattering of multi-particle ina layered medium. Assume the medium has three layersand a large number of dielectric particles are randomlydistributed and well separated in the middle layer. Thesize of each particle is comparable to the wavelength andthe shape of each particle is the same up to a rotationbut not restricted to be a disk. The field is excited bysome external source. Direct evaluation for the scatteredfield is notoriously slow due to the large number of un-knowns. We propose a method based on the combinationof Sommerfeld integral, scattering matrix and fast multiplemethod(FMM), which can dramatically speed up the cal-culation. Numerical experiments will be shown to confirmthe efficiency. This is a joint work with Leslie Greengardand Motoki Kobayashi.

Jun LaiCourant Institute of Mathematical Sciencelai@cims.nyu.edu

MS103

The Factorization Method for a Cavity in An In-homogeneous Medium

We consider the inverse scattering problem for a cavitythat is bounded by a penetrable anisotropic inhomoge-neous medium of compact support and seek to determinethe shape of the cavity from internal measurements on acurve or surface inside the cavity. We derive a factorizationmethod which provides a rigorous characterization of thesupport of the cavity in terms of the range of an operatorwhich is computable from the measured data. The supportof the cavity is determined without any a-priori knowledgeof the properties of the surrounding anisotropic medium.Numerical examples are given showing the viability of ourmethod.

Shixu MengUniversity of Delawaresxmeng@math.udel.edu

Houssem HaddarCMAP, Ecole Polytechniquehoussem.haddar@inria.fr

Fioralba Cakoni

AN14 Abstracts 105

University of Delawarecakoni@math.udel.edu

MS103

Surface Plasmon Enhancement in Nano DielectricLayer

We consider the experiments done by Brian Cullum and hisgroup at UMBC of multilayer silver film over nanostructuresubstrates that provide much greater surface-enhanced Ra-man scattering signal compared to single layer of silver withthe same thickness as multilayer. We are going to discussthe multilayer and nano gap effects mathematically in anexperimental related set up and compare the results withthat of the experiments.

Yannan ShenUniversity of Minnesotayxs135630@utd.edu

MS104

Improving Computing Skills of STEM Graduates

Computing skills are today a requirement for any STEMgraduate, yet we still have not found a way to embed com-puting throughout the curriculum in engineering and math-ematics. Many students only experience an ”introductionto programming” class in their freshman year, and then weexpect them to teach themselves whatever they might needto succeed in other courses, and in their careers. It’s nowonder that so many scientist and engineers don’t use bestpractices for scientific computing, including good softwaredesign and development, reproducibility, testing and ensur-ing the permanence of the scientific evidence they create. Afew trends are taking hold that have potential to improvethis situation. Efforts like Software Carpentry (MozillaFoundation) are spreading best practices in software cre-ation and curation: version control, testing, automation,provenance, sharing. Less commonly, some schools are re-vising their approach to computing in the curriculum. Weare conducting a pilot study using just-in-time online mod-ules that teach context-based computing for engineers. Thecontext-based approach has already demonstrated its effec-tiveness, e.g., in the media computing course introduced atGeorgia Tech some years back (which not only improvedstudent success, but also reduced the gender achievementgap in computing). We are extending this approach withthe just-in-time delivery of skills, as a ”performance sup-port” device. In this talk, we will present our theory of ac-tion for this educational intervention, the design concepts,and the preliminary data from our evaluation.

Lorena A. BarbaDepartment of Mechanical EngineeringBoston Universitylabarba@gwu.edu

MS104

Towards Verifiable Publications

Research papers provide the primary mechanism for shar-ing novel methods and data. Papers describe experimentsinvolving small amount of data, derivations on that data,and associated methods and algorithms. Readers repro-duce the results by repeating physical experiments, per-forming hand calculations, and setting forth logical argu-ments. The scientific method in this decade has become de-cisively computational, involving large quantities of data,

complex data manipulation tasks, and large, and often dis-tributed software stacks. The research paper, in its currenttext form, is only able to summarize the associated dataand computation and not able to reproduce it computa-tionally. While papers corroborate descriptions through in-direct means, such as by building companion websites thatshare data and software packages, these external websitescontinue to remain disconnected from the content withinthe paper, making it difficult to verify claims and repro-duce results. There is a critical need for systems that min-imize this disconnect. We describe Science Object Linkingand Embedding (SOLE), a framework for creating verifi-able publications by linking them with associated scienceobjects, such as source code, datasets, annotations, work-flows, re-playable packages, and virtual machine images.SOLE provides a suite of tools that assist the authors tocreate and host science objects that can then be linked withresearch papers for the purpose of assessment, repeatabil-ity, and verification of research. The framework also cre-ates a linkable representation of the science object with thepublication and manages a bibliography-like specificationof science objects. In this presentation, we will introduceSOLE through examples from climate science, chemistry,biology, and computer science, and describe its use for aug-menting the content of computation-based scientific publi-cations.

Tanu MalikComputation InstituteUniversity of Chicagotanum@ci.uchicago.edu

MS104

What Is Worth Reproducing in Computational Sci-ence?

What is driving the call for reproducible science? Thesentiment is that the archival literature should have a re-producible basis and computational science is particularlyephemeral due to the ever-changing landscape of compu-tation. Simultaneously, we see an explosion of papers thatexceeds the ability of scientists to keep up with. Should weadd to this tsunami of data with reproducibility? Perhapsreproducibility will stem the tide and make the literaturemore compact and valuable.

William J. RiderSandia National Laboratorywjrider@sandia.gov

MS104

Constructing Guaranteed Automatic NumericalAlgorithms for Univariate Integration

The project establishes an automatic, adaptive algorithmfor solving univariate integration problems using trape-zoidal rule. The algorithm provides rigorous guaranteesof success and computational cost. The key idea is thatthe error analysis should be done for cones of input func-tions rather than balls. Theoretical and numerical resultsare provided.

Yizhi ZhangDepartment of Applied MathematicsIllinois Institute of Technology

106 AN14 Abstracts

yzhang97.iit@gmail.com

MS105

A Practical Guide to Measure-Theoretic Inversion:Algorithms and Error Estimation

We describe the practical elements of a measure-theoreticframework for solving stochastic inverse problems for de-terministic models with uncertain parameters. Theoreticalresults on the existence and uniqueness of solutions arepresented that outline a basic computational algorithm forapproximation of solutions. We extend the algorithm forestimating solutions in high dimensional parameter spacesand explore an a posteriori error analysis on computedprobabilities of events.

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

Don Estep, Simon TavenerColorado State Universityestep@stat.colostate.edu, tavener@math.colostate.edu

MS105

Spatially Heterogeneous Parameter EstimationWithin the Advanced Circulation (ADCIRC)Model

We describe a framework for estimating spatially heteroge-neous paramters critical to the accuracy of model forecastsof storm surge. We use pixelated land cover data to de-termine the spatial distribtion of land cover classificationswhich we consider certain. We estimate the Manning’s n(a bottom friction paramter) value associated with theseland cover classifications. We solve an inverse problem forthese values using a measure-theoretic approach applied tothe ADCIRC storm surge model.

Lindley GrahamUniversity of Austin at TexasInstitute for Computational Engineering and Sciences(ICES)lgraham@ices.utexas.edu

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Donald EstepColorado State Universityestep@math.colostate.edu or don.estep@gmail.com

Joannes WesterinkDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damejjw@nd.edu

MS105

Uncertainty Quantification and Parameter Estima-

tion for Groundwater Contaminant Transport

The movement of contaminant plumes in undergroundaquifers is highly dependent on many hydrogeological pa-rameters. It is often prohibitively expensive or impossibleto make accurate and reliable measurements of these pa-rameters in the field. We utilize a measure-theoretic inverseframework to perform uncertainty quantification and esti-mation for these parameters. Forward problem calculationsof quantities of interest are improved using a posteriori er-ror estimates calculated by solving adjoint problems.

Steven MattisUniversity of Texas at Austinsteve.a.mattis@gmail.com

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Troy ButlerColorado State Universitybutler@stat.colostate.edu

Donald EstepDepartment of StatisticsColorado State Universityestep@stat.colostate.edu

MS105

Advanced Coastal/Subsurface Models and aMeasure-Theoretic Uq Framework Using RealData

In this talk we’ll focus on advanced models for near shoreflows and multiphase flows in the subsurface. In partic-ular, the focus will be on identifying the computationalissues that need to be addressed in estimating parametersespecially in highly heterogeneous materials in the case ofsubsurface flows. We will also describe methods of dealingwith real data to quantify uncertainties.

Nishant PandaUniversity of Texas at AustinColorado State University¡nishant.panda@gmail.com

MS106

Novelty, Convention and Scientific Impact

Analyzing all 17 million papers in the Web of Sciencedatabase, we employ a methodology based on journal pair-ings that characterizes each paper by the convention andnovelty of the prior work combined. We measure the rel-ative conventionality and novelty of the prior work that apaper combines by examining the journals referenced.

Satyam MukherjeeKellogg School of ManagementNorthwestern Institute on Complex Systemssatyam,mukherjee@gmail.com

MS106

Modeling the Dynamics of Vector-Host Interactionof Easter Equine Encephalitis

Eastern equine encephalitis (EEE) virus is a highly

AN14 Abstracts 107

pathogenic mosquito-borne infectious disease that is re-sponsible for outbreaks in humans and equines, resulting inhigh mortality or severe neurological impairment in mostsurvivors. In the northeastern United States, EEE virusis maintained in an enzootic cycle involving the mosquito,Culiseta melanura, and perching birds in freshwater swamphabitats. Utilizing the SIR model, we examine the influ-ence of the different bird species and time of year in thespread and survival of EEE.

Timothy MullerDepartment of MathematicsOregon State Universitymullert@onid.orst.edu

MS106

Controllability Of Infections In Models ExhibitingMultiple Endemic Equilibria

In mathematical infectious disease epidemiology, reducingR0 to slightly below 1 is sufficient to control the infectionunder consideration. This is true only if the model doesntshow the existence of endemic equilibria for R0 < 1. How-ever, some models of infections exhibits backward bifurca-tion or even hysteresis. In this case reducing R0 to below1 is necessary but not sufficient to eliminate the infection.We show a family of models showing hysteresis and find theconditions on model parameters assuring the elimination ofthe infection.

Muntaser SafanDepartment of Mathematics, Faculty of Science,Mansoura UnivMathematical Computational and Modeling SciencesCenter, ASUmuntaser.safan@asu.edu

MS106

Modeling the Transmission Dynamics of H7N9Avian Influenza Outbreak: Poultry Markets

The outbreak of H7N9 avian influenza in humans in Asiaduring 2013 and 2014 underlines the need for better un-derstanding of the mechanisms by which avian influenzaspreads among bird flocks in live markets. Here we employand susceptible, exposed, infected, recovered (SEIR) modeland fit the parameters of the model to low-pathogenic avianinfluenza prevalence data collected in in Hong Kong livebird markets between 1999 to 2005. In conjunction withclimate data from the Hong Kong observatory, we exam-ine the dependence of model parameters on temperature,relative humidity, and absolute humidity.

Sherry TowersMathematical and Computational Modeling SciencesCenter, ASUsmtowers@asu.edu

MS108

Comparison and Integration of Genomic ProfilesPredict Brain Cancer Survival and Drug Targets

Recently, we demonstrated the effectiveness of the GSVDin comparing patient-matched genomic profiles and identi-fying a pattern of DNA copy-number aberrations that cor-relates with glioblastoma survival. Here, we show cross-platform validation of this signature, bringing it a stepcloser to the clinic. Surprisingly, we also find that the prog-nostic value of the signature is maintained for lower-grade

astrocytomas (LGAs). GSVD of LGA patient-matchedprofiles uncovers molecular similarities and differences be-tween glioblastoma and LGA that suggest drug targets.

Katherine A. AielloSci Comp & Imaging (SCI) Inst & Dept of BioengUniversity of Utahkaiello@sci.utah.edu

Orly AlterSci Comp & Imaging (SCI) Inst, Bioeng & HumanGenetics DeptsUniversity of Utahorly@sci.utah.edu

MS108

Network-Based Methods for Understanding Dis-ease and Predicting Therapy

Cellular processes are driven by complex interacting net-works comprised of diverse cellular components. Althoughwe have seen a revolution in our ability to generate multi-omic data, our ability to use these data to infer informa-tive cellular networks has lagged. We will present data-driven methods that incorporate knowledge about poten-tial network structure that capture essential network fea-tures, leading to clinically-relevant insight into disease pro-cesses.

Kimberly Glass, John QuackenbushDana-Farber Cancer InstituteHarvard School of Public Healthkglass@jimmy.harvard.edu, johnq@jimmy.harvard.edu

MS108

Variant Prioritization by Genomic Data Fusion

Exome sequencing has revolutionized the discovery of mu-tations causing rare monogenic disorders. However, se-quencing identifies many candidate mutations and we needbetter methods to prioritize variants for validation. Ourmethodology for genomic data fusion uses machine learn-ing to integrate multiple strategies to detect deleteriousnessof mutations. Our key innovation is the incorporation of acomputational method for gene prioritization, which scoresmutated genes based on their similarity to known diseasegenes.

Yves MoreauK.U. Leuven, Dept. of Electrical Engineering ESAT-SCDyves.moreau@esat.kuleuven.be

MS108

Discovery of Multidimensional Modules in CancerGenomic Data

Recent technology has made it possible to simultaneouslyperform multi-platform genomic profiling of biological sam-ples, resulting in so-called multidimensional genomic data.Such data provide unique opportunities to study the coor-dination between regulatory mechanisms on multiple lev-els. However, integrative analysis of multidimensional ge-nomics data for the discovery of combinatorial patterns iscurrently lacking. Here, we develop a series of methods toaddress this challenge. We applied this method to datafrom The Cancer Genome Atlas, and prove its utilities inidentifying subtly perturbed cancer pathways and distin-

108 AN14 Abstracts

guishing patients with different survival time.

Xianghong J. ZhouBiological Science and Computer ScienceUniversity of Southern Californiaxjzhou@dornsife.usc.edu

MS109

The Role of Numerical Boundary Procedures in theStability of Perfectly Matched Layers

We address the temporal energy growth associated withnumerical approximations of the perfectly matched layer(PML) for Maxwell’s equations in first order form. Inthe literature, several studies have shown that a numer-ical method which is stable in the absence of the PML canbecome unstable when the PML is introduced. We demon-strate in this talk that this instability can be directly re-lated to numerical treatment of boundary conditions in thePML. At the continuous level, we establish the stability ofthe constant coefficient initial boundary value problem forthe PML. To enable the construction of stable numericalboundary procedures, we derive energy estimates for thevariable coefficient PML. Numerical experiments verify thetheoretical results

Kenneth DuruDepartment of Geophysics, Stanford University, StanfordCAStanford Universitykduru@stanford.edu

MS109

A Fast Algorithm for 3D Azimuthally AnisotropicVelocity Scan

Conventional velocity scan can be computationally expen-sive for large-size seismic data, particularly when the pres-ence of anisotropy requires multiparameter scanning. Weintroduce a fast algorithm for 3D azimuthally anisotropicvelocity scan by generalizing the previously proposed 2Dbutterfly algorithm for hyperbolic Radon transform. Tocompute semblance in a two-parameter residual move-out domain, the numerical complexity of our algorithm isroughly O(N3 logN) as opposed to O(N5) of the straight-forward velocity scan, with N being the representative ofthe number of points in either dimension of data spaceor parameter space. Synthetic and field-data examplesdemonstrate the superior efficiency of the proposed algo-rithm.

Jingwei HuThe University of Texas at Austinhu@ices.utexas.edu

Sergey FomelUniversity of Texas at Austinsergey.fomel@beg.utexas.edu

Lexing YingStanford UniversityDepartment of Mathematicslexing@math.stanford.edu

MS109

Uncertainty Quantification for Large-ScaleBayesian Inverse Problems with Application

to Ice Sheet Models

Modeling the dynamics of polar ice sheets is critical forprojections of future sea level rise. Yet, there remain largeuncertainties in the basal boundary conditions employedwithin ice sheet models, which rely on the incompressibleStokes equations with shear thinning rheology to describethe behavior of ice sheets. We address the problem of quan-tifying uncertainties in the inference of basal boundary con-ditions for large-scale ice sheet inverse problems within theframework of Bayesian inference.

Noemi PetraInstitute for Computational Engineering and Sciences(ICES)The University of Texas at Austinnoemi@ices.utexas.edu

Tobin Isaac, Georg StadlerUniversity of Texas at Austintisaac@ices.utexas.edu, georgst@ices.utexas.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

MS110

Bio-inspired Wing Design for Flying Micro Robots

Low Reynolds number aerodynamics is of great importancefor the optimization of Micro Air Vehicles (MAV). A possi-bility to improve the flight performance of MAVs is to takeinspiration from efficient flyers and swimmers in nature.Studies have shown that the scales on the wing of a but-terfly as well as the ribs present on the dermal denticles ofsharks can have a positive effect on the fluid dynamic per-formance, using different principles of flow boundary layercontrol which increase the lift to drag ratio. In this talk, Iwill present different fabrication methods for mimicking thescales on the wings of butterflies as well as the ribs presenton the skin of sharks. Furthermore, I will present recentwork on high-performance butterfly-inspired wing shapesthat can be used for MAVs and I will outline how optimizedwing designs in robotics can give insights to questions inevolutionary biology.

Mirko KovacFaculty of Engineering, Department of AeronauticsImperial College Londonm.kovac@imperial.ac.uk

MS110

Sharks and Butterflies: Micro-Sized Scales HaveMacro Effects

Sharks and butterflies swim and fly in two completely dif-ferent flow regimes, yet the structure of their surfaces inter-acting with the surrounding fluid look amazingly similar.Both are not smooth but have unique microgeometries thatpotentially work to control the flow. Sharks have move-able scales that appear to act as a passive, flow-actuateddynamic roughness for separation control. Alternatively,butterfly scales appear to fundamentally alter the local skinfriction drag depending on flow orientation.

Amy LangAerospace Engineering and MechanicsUniversity of Alabama

AN14 Abstracts 109

alang@eng.ua.edu

MS110

Friction Enhancement in Snake Locomotion

Snakes are one of the worlds most versatile organisms,at ease slithering through rubble or climbing vertical treetrunks. In this study, we elucidate the physics of snakeinteractions with its complex environment. We present aseries of experiments and supporting mathematical modelsdemonstrating how snakes optimize their speed and effi-ciency by adjusting their frictional properties as a functionof position and time. We use this discovery to build twosnake-robots with enhanced climbing capabilities.

Hamidreza MarviCarnegie Mellon UniversityRobotics Institute and Department of MechanicalEngineeringhmarvi@andrew.cmu.edu

Jeffrey Streator, David HuGeorgia Institute of Technologyjeffrey.streator@me.gatech.edu, hu@me.gatech.edu

MS110

Bioinspired Transformative Skins: From Funda-mental Physics to Applications

As human beings age, our skins develop wrinkles and foldsan undesirable feature that has fueled a multi-billion-dollarskin care industry. Conversely, many animals such ascephalopods can reversibly create skin patterns to matchsurrounding textures for active camouflage. This talk willpresent a unified model that can predict various modesof instabilities and patterns on skins. We will then dis-cuss novel transformative applications of surface instabil-ities such as tunable superhydrophobicity and on-demandstem-cell alignment by seeking bioinspirations.

Xuanhe ZhaoDepartment of Mechanical Engineering & MaterialsScienceDuke Universityxuanhe.zhao@duke.edu

MS111

A Nonlinear QR Algorithm for UnstructurallyBanded Nonlinear Eigenvalue Problems

A variation of Kublanovskaya’s method for solving nonlin-ear eigenvalue problems will be presented for the case ofunstructurally banded problems. The new method is iter-ative and specifically designed for problems too large to usedense linear algebra techniques. A new data structure willalso be presented for storing the matrices to keep memoryand computational costs low. In addition, an algorithmwill be presented for computing several nearby eigenvaluesto already computed eigenvalues.

Charles K. GarrettOak Ridge National Laboratorygarrettck@ornl.gov

Zhaojun BaiDepartments of Computer Science and MathematicsUniversity of California, Davisbai@cs.ucdavis.edu

Ren-Cang LiUniversity of Texas - Arlingtonrcli@uta.edu

MS111

High-Performance Algorithms for ComputingPseudospectra

While numerous authors investigated parallel schemes forcomputing pseudospectra over the past two decades, notechnique has yet emerged as a massively-parallel black-box replacement for Liu’s algorithm, which uses the shiftedSchur factor to drive inverse iteration. This talk proposesand evaluates two classes of distributed-memory algorithmswhich interleave many Lanczos processes in order to greatlyincrease efficiency relative to traditional schemes: (1) Schurdecomposition followed by simultaneous shifted triangu-lar solves, and (2) reduction to Hessenberg form followedby simultaneous shifted Hessenberg solves. While the un-derlying high-performance computational kernels of thesetwo inverse iteration procedures were proposed nearly twodecades ago by Henry in the context of control theory, theyseem to be underappreciated by the pseudospectra commu-nity.

Jack PoulsonGeorgia Institute of Technologyjpoulson@cc.gatech.edu

Greg HenryIntel Corporationgreg.henry@intel.com

MS111

An Indefinite Variant of LOBPCG for Definite Ma-trix Pencils

We propose a novel preconditioned solver for generalizedHermitian eigenvalue problems. More specifically, we ad-dress the case of a definite matrix pencil A − λB (i.e., A,B are Hermitian and there is a shift λ0 such that A−λ0Bis definite). Our new method is a variant of the popularLOBPCG method operating in an indefinite inner product.It also turns out to be a generalization of the recently pro-posed LOBP4DCG method for solving product eigenvalueproblems.

Meiyue ShaoMATHICSEEPF Lausannemeiyue.shao@epfl.ch

MS111

Preconditioned Locally Minimal Residual Methodsfor Large-Scale Eigenproblems

We study the preconditioned locally minimal residualmethod (PLMR) for computing invariant pairs of non-linear eigenproblems of the form T (λ)v = 0. PLMR isa newly-developed preconditioned eigensolver which doesnot require the computation of shift-invert matrix vectorproducts. It bears close connections to several well-knownalgorithms, including LOPCG, Jacobi-Davidson and theinverse-free preconditioned Krylov subspace method. Nu-merical experiments show the flexibility and competitive-ness of PLMR on large-scale benchmark nonlinear eigen-

110 AN14 Abstracts

problems.

Fei XueLouisiana State Universityfxx6187@louisiana.edu

MS112

Multiscale 3D Simulation of Whole Blood in Com-plex Geometry

A 3D multiscale immersed-boundary method is developedto simultaneously simulate major hemodynamics processesin whole blood flowing in microvascular network. Thewhole blood is represented as a suspension of red bloodcells, white blood cells and platelets. The dynamics of eachcell is resolved using a front-tracking method. The vascu-lar network in 3D is modeled directly using a ghost-nodeimmersed-boundary method. The method simulates inter-action among blood cells, platelet adhesion, WBC rollingadhesion, and dispersion of drug-carriers in vascular net-work.

Prosenjit Bagchi, Koohyar Vahidkhah, Peter Balogh,Daniel CordascoRutgers Universitypbagchi@jove.rutgers.edu, k.vahidkhah@gmail.com, pete-balogh1@gmail.com, dan.cordasco@gmail.com

MS112

Simulation of Cellular Blood Flow in Microvessels

The cellular character of blood leads to complex flow phe-nomenology in vessels of comparable size to the blood cells.We have designed a fast spectral boundary integral algo-rithm that simultaneously solves for the dynamics of thehighly deformable blood cells and their flow in such con-figurations. The talk will include an outline this methodand discussion of two applications: the transport of mag-netic nanoparticles amongst the flow blood cells the flowof red-blood cells through a model spleenic slit.

Jonathan B. FreundUIUCjbfreund@illinois.edu

MS112

Long-Wave Dynamics of An Inextensible PlannarMembrane in An Electric Field

We investigate the long-wave nonlinear dynamics of an in-extensible capacitive elastic membrane under ac and dcelectric fields. In the lubrication framework we derive anonlinear evolution equation for the membrane height withan integral constraint. Different membrane dynamics, suchas undulation and flip-flop are found at different electricfield strengths and membrane area. In particular an alter-nating wave on the membrane is found as a response to anac field in the perpendicular direction.

Yuan-Nan YoungDepartment of Mathematical SciencesNJITyyoung@oak.njit.edu

Shravan VeerapaneniDepartment of MathematicsUniversity of Michiganshravan@umich.edu

Michael MiksisDepartment of Engineering Science and AppliedMathematicsNorthwestern Universitymiksis@northwestern.edu

MS112

Extensional Dynamics of Vesicles: AsymmetricRayleigh-Plateau, Burst, and Pearling

When deformable vesicles with an aspect ratio of at least3.5 are subject to extensional flow, they undergo an elon-gational transition above a critical capillary number. Wecomplete 3D boundary integral simulations and develop amultipole expansion spectral theory for vesicles with aspectratios up to 10. We demonstrate that the critical conditionscan be predicted quantitatively. Moreover, a second bursttransition at higher Capillary number which is a preludeto pearling is demonstrated.

Eric S. ShaqfehProfessor, Chemical Engineering & MechanicalEngineeringStanford University, Stanford, CAesgs@stanford.edu

MS113

A Difference Equations Approach to Studying Os-cillations in a Suspension Bridge involving a Non-linear Cable Function

In their 2000 paper ’Multiple Periodic Solutions to aSuspension Bridge Ordinary Differential Equation’, P. J.McKenna and K. S. Moore studied oscillations in a suspen-sion bridge by analyzing periodic solutions to the systemof nonlinear ordinary differential equations

θ′ = − 6K

mcos θ sin θ − δ1 θ

′ + f(t)

y′ = − 2K

my − δ2 y

′ + g

(3)

where δ1, δ2 are damping constants, K, m are positive pa-rameters, g is the force due to gravity and f(t) is an exter-nal force at time t. They used Leray-Schauder Degree The-ory along with numerical methods like the Runge-KuttaMethod to do so. In this talk, I will analyze the periodicsolutions of (1) using a slightly newer more nontraditionalmethod. More specifically, I will introduce a nonlinear ca-ble function c(t) in the y′-equation in (1), discretize theresulting system into a system of two coupled second-ordersecond-degree difference equations and then perform a lo-cal and global stability analysis of this new system usingthe mathematical theory of difference equations. One ofthe biggest challenges of this study will be setting up theglobal analysis framework for general second-order second-degree difference equations along the way since this topicis still largely an open research area. However if success-ful, this study will provide a way to analyze the local andglobal dynamics of periodic solutions of (1) for entire re-gions of initial conditions and parameter values as opposedto a limited number of initial conditions and parametervalues as is generally possible using numerical methods.

Sukanya BasuWentworth Institute of Technology

AN14 Abstracts 111

sukanyabasu@yahoo.com

MS113

From Billiard Dynamics to Thermodynamics

We develop a stochastic approach to thermodynamics us-ing a model of gas-surface interactions derived from a ran-domized version of billiard dynamical systems. We firstrecover some classical results from the kinetic theory ofgases, specifically Knudsen’s Law for angle of reflection.We then derive diffusion constants for particles moving ina channel with rough walls. Finally, we develop notions oftemperature, heat flow, and entropy production, leading tomodels of simple machines.

Scott CookSwarthmore Collegescook3@swarthmore.edu

Tim ChumleyIowa State Universitytchumley@gmail.com

Renato FeresWashington University in St. Louisferes@math.wustl.edu

MS113

Predictor-Based Tracking for Neuromuscular Elec-trical Stimulation

Neuromuscular electrical stimulation is a technology thathelps restore functionality to human limbs. We study neu-romuscular electrical stimulation of the human knee, byproviding a tracking controller such that the tracking errorglobally asymptotically converges to zero, under any inputdelay, a state constraint on the knee position, and sampledstate measurements. We use a new method for construct-ing predictors. This work is joint with Iasson Karafyllis,Marcio de Queiroz, Miroslav Krstic, and Ruzhou Yang.

Michael MalisoffDepartment of MathematicsLouisiana State Universitymalisoff@math.lsu.edu

MS113

Solving Linear Differential Equations and InvertingMatrices: Key Formulas

In preparing a new textbook on Differential Equations andLinear Algebra, one function and one formula took a cen-tral place: the solution g(t) with driving function δ(t) =impulse response = Green’s function = fundamental solu-tion. When the driving function is f(t), the solution is theintegral of g(t− s)f(s). The talk will connect the differentways to find this growth factor g(t). Separately we call at-tention to an amazing expression for A−1 when that matrixis tridiagonal.

Gilbert StrangMITgilstrang@gmail.com

MS114

Boundary Integral Equation for an Ion Channel in

Electrolyte Media

In this talk, computation of the electrostatic potential aris-ing from the hybrid solvation model for ion channels will bediscussed. The Poisson-Boltzmann (P-B) equation is con-sidered. In order to model the cell membrane where theion channel is located, the layered media Green’s functionof the P-B equation is used to develop a boundary integralequation for a finite hight hollow cylinder. Two fictitioushalf spheres are attached top and bottom of the cylinderto avoid edge singularities. Then, a body-fitted mesh isused to discretize the boundary of the cylinder. Severalnumerical examples will be presented.

Min Hyung ChoDepartment of MathematicsDartmouth Collegemin.h.cho@dartmouth.edu

MS114

Life after Sweeping: Hopping for the HelmholtzEquation

The high-frequency 3D Helmholtz equation in a heteroge-neous medium is a difficult question in numerical analysis.Direct solvers are either unwieldy to set up for the prob-lem as a whole, or are hard to link up in a domain decom-position framework. In this work we consider an upwind,incomplete form of Green’s identity as a high-quality trans-mission boundary condition, and use it to define polarizedwaves at interfaces between subdomains. This approach isattractive when local Green’s functions are precomputed,and a fast algorithm is available for their application: weobtain an algorithm with complexity sublinear in the num-ber of unknowns normally needed to represent the solutionin the volume. The new method can be seen as a gener-alization of the sweeping preconditioner of Engquist-Yingto larger subdomains. Joint work with Leonardo Zepeda-Nunez.

Laurent DemanetMathematics, MITdemanet@gmail.com

MS114

A Robust Maxwell Solver in Axisymmetric Geome-tries

Several integral equations used for electromagnetic scat-tering problems suffer from instabilities at low frequencies.Some instabilities occur from purely numerical consider-ations, others from non-trivial topology of the scatterer.In this talk, we review an integral equation formulationbased on generalized Debye sources which addresses bothof these forms of low-frequency breakdown. We will presenta high-order solver based on this formulation for axisym-metric geometries, both for perfect conductor and dielectricproblems.

Michael O’NeilCourant InstituteNew York Universityoneil@courant.nyu.edu

MS114

Scalable Quasi-direct Solvers for 3D Elliptic Prob-lems

While scalable distributed-memory techniques have re-

112 AN14 Abstracts

cently been proposed for the approximate factorization ofHSS/H2/H-matrices defined through a “weak” admissi-bility condition, no scalable HSS/H2/H-matrix factoriza-tion strategy is known which can handle the “strong” ad-missibility condition needed to represent Green’s functionsof 3D elliptic problems. This talk evaluates two direc-tions for circumventing this problem: (1) an approximateNewton-Schulz iteration based upon a new parallelizationof H-matrix/H-matrix multiplication and (2) the recentlyintroduced Hierarchical Interpolative Factorization.

Jack PoulsonInstitute for Computational Engineering and SciencesThe University of Texas at Austinjpoulson@cc.gatech.edu

Austin BensonUC Berkeleyarbenson@stanford.edu

Kenneth L. HoDepartment of MathematicsStanford Universityklho@stanford.edu

Yingzhou LiStanfordryanli@stanford.edu

Lexing YingStanford UniversityDepartment of Mathematicslexing@math.stanford.edu

MS115

A Treecode-Accelerated Boundary IntegralPoisson-Boltzmann Solver for Solvated Proteins

We present a treecode-accelerated boundary integral(TABI) solver for electrostatics of solvated proteins de-scribed by the linear Poisson-Boltzmann equation. Theintegral equations are discretized by centroid collocation.The linear system is solved by GMRES and the matrix-vector product is carried out by a treecode. We computethe electrostatic solvation energy for a protein. We com-pare TABI results with those obtained using the grid-basedAPBS code and we present parallel TABI simulations.

Robert KrasnyUniversity of MichiganDepartment of Mathematicskrasny@umich.edu

Weihua GengSouthern Methodist Universitywgeng@mail.smu.edu

MS115

A Hybrid Immersed Boundary and Immersed In-terface Method for Two-Phase Electrohydrody-namic Simulations

In this talk, we introduce a hybrid immersed boundary(IB) and immersed interface method (IIM) to simulate thedynamics of a drop under the influence of electric field inNavier-Stokes flows. Instead of applying the volume elec-tric force arising from the Maxwell stress tensor, we al-ternatively treat the electric effect as an interfacial force

bearing the normal jump of Maxwell stress on the inter-face. A series of numerical tests with different permittivityand conductivity ratios are performed and compared withthe results obtained by the small deformation theory.

Ming-Chih LaiNCTU, TaiwanDepartment of Applied Mathmclai@math.nctu.edu.tw

MS115

Electro-Hydrodynamics of Vesicle Suspensions

We investigate the mechanics of inextensible capacitiveelastic membranes in applied electric fields. A new bound-ary integral formulation for the coupled electric and hydro-dynamic governing equations will be presented. The mem-brane evolution is characterized by a competition betweenelastic energy, inextensibility, non-local hydrodynamic in-teraction, electric potential and the a.c. field field fre-quency. We will discuss new insights gained via numericalsimulations.

Shravan VeerapaneniDepartment of MathematicsUniversity of Michiganshravan@umich.edu

MS115

Recent Developments of Grid Based ParticleMethod

Grid based particle method (GBPM) is a meshless pointmethod for moving interface problems. GBPM has a par-ticle method nature which can capture a moving interfaceaccurately and efficiently. At the same time these meshlessparticles carry both Lagrangian and Eulerian informationsimultaneously with the help of a underlying grid whichallows one to handle different kind of topological changeseasily. Also adaptivity can be incorporated into GBPMnaturally. In this presentation, I will talk about some re-cent developments in GBPM and using it to model variousmoving interface problems.

Hongkai ZhaoUniversity of California, IrvineDepartment of Mathematicszhao@math.uci.edu

MS116

Ten Good Reasons for using Kernel Reconstruc-tions in Adaptive Finite Volume Particle Methods

This talk discusses the utility of meshfree kernel techniquesin adaptive finite volume particle methods (FVPM). Tothis end, we give ten good reasons in favour of using kernel-based reconstructions in the recovery step of FVPM, whereour discussion addresses relevant computational aspectsconcerning numerical stability and accuracy, as well asmore specific points concerning efficient implementation.Special emphasis is finally placed on more recent advancesin the construction of adaptive FVPM, where WENO re-constructions by polyharmonic spline kernels are used incombination with ADER flux evaluations to obtain highorder methods for hyperbolic problems.

Armin IskeUniversity of HamburgDepartment of Mathematics

AN14 Abstracts 113

armin.iske@uni-hamburg.de

MS116

Model Selections for Polynomial Kernel Regres-sions

Polynomial kernel regression is one of the most commonlyused methods in numerical analysis and statistics. How-ever, in dealing with many real world problems, choosingthe right degree of a polynomial kernel is a challengingissue, as poor choices often lead to either “under-fitting”or “over-fitting”. We propose and study criteria and newstrategies especially designed for this purpose. We provideboth theoretical analysis and numerical simulations to il-lustrate the performance of the new strategies.

Xingping SunMissouri State Universityxsun@missouristate.edu

MS116

Multiscale Rbf Interpolation and Collocation

The combination of compactly supported radial basis func-tions with a residual correction scheme has proven to be nu-merically extremely efficient and accurate for solving bothscattered data interpolation and collocation problems. Inthis talk I will give a short survey of what is known sofar and address recent developments particularly when itcomes to solving partial differential equations. For exam-ple, I will address adaptivity, boundary conditions and scal-ing.

Holger WendlandUniv. GoettingenGermanyholger.wendland@uni-bayreuth.de

MS117

Conjugate Gradient Iterative Hard Thesholding

Conjugate Gradient Iterative Hard Thresholding is agreedy algorithm for solving the compressed sensing andmatrix completion problems combining the advantagesof the low per iteration complexity of Normalized Itera-tive Hard Thresholding and the effectiveness of projectionbased algorithms such as Hard Thresholding Pursuit andCompressive Sampling Matching Pursuit. This talk willalso introduce the compressed sensing and matrix comple-tion problems as examples of low dimensional models.

Jeffrey D. BlanchardDepartment of Mathematics and StatisticsGrinnell Collegejeff@math.grinnell.edu

Jared TannerUniversity of Oxfordtanner@maths.ox.ac.uk

Ke WeiMathematics InstituteUniversity of Oxford

wei@maths.ox.ac.uk

MS117

Denoising Simultaneously Structured Signals

Models or signals exhibiting low dimensional behavior (e.g.,sparse signals, low rank matrices) arise in many applica-tions in signal processing and machine learning. We focuson models that have multiple structures simultaneously;e.g., matrices that are both low rank and sparse, arising inphase retrieval, quadratic compressed sensing, and clusterdetection in social networks. We consider the estimation ofsuch models from direct observations corrupted by additiveGaussian noise. Our main result is to provide tight upperand lower bounds on the mean squared error (MSE) of aconvex denoising program that uses a combination of reg-ularizers to induce multiple structures. In the case of lowrank and sparse matrices, we quantify the gap between theMSE of the convex program and the best achievable error,and also compare it with a simple nonconvex thresholdingalgorithm in a certain regime of signal-to-noise ratio.

Maryam FazelUniversity of WashingtonElectrical Engineeringmfazel@ee.washington.edu

Samet OymakCalifornia Institute of Technologysoymak@caltech.edu

Amin JalaliUniversity of Washingtonamjalali@uw.edu

Babak HassibiElectrical Eng. DeptCaltech, Pasadena, CAhassibi@systems.caltech.edu

MS117

Frontiers of Atomic Norm Minimization

We often model signals from the physical world withcontinuous parameterizations. Unfortunately, continuousmodels pose problems for the tools of sparse approxima-tion, and popular discrete approximations are fraught withtheoretical and algorithmic issues. In this talk, I willpropose a general, convex-optimization framework—calledatomic-norm minimization—-that obviates discretizationand gridding by generalizing sparse approximation to con-tinuous dictionaries. I will discuss recent theoretical andalgorithmic advances that demonstrate the utility of thisframework in a diverse set of applications.

Ben RechtUC Berkeleybrecht@eecs.berkeley.edu

MS117

Modal Analysis with Compressive Measurements

We consider the problem of determining the mode shapesof a structure from a compressed collection of vibrationaltime series recordings, as might be collected by a networkof wireless sensor nodes performing Compressive Sensing(CS). We consider three different CS strategies, analyze asimple SVD-based method for estimating the mode shapes

114 AN14 Abstracts

from compressive samples without performing CS recon-struction, and provide novel finite sample reconstructionbounds. This work has potential applications in structuralhealth monitoring.

Jae Young ParkEECS DepartmentUniversity of Michiganjaeypark@umich.edu

Michael B. WakinDept. of Electrical Engineering and Computer ScienceColorado School of Minesmwakin@mines.edu

Anna GilbertDepartment of MathematicsUniversity of Michiganannacg@umich.edu

MS118

Universe Geometry

This brief history will elucidate the role of supercomput-ers in enhancing progress in mathematics. Moving throughthe exciting history of supercomputing, we will broach thetop supercomputers of its time and its important applica-tions. This will be followed by a stimulating story about asupercomputer simulation that has proven the validity ofa theory that was proposed 40 years ago for the evolutionof the universe.

Samar A. AseeriComputational Scientist at the KAUST SupercomputingLaboratorysamar.aseeri@kaust.edu.sa

MS118

Understanding the Universe with Petascale Simu-lations - the Enzo Cosmology Code

Abstract not available at time of publication.

Brian O’SheaDepartment of Physics and AstronomyMichigan State Universityoshea@msu.edu

MS118

Talk title: Creating a Virtual Universe

Abstract not available at time of publication.

Mark VogelsbergerMITaddress:vmvogelsb@cfa.harvard.edu

MS119

Irregular Polyomino Tiling via Integer Program-ming with Application in Phased Array AntennaDesign

A polyomino is a generalization of the domino and is cre-ated by connecting a fixed number of unit squares alongedges. Tiling a region with a given set of polyominoesis a hard combinatorial optimization problem. This workis motivated by a recent application of irregular poly-omino tilings in the design of phased array antennas. Ex-

act, approximate, and heuristic solution methodologies areproposed. Encouraging computational results includingphased array antenna simulations are reported.

Serdar KarademirUniversity of Floridakarademir@ufl.edu

Oleg A. ProkopyevUniversity of Pittsburghprokopyev@engr.pitt.edu

MS119

Accelerated Bregman Operator Splitting withVariable Stepsizes

In this talk, we present a novel scheme, namely accel-erated Bregman operator splitting with variable stepsize(ABOSVS), for solving problems of the type min{1/2||Au−f ||22 + φ(Bu)}, where φ may possibly be nonsmooth. Ourproposed algorithm incorporates a multi-step accelerationscheme into BOSVS to improve the convergence rate.ABOSVS is compared with other state-of-art algorithmsby using partially parallel magnetic image reconstruction.The numerical results show that the proposed ABOSVS al-gorithm performs more efficiently in terms of image qualityand CPU time.

Xianqi Li, Yunmei ChenDepartment of MathematicsUniversity of Floridaxianqili@ufl.edu, yun@ufl.edu

Yuyuan OuyangDepartment of Mathematics, University of Floridaouyang@ufl.edu

MS119

Accelerated First-Order Method for Convex Com-posite Optimization and the Applications in ImageAnalysis

We present an accelerated scheme for solving a class of con-vex composite optimization problems and its application inimage analysis. The proposed AL-ADMM method, namelyaccelerating linearized alternating direction method of mul-tipliers, has accelerated rate of convergence in terms ofits dependence on Lipschitz constant of the smooth com-ponent. A backtracking technique for searching Lipschitzconstant is also proposed for practical performance.

Yuyuan OuyangDepartment of Mathematics, University of Floridaouyang@ufl.edu

Yunmei ChenDepartment of MathematicsUniversity of Floridayun@ufl.edu

Guanghui LanDepartment of Industrial and SystemsUniversity of Floridaglan@ise.ufl.edu

Eduardo Pasiliao Jr.AFRL Munitions Directorate, Air Force ResearchLaboratory

AN14 Abstracts 115

eduardo.pasiliao@eglin.af.mil

MS119

Image Reconstruction for Dynamic Cone BeamComputed Tomography

Dynamic cone beam computed tomography (CBCT) hasbeen developed to provide respiratory phase correlatedimaging in image guided therapy. The difficulty of acqui-sition of dynamic CBCT images is due to the fact thatmultiple phase binning of CBCT scans leading to insuffi-cient number of projections available for image reconstruc-tion. By making use of the redundant information sharedby constituent scans, we proposed a computational modelto reconstruct dynamic CBCT images with relatively highspatial resolution as well as utilizing the temporal coher-ence.

Hao ZhangDepartment of Mathematicshza39@ufl.edu

Yunmei ChenDepartment of MathematicsUniversity of Floridayun@ufl.edu

MS120

Qualitative Assessment of the Role of ClimateChange on Malaria Transmission Dynamics

A new model for assessing the impact of climate change onmalaria transmission dynamics is developed. The disease-free periodic solution of the resulting non-autonomous de-terministic model is shown to be locally-asymptotically sta-ble when the associated basic reproduction ratio is less thanunity. The disease persists in the community when the re-production ratio is greater than unity. The effect of un-certainties of the estimates of the parameter values used inthe numerical simulations of the model is analyzed. Nu-merical simulations of the model suggest that disease bur-den increases with increasing temperature (as measured interms of the cumulative number of new cases and malaria-induced mortality) in the community. Furthermore, simu-lations of the autonomous version of the model suggest thatpersonal protection measures (against mosquito bites) aremarginally more effective than mosquito-reduction mea-sures. As expected, the universal anti-malaria strategy(which combines both mosquito-reduction and personalprotection strategies) is the most effective means to combatthe spread of malaria in the population.

Folashade AgustoAustin Peay State Universityfbagusto@gmail.com

MS120

A Structured Avian Influenza Model with Imper-fect Vaccination

We introduce a model of avian influenza in domestic birdswith imperfect vaccination and age-since-vaccination struc-ture. The model has four components: susceptible birds,vaccinated birds (stratified by vaccination-age), asymp-tomatically infected birds, and infected birds. The modelincludes reduction of probability of infection, decreasingseverity of disease of vaccinated birds and vaccine waning.The basic reproduction number, R0, is calculated. The

disease-free equilibrium is found to be globally stable un-der certain conditions when R0 < 1. When R0 > 1, exis-tence of an endemic equilibrium is proved (with uniquenessfor the ODE case and local stability under stricter condi-tions) and uniform persistence of the disease is established.The inclusion of reduction in susceptibility of vaccinatedbirds, reduction in infectiousness of asymptomatically in-fected birds and vaccine waning can have important im-plications for disease control. We analytically and numer-ically demonstrate that vaccination can paradoxically in-crease the total number of infected, resulting in the “silentspread’ of the disease. We also study the effects of vac-cine efficacy on disease prevalence and the minimum criti-cal vaccination coverage, a threshold value for vaccinationcoverage to avoid an increase in total disease prevalencedue to asymptomatic infection.

Hayriye Gulbudak, Maia MartchevaUniversity of Floridahgulbudak@ufl.edu, maia@ufl.edu

MS120

Modeling Avian Influenza and Implications forControl

A mathematical model of avian influenza which involveshuman influenza is introduced to better understand thecomplex epidemiology of avian influenza. The model isused to rank the efficacy of the current control measures.We find that culling without re-population and vaccinationare the two most efficient control measures. Control mea-sures applied to humans, such as wearing protective gear,are not very efficient. Furthermore, we find that shoulda pandemic strain emerge, it will invade, possibly displac-ing the human influenza virus in circulation at that time.Moreover, higher prevalence levels of human influenza willobstruct the invasion capabilities of the pandemic H5N1strain. This effect is not very pronounced, as we find that1% increase in human influenza prevalence will decrease theinvasion capabilities of the pandemic strain with 0.006%.

Maia MartchevaUniversity of Floridamaia@ufl.edu

MS120

Evaluation of Malaria Vaccines as a Control Strat-egy in a Region with Naturally Acquired Immunity

The malaria vaccine RTS,S has reached the final stages ofvaccine trials, demonstrating an efficacy of roughly 50%in children. Regions with high prevalence tend to havehigh levels of naturally acquired immunity (NAI) to severemalaria. I will introduce a model developed to addressconcerns about how these vaccines will perform in regionswith existing NAI, discuss some analytic results and theirpublic health implications, and reframe our question as anoptimal control problem.

Olivia ProsperUniversity of Floridaprosper.olivia@gmail.com

Nick RuktanonchaiUniversity of FloridaDepartment of Biologynrukt00@gmail.com

Maia Martcheva

116 AN14 Abstracts

University of Floridamaia@ufl.edu

MS121

Undergraduate Modeling Curricula

Abstract not available at time of publication.

Jeff HumpherysDepartment of MathematicsBrigham Young Universityjeffh@math.byu.edu

MS121

Modeling in the Early Grades

Abstract not available at time of publication.

Rachel LevyHarvey Mudd Collegelevy@hmc.edu

MS121

Mathematical Modeling in High School

Abstract not available at time of publication.

Katherine SochaMath for Americaksocha@mathforamerica.org

MS121

SIAM-NSF Modeling across the Curriculum initia-tive and Workshops: Introduction

Abstract not available at time of publication.

Peter R. TurnerClarkson UniversitySchool of Arts & Sciencespturner@clarkson.edu

MS122

Reduced Order Modeling of the Quasi-GeostrophicEquations

This talk surveys some recent developments in the mod-eling, analysis and numerical simulation of the quasi-geostrophic equations, which describe the wind-drivenlarge scale ocean circulation. A new large eddy simula-tion model, which is based on approximate deconvolution,is proposed for the numerical simulation of the one-layerand two-layer quasi-geostrophic equations. A reduced or-der model based on the proper orthogonal decomposition isalso proposed as an accurate and computationally efficienttool for the numerical simulation of the quasi-geostrophicequations. The error analysis for the finite element dis-cretization and the numerical investigation of the new mod-els are also presented.

Traian IliescuDepartment of MathematicsVirginia Tech

iliescu@vt.edu

MS122

Fluid-Structure Interaction Decoupling by Opti-mization

Simulating fluid-structure interactions is challenging dueto the tight coupling between the fluid and solid substruc-tures. An approach is presented that allows the problemto be decoupled by reformulating it in an optimal controlsetting. A control is introduced to minimize the jump in ve-locity and stress on the interface. An analytical frameworkis developed to show the well-posedness of the optimalitysystem for the time dependent case.

Paul A. KuberryClemson Universitypkuberr@clemson.edu

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

MS122

Numerical Approximation of Non-Newtonian Fluid- Structure Interaction Problems

Fluid-structure interaction (FSI) problems governed bynon-Newtonian fluid models are considered. For viscoelas-tic and quasi-Newtonian fluid models variational formula-tions of the coupled FIS systems are developed based onthe Arbitrary Lagrangian-Eulerian (ALE) method. Stabil-ity of the time discretized systems and finite element errorestimates are discussed, and numerical results will be pre-sented.

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

Shuhan XuClemson Univeristyshuhanx@g.clemson.edu

MS122

Greenland Ice-sheet Initialization: Optimal Con-trol and Bayesian Calibration Approaches

Greenland ice sheet plays a significant role in climatologyand, in particular, in sea-level rise. In order to simulatethe evolution of the ice sheets we need to know the currentthermomechanical state of the system. In this talk, weseek an initial state for the Greenland ice sheet via theestimation of the basal sliding coefficient and the bedrocktopography. We consider both a deterministic approach(PDE constrained optimization) and a Bayesian calibrationapproach.

Michael S. EldredSandia National LaboratoriesOptimization and Uncertainty Quantification Dept.mseldre@sandia.gov

John D. JakemanSandia National Labsjdjakem@sandia.gov

AN14 Abstracts 117

Irina KalashnikovaSandia National Laboratoriesikalash@sandia.gov

Mauro PeregoCSRI Sandia National Laboratoriesmperego@fsu.edu

Stephen PriceLos Alamos National Laboratorysprice@lanl.gov

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

Georg StadlerUniversity of Texas at Austingeorgst@ices.utexas.edu

MS123

Optimal Shrinkage of Singular Values

It is common practice in multivariate statistical analysisto reduce dimensionality by performing SVD or PCA, andkeeping only r singular values. For white noise and ap-propriate asymptotic frameworks, random matrix theorydescribes the random behavior of the singular values andvectors of Y. It delivers simple, convincing answers to arange of fundamental questions, such as the location of theoptimal singular value threshold and the shape of the op-timal singular value shrinker.

Matan GavishDepartment of StatisticsStanford Universitygavish@stanford.edu

David L. DonohoStanford UniversityDepartment of Statisticsdonoho@stanford.edu

MS123

Tensor GSVD for Comparison of Two Column-Matched and Row-Independent Large-ScaleBiomedical Datasets

There exists a fundamental need for frameworks that cansimultaneously compare and contrast large-scale data ten-sors, e.g., biomedical datasets recording multiple aspectsof a disease across a set of patients. We describe a novelexact and unique simultaneous decomposition for two ten-sors that generalizes the GSVD to a tensor GSVD. Weshow that tensor GSVD comparisons of two ovarian cancerpatient- and platform-matched genomic datasets from TheCancer Genome Atlas predict survival and drug targets.

Theodore E. Schomay, Preethi Sankaranarayanan

Sci Comp & Imaging (SCI) Inst & Dept of BioengUniversity of Utahtschomay@sci.utah.edu, preethi@sci.utah.edu

Orly AlterSci Comp & Imaging (SCI) Inst, Bioeng & HumanGenetics DeptsUniversity of Utah

orly@sci.utah.edu

MS123

Pattern Discovery and Cancer Gene Identificationin Integrated Cancer Genomic Data

We propose a latent variable approach for joint clusteringof discrete and continuous variables that arise from inte-grated genomic, epigenomic, and transcriptomic profilingin large-scale genome characterization studies. A penalizedlikelihood approach is implemented for variable selection.We show application of the method to The Cancer GenomeAtlas (TCGA) pan-cancer cohort with whole-exome DNAsequencing, SNP 6.0 array, and mRNA sequencing data in3,000 patient samples spanning 12 cancer types.

Ronglai ShenDepartment of Epidemiology & BiostatisticsMemorial Sloan-Kettering Cancer Centershenr@mskcc.org

MS123

Breaking the Curse of Dimensionality Using De-compositions of Incomplete Tensors

The number of elements in higher-order tensors scales ex-ponentially in the number of dimensions as do the compu-tation and memory costs. Because of this, working withvery large full tensors becomes infeasible. To alleviate orbreak this curse of dimensionality, tensor decompositionscan be used instead. We discuss such decompositions andstructure-exploiting, compressed sensing-type algorithmsto compute these decompositions of large tensors while us-ing only a small fraction of known elements.

Nico Vervliet, Otto DebalsDepartment of Electrical Engineering (ESAT)KU Leuvennico.vervliet@esat.kuleuven.be,otto.debals@esat.kuleuven.be

Laurent Sorber, Lieven De LathauwerKatholieke Universiteit LeuvenLaurent.Sorber@cs.kuleuven.be,lieven.delathauwer@kuleuven-kulak.be

MS124

Div First-Order System LL* for Elliptic Systems

The first-order system LL* (FOSLL*) approach was in-troduced in order to retain the full efficiency of the L2

norm first-order system least-squares (FOSLS) approachwhile exhibiting the generality of the inverse-norm FOSLSapproach. In this talk, we will present the div FOSLL*approach to the Stokes and linear elasticity equations andthe a priori and a posteriori error estimations.

Zhiqiang CaiPurdue UniversityDepartment of Mathematicszcai@math.purdue.edu

MS124

What Kinds of Singularities can we Deduce fromthe Corner Singularity Theory of the CompressibleViscous Stokes Flows?

Based on some known corner singularity and regularity re-

118 AN14 Abstracts

sults for the compressible viscous Stokes equations, I willdescribe certain singularities of solutions in the domain,for instance, interior layer, jump discontinuities of the den-sity solution across the streamline emanating from the non-convex vertex or grazing vertex.

Jae Ryong Kweon

POSTECH(Pohang University of Science and Technology)Koreakweon@postech.ac.kr

MS124

Compact Implicit Integration Factor Method forHigh Order Differential Equations

When developing efficient numerical methods for solvingparabolic types of equations, severe temporal stability con-straints on the time step are often required due to the high-order spatial derivatives and/or stiff reactions. The im-plicit integration factor (IIF) method, which treats spatialderivative terms explicitly and reaction terms implicitly,can provide excellent stability properties in time with niceaccuracy. One major challenge for the IIF is the storageand calculation of the dense exponentials of the sparse dis-cretization matrices resulted from the linear differential op-erators. The compact representation of the IIF (cIIF) canovercome this shortcoming and greatly save computationalcost and storage. On the other hand, the cIIF is oftenhard to be directly applied to deal with problems involvingcross derivatives. In this talk, by treating the discretiza-tion matrices in diagonalized forms, we present an efficientcIIF method for solving a family of semilinear fourth-orderparabolic equations, in which the bi-Laplace operator is ex-plicitly handled and the computational cost and storage re-main the same as to the classic cIIF for second-order prob-lems. In particular, the proposed method can deal with notonly stiff nonlinear reaction terms but also various types ofhomogeneous or inhomogeneous boundary conditions. Nu-merical experiments are finally presented to demonstrateeffectiveness and accuracy of the proposed method.

Xingfeng LiuUniversity of South Carolinaxfliu@math.sc.edu

MS124

An Asymptotic Splitting Approximation for HighlyAccurate Numerical Solutions of Differential Equa-tions

This talk explores applications of the asymptotic splittingmethod for approximating highly oscillatory solutions ofthe systems of paraxial Helmholtz equations. An eikonaltransformation is introduced for oscillation-free platformsand matrix operator decompositions. It is found that thesequential, parallel and combined exponential splitting for-mulas possess not only anticipated algorithmic simplicityand efficiency, but also the accuracy and asymptotic sta-bility required for highly oscillatory wave computations viasystems of partial differential equations.

Qin ShengDepartment of MathematicsBaylor UniversityQin Sheng@baylor.edu

Hai-Wei SunDepartment of MathematicsUniversity of Macau

hsun@umac.mo

MS125

Recent Progress in MatCont Development

MatCont is an interactive MATLAB software for numeri-cal analysis of ODEs in Rn. It allows to simulate ODEs,continue equlibria and cycles in one parameter, and studybifurcations of equilibria, cycles, and homoclinic orbits intwo-parameter ODEs. Recent features of MatCont will bepresented, including normal form computations for codim2 bifurcations of cycles and initialization of homoclinic or-bits. Decisions made during the development and futureof the software will be discussed.

Iourii KouznetsovDepartment of Mathematics, Utrecht UniversityThe NetherlandsI.A.Kouznetsov@uu.nl

MS125

Numerical Analysis of Travelling Waves in NeuralFields

We consider waves in integro-differential systems modellingneural activity. For special cases of spatial coupling a suit-able ODE can be derived whose solutions correspond topatterns of the original system. We exploit the numericaltoolbox MATCONT to construct a complete bifurcationdiagram for smooth nonlinearities. For more general, buttranslationally invariant connectivity including transmis-sion delays, we propose novel numerical schemes to com-pute travelling waves and discuss its implementation.

Hil MeijerTwente University, NLh.g.e.meijer@utwente.nl

MS125

(Parallel) Auto and Applications: Past, Presentand Future

We show how the numerical continuation package AUTO-07p can effectively run in parallel using MPI on modernHPC clusters, and explain its algorithms. Much largerproblems can now be continued than was reasonably pos-sible in the past. Combining with the method of continua-tion of orbit segments we can investigate how certain ODEand PDE solutions suddenly change as parameters crosscritical values. Several examples illustrate this technique.Lastly, possible future directions for AUTO are given.

Bart E. OldemanCLUMEQ (McGill, ETS)bart.oldeman@mcgill.ca

MS125

Analysis of Nonsmooth Systems: Perspectives andDirections

The realisation that many real-world systems possess nons-mooth characteristics has opened up a plethora of differentdirections for the analysis of such systems. In this presen-tation I will give a background to nonsmooth systems, de-scribe a few of the analysis techniques employed, and alsodiscuss where the field is heading. Open problems that willkeep the dynamical systems community busy for years to

AN14 Abstracts 119

come will be highlighted through a couple of examples.

Petri T. PiiroinenSchool of Mathematics, Statistics and AppliedMathematicsNational University of Ireland, Galwaypetri.piiroinen@nuigalway.ie

MS126

A Locally Accelerated Block Preconditioned Steep-est Descent Method for Ill-conditioned GeneralizedHermitian Eigenvalue Problems

In this talk, we first present a locally accelerated block pre-conditioned steepest descent (LABPSD) algorithm for solv-ing ill-conditioned generalized Hermitian eigenvalue prob-lems, such as arising in orbital based ab initio methods forelectronic structure calculations. We then revisit the classi-cal convergence analysis of steepest descent algorithms andprovide a new analysis to justify the efficiency of LABPSD.

Zhaojun BaiDepartments of Computer Science and MathematicsUniversity of California, Davisbai@cs.ucdavis.edu

Yunfeng CaiPeking University, P. R. Chinayfcai@math.pku.edu.cn

John PaskLawrence Livemore National Labpask1@llnl.gov

N. SukumarUniversity of California, Davisnsukumar@ucdavis.edu

MS126

Structured Eigensolvers for the Analysis ofSymmetry-Breaking in Next Generation Gyro-scopes

In 1890, G. H. Bryan demonstrated that when a ring-ing wine glass rotates, the shape of the vibration patternprecesses. This effect is the basis for a family of high-precision gyroscopes. Mathematically, the precession canbe described in terms of a symmetry-breaking perturbationdue to gyroscopic effects of a geometrically degenerate pairof vibration modes. Unfortunately, current attempts tominiaturize these gyroscope designs are subject to fabrica-tion imperfections that also break the device symmetry. Inthis talk, we describe the structure of the eigenvalue prob-lems that arise in simulation of both ideal and imperfectgeometries, and show how to use this structure in accurateand efficient simulations.

David Bindel, Erdal YilmazCornell Universitybindel@cs.cornell.edu, ey45@cornell.edu

MS126

Fast Spectral Computations for QuasiperiodicSchroedinger Operators

Discrete Schrodinger operators with quasiperiodic poten-tials arise as mathematical models of quasicrystals. Their

spectra exhibit exotic properties that are more challengingto analyze than periodic or random potentials; often thesespectra are Cantor sets. Quasiperiodic potentials can beapproximated by periodic potentials, whose spectrum canbe computed by solving finite dimensional eigenvalue prob-lems. Accurate estimates require long periods. We showhow to compute such approximations quickly and addressthe need for high accuracy.

Mark Embree, Charles PuelzDepartment of Computational and Applied MathematicsRice Universityembree@vt.edu, cp16@rice.edu

MS126

Eigenvalue Problems in Electron Excitation

Single-electron excitation can be described by a nonlin-ear eigenvalue known as Dyson’s equation in which theHamiltonian operator is a function of an eigenvalue to bedetermined. We will describe the nonlinear structure ofthe eigenvalue problem and examine numerical methodsfor solving this type of problem.

Chao YangLawrence Berkeley National Labchao yang cyang@lbl.gov

Fang LiuCentral Univerisity of Finance and EconomicsPeking, Chinacufe.fliu@gmail.com

Lin LinLawrence Berkeley Lablinline@lbl.gov

Alexander KemperLawrence Berkeley National LabBerkeley, CAafkemper@lbl.gov

MS127

Rheology of Sickle Cell Anemia: Effects of Hetero-geneous RBC Shapes

Sickle cell anemia (SCA) is a a highly complex, inheritedblood disorder exhibiting heterogeneous cell morphologyand abnormal rheology. To better understand the rela-tionship between rheological behavior and cell morpholog-ical characteristics of blood in SCA, we present a multi-scale sickle red blood cell (SS-RBC) model, accounting fordiversity in both cell shape and rigidity. The proposedmodel provides a systematical approach to quantify therheological behavior and hemodynamics of SS-RBC sus-pensions. We quantify the heterogeneous shear viscosity ofSS-RBC suspensions with different cell morphologies, i.e.,the SS-RBC suspensions with granular shapes are the mostviscous; while the shear viscosity of SS-RBC suspensionscontaining elongated cells show a dramatic decrease. Incombination with the experimental data of SS-RBCs frompatients treated with and without hydroxyurea, we alsopredict the shear viscosity of SS-RBC suspensions underdifferent conditions. These findings lead to useful insightsinto the abnormal rheological behavior of blood in SCA.

Xuejin LiBrown Universityxuejin li@brown.edu

120 AN14 Abstracts

Huan LeiPacific Northwest National Laboratoryhuan.lei@pnnl.gov

E Du, Ming DaoMassachusetts Institute of Technologysarahedu@mit.edu, mingdao@mit.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

MS127

Lipid Bilayer and Cytoskeletal Interactions in aRed Blood Cell

We developed a two-component model of red blood cell(RBC) membranes to study interactions between the lipidbilayer and the cytoskeleton for healthy and diseasedRBCs. We modeled the bilayer and the cytoskeleton astwo distinct components and consider the normal elasticinteraction and tangential viscous friction between them.We implemented this model using both a three-level multi-scale continuum approach and Dissipative Particle Dynam-ics, and investigated RBC-related diseases such as malariaand sickle cell disease.

Zhangli PengMITzhpeng@mit.edu

MS127

Three-Dimensional Vesicle Electrohydrodynamics:A Level Set Method

The electrohydrodynamics of three-dimensional vesicles isinvestigated using a combined Jet level set/continuum forcemethod. The electric field in the domain is obtained by animmersed interface method, for which the necessary jumpconditions have been developed. Numerical results matchwell with the dynamics observed experimentally. A investi-gation of parameters influencing the vesicles dynamics willalso be presented.

David SalacUniversity at Buffalo - SUNYdavidsal@buffalo.edu

Mohammad KolahdouzUniversity at Buffalo, SUNYmkolahdo@buffalo.edu

MS127

A Hybrid Numerical Method for Electro-KineticFlow with Deformable Membranes

We consider two-phase flow of ionic fluids whose motionis driven by an imposed electric field. At a fluid-fluid in-terface, a screening cloud of ions develops and forms anelectro-chemical double layer or ‘Debye layer’. The ap-plied electric field acts on the ionic cloud it induces, result-ing in a strong slip flow near the interface. This is knownas ‘induced-charge electro-kinetic flow’, and is an impor-tant phenomenon in microfluidic applications and in themanipulation of biological cells. We address a significantchallenge in the numerical computation of such flows inthe thin-double-layer limit, by using the slenderness of the

layer to develop a fast and accurate ‘hybrid’ or multiscalenumerical method. The method incorporates an asymp-totic analysis of the electric potential and fluid dynamicsin the Debye layer into a boundary integral numerical so-lution of the full moving boundary problem.

Michael SiegelNew Jersey Institute of Technologymisieg@njit.edu

MS128

Integral Equations on Domains with Edges

We will discuss the discretization of integral equations onsurfaces with edges and corner points. Although achievinghigh accuracy in this setting is not that difficult, there area number of issues (such as the need for highly anisotropicmeshes) which make the construction of efficient discretiza-tion procedures challenging. We will discuss our progresson addressing these issues.

James BremerUC Davisbremer@math.ucdavis.edu

MS128

Integral Equation Techniques for Solving EllipticProblems with Mixed Boundary Conditions

This talk describes integral equation techniques for solvingelliptic problems with mixed boundary conditions (i.e. aportion of the obstacle has Dirichlet boundary conditionswhile the remainder has Neumann boundary conditions.)The proposed approach avoids using a hypersingular ker-nel as a result the system is better conditioned than exist-ing integral equation based methods. For many problems,the discretized system is amenable linear scaling solvers.Numerical experiments illustrate the performance of thesolution technique.

Adrianna GillmanDartmouth CollegeDepartment of Mathematicsadrianna.gillman@dartmouth.edu

MS128

Practical and Efficient Direct Solvers for BIEs

The last several years have seen rapid progress on con-structing direct solvers for the dense linear systems arisingupon discretization of BIEs. The goal is to build directsolvers with O(Np) complexity, where p is one, or closeto one, and with high practical efficiency. This talk willdescribe techniques aimed at improving performance andsimplifying coding by using randomized methods to accel-erate certain structured matrix computations.

Gunnar MartinssonUniv. of Colorado at Bouldermartinss@colorado.edu

MS128

Updating Techniques for Hierarchical Factoriza-tions

Many fast direct algorithms for solving linear systems aris-ing from discretized partial differential equations or bound-ary integral equations rely on a hierarchical tree decompo-

AN14 Abstracts 121

sition of the domain, e.g., methods based on nested dis-section for PDEs or recursive skeletonization for integralequations. In this talk we will show that, given a factor-ization corresponding to a given problem, we can updatethe factorization to solve problems related by local changessuch as localized modification of the PDE coefficients orperturbation of the problem geometry. In cases where thecomputational cost per tree node is the same across allnodes, updating is both asymptotically and practically lessexpensive than re-doing the complete factorization.

Victor MindenStanfordvminden@standford.edu

MS129

Diffusion-Limited Growth and Decay of 2D Epitax-ial Nanoclusters: Atomistic and Coarse-GrainedModeling

Random deposition onto isotropic or anisotropic crystallinesurfaces leads to diffusion-mediated formation of an en-semble of epitaxial 2D islands or nanoclusters. The pro-cess might be described by stochastic fully atomistic-levelmodels or by coarse-grained 2D continuum descriptionsof surface diffusion and aggregation. However, the lat-ter must retain the stochastic aspects of nucleation, andan open challenge is to capture far-from equilibrium is-land growth shapes (as this requires precise treatment ofnon-equilibrium diffusion around island edges). After de-position, these island ensembles coarsen usually by Ost-wald ripening. Again atomistic or continuum-level treat-ment is possible, the latter being more common. How-ever, recent experiments reveal shortcomings of standardcontinuum formulations for strongly anisotropic systems, afeature which we address.

Jim W. EvansAmes Laboratory USDOE and Iowa State Universityevans@ameslab.gov

Yong HanIOwa State Universityyhan.ameslab@gmail.com

MS129

Efficient Numerical Methods for Molecular BeamEpitaxial Growth

This work is concerned with efficient numerical methods forthe simulation of the dynamics of molecular beam epitax-ial (MBE) growth. Numerical simulations of MBE mod-els require long time computations, and therefore largetime-stepping methods become necessary. In this work,we present some unconditionally energy stable finite dif-ference schemes for MBE models. We will also discuss onsome time adaptive strategies.

Zhonghua QiaoApplied Math Dept.The Hong Kong Polytechnic University Hong Kongzhonghua.qiao@polyu.edu.hk

MS129

Stable and Convergent Numerical Schemes forPhase Field Crystal Models

Crystalline materials have atomic-scale imperfections in

the form of defects – such as vacancies, grain boundaries,and dislocations – and controlling, or at least predicting,the formation and evolution of such imperfections is a ma-jor challenge. The phase field crystal (PFC) methodologyhas emerged as a important, increasingly-preferred mod-eling framework for investigating materials with atomic-scale structures on diffusive time scales. In essence, thefast atomic vibrational time-scale phenomena are averagedout, but the atomic spatial resolution is preserved. In thistalk, I describe some efficient, stable, and convergent nu-merical methods for some PFC and PFC-type equations, afamily of highly nonlinear hyperbolic-parabolic PDE andintegro-PDE. I will also discuss a new PFC framework formulti-spatial-scale modeling based on the recent method ofamplitude expansions.

Steven M. WiseMathematics DepartmentUniversity of Tennesseeswise@math.utk.edu

MS129

Continuum Framework for Dislocation Structure,Energy and Dynamics of Dislocation Arrays andLow Angle Grain Boundaries

We present a continuum framework for dislocation struc-ture, energy and dynamics of dislocation arrays and low an-gle grain boundaries which may be nonplanar and nonequi-librium. In our continuum framework, we define a dislo-cation density potential function on the dislocation arraysurface or grain boundary to describe the orientation de-pendent continuous distribution of dislocation in a verysimple and accurate way. The continuum formulations ofenergy and dynamics include the long-range interaction ofconstituent dislocations, local line tension effect of dislo-cations and the cooperative motion of dislocations, whichare derived from the discrete dislocation model. We alsopresent numerical simulations using this continuum modelincluding applications to dislocation structures of low anglegrain boundaries and interfaces with misfitting sphericalinclusions.

Yang XiangHong Kong University of Science and Technologymaxiang@ust.hk

Xiaohong ZhuJinan Universitymaxhzhu@163.com

MS130

An Adaptive RBF-WENO Method for HyperbolicProblems

An adaptive RBF-WENO method is proposed. The RBF-WENO hybrid method is to use the radial basis functioninterpolation replacing the polynomial interpolation. Weshow that the locally adapted shape parameters can el-evate the regular WENO order resulting better accuracyand convergence. Numerical examples are provided.

Jae-Hun JungSUNY at Buffalojaehun@buffalo.edu

MS130

Matrix-Valued Kernels Associated to Vector-

122 AN14 Abstracts

Valued Random Fields with Correlated Compo-nents

We propose a class of nonseparable space-time compactlysupported correlation functions, termed here quasi-tapers,to mean that such correlations can be dynamically com-pactly supported over space or time. An important featureof the quasi-taper is given by a spatial (temporal) compactsupport being a decreasing function of the temporal lag(spatial distance), so that the spatial (temporal) compactsupport becomes smaller when the temporal (spatial) de-pendence becomes weaker. We propose general classes aswell as some examples that generalize the Wendland tapersto the space-time setting. Then a non separable space-timetaper with spatial and temporal compact support is ob-tained as tensor product of quasi-tapers. Our space-timetaper includes all the known constructions as special casesand will be shown to have great exibility. Covariance ta-pering is then explored as an alternative to maximum like-lihood when estimating the covariance model of a space-time Gaussian random field in the case of large datasets.The proposed quasi and space-time tapers allows to per-form covariance tapering when dealing with data that aredensely observed in time (space) but sparse in space (time)or densely observed both in time and space. The statisti-cal and computational properties of the space-time covari-ance tapering is addressed under increasing domain asymp-totics. A simulation study and two real data examplesillustrate the statistical and computational performancesof the covariance tapering with respect to the maximumlikelihood method using the space-time tapers proposed.

Emilio PorcuInstitute for Mathematical StochasticsGeorg-August-Universitaet, Goettingen, Germanyemilio.porcu@usm.cl

MS130

Improved Exponential Convergence Rates for Reg-ularized Approximation by Oversampling Near theBoundary

We discuss convergence rates for kernel based approxima-tion in smooth settings. Typical examples range from clas-sical function approximation to the approximate solutionof partial differential equations. In smooth settings oneexpects exponential convergence orders, but the numeri-cal schemes are notoriously ill conditioned, which enforcessome kind of regularization. Further, in smooth settingsone often observes boundary effects, i.e., the determinis-tic approximation rates for scattered data approximationare improved globally if the data sets are distributed moredensely near the boundary. In this talk, such boundaryeffects for regularized approximation schemes are analyzedby means of sampling inequalities for smooth functions.The latter provide a bound on a continuous norm in termsof a discrete norm and an error term that tends to zeroexponentially as the discrete data set becomes dense. Weshow that the exponential convergence rates are improvedby oversampling near the boundary.This is partly based on joint works with Christian Rieger(Bonn) and Robert Schaback (Gottingen).

Barbara ZwicknaglUniversity of Bonnzwicknagl@iam.uni-bonn.de

MS130

Recurrence Operators for Zonal Basis Functions on

the Sphere

One approach for simulation of stationary random fields inthe Euclidean space is based on Matheron’s turning bandsmethods. The idea behind this method is to relate positivedefinite radial functions in the R

d to corresponing ones onthe circle using averaging. The explicit form of the turningbands operator turns out to be a special case of a well-known recurrence relation for Bessel functions. Aiming atsimilar recurrences for zonal basis functions on the sphere,we can use relations between Gegenbauer polynomials ofdifferent parameters. Interestingly, there is a set of opera-tors which can be used to derive analogous relations. Wewill discuss some of these operators and their interrelations.

Wolfgang zu CastellHelmholtz Zentrum Muenchen, German Research Centerfor EnvirIngolstaedter Landstrasse 1, 85764 Neuherberg, Germanycastell@gsf.de

MS131

Tracking a Low-Dimensional Vector Via QuantizedMeasurements Or Pairwise Comparisons

Suppose that we wish to track a point xt ∈ Rk as its posi-

tion changes in time. In this talk I will describe approachesto this problem in two practical settings. First, I willconsider the case where the observations consist of highlyquantized linear measurements. Next I will describe the re-lated case where our data is given by pairwise comparisonsbetween between xt and various points x1, . . . , xn ∈ R

k

with known position. I will describe practical algorithmsfor handling both cases.

Mark DavenportGeorgia Institute of Technologymdav@gatech.edu

MS131

Intrinsic Volumes of Convex Cones: Theory andApplications

Spherical intrinsic volumes are fundamental statistics ofconvex cones, and occupy a central role in integral geom-etry. They also appear in various guises in statistics, con-vex optimization, compressed sensing (polytope angles),algebraic combinatorics, and differential geometry, amongother fields. In particular, they are the main ingredientsof the classical kinematic formulas, which describe the ex-act intersection probabilities of randomly oriented cones.Combining the kinematic formula with another pillar ofintegral geometry, the spherical Steiner formula, and con-centration of measure arguments, gives rise to a completeexplanation of phase transition phenomena for general ran-dom convex optimization problems. This talk surveys thetheory of intrinsic volumes, present methods of computa-tion, and highlights connections to problems in statistics,convex regularization, and to the theory of condition num-bers for convex optimization. Based on joint work withDennis Amelunxen, Mike McCoy and Joel Tropp

Martin LotzSchool of MathematicsThe University of Manchester

AN14 Abstracts 123

martin.lotz@manchester.ac.uk

MS131

The Achievable Performance of Demixing

Demixing is the problem of disentangling multiple informa-tive signals from a single observation. These problems ap-pear frequently in image processing, wireless communica-tions, machine learning, statistics, and other data-intensivefields. Convex optimization provides a powerful frameworkfor creating tractable demixing procedures that work rightout of the box. In this talk, we describe a geometric the-ory that precisely characterizes the performance of convexdemixing methods under a generic model. This theory pre-cisely identifies when demixing can succeed, and when itcannot, and further indicates that a sharp phase transi-tion between success and failure is a ubiquitous feature ofthese programs. Our results admit an elegant interpre-tation: Each signal has an intrinsic dimensionality, anddemixing can succeed if (and only if) the number of mea-surements exceeds the total dimensionality in the signal.Joint work with Joel A. Tropp.

Michael B. McCoy, Joel A. TroppCaltech CMSmccoy@caltech.edu, jtropp@cms.caltech.edu

MS131

Adaptively Sensing in Compressive Sensing Appli-cations

In this talk we will present new results in compressive sens-ing using adaptive sampling. Compressive sensing is a newsignal acquisition technology which reconstructs a high di-mensional signal from a small number of linear measure-ments. In the typical setting, these measurements are de-termined a priori. However, in some cases selecting thesemeasurements adaptively can lead to improvements bothin error and in the number of samples required. We discusssome fundamental limitations of this sampling scheme, aswell as some new encouraging results which show compres-sive sensing can benefit from adaptivity.

Deanna NeedellDepartment of MathematicsClaremont McKenna Collegedneedell@cmc.edu

MS132

Building Meso-Scale Stochastic Models Using theMori-Zwanzig Formalism

We present a meso-scale model built from the Mori-Zwanzig (MZ) formalism. The meso-scale model is builtwith the projection operator that is applied on the dis-cretized MZ equation in time. The projection operator isused to calculate the memory function with a simple re-currence without having to compute orthogonal dynamics,or esQL. Assuming that the memory function can be well-approximated by exponentials, we can generate the cor-responding fluctuation using Ornstein-Ulenbeck process.Then we can obtain the generalized Langevin equation.Our approach was validated by the simple heat bath model,in which the analytical solution is known. The DissipativeParticle Dynamics (DPD) system with one tagged particlewas also used as a numerical test case. Finally, we applyour framework to generate the meso-scale model of alaninedipeptide (in Φ and Ψ dihedral angle) to correctly predict

kinetics of the bio-molecule.

Hee Sun Lee, Surl-Hee AhnStanford Universityhslee88@stanford.edu, sahn1@stanford.edu

MS132

The Reduction of Molecular Dynamics Models Us-ing Mori-Zwanzig Projection Formalism

Molecular dynamics models find applications in many ar-eas of applied sciences. One often needs to restrict thesimulations to localized regions to minimize the computa-tional cost. I will present the Mori-Zwanzig formalism asa systematic approach to coarse-grain molecular dynamicsmodels. In particular, I will discuss how to approximatethe memory functions, and how to sample random noises.As example, simulations of crack propagation, dislocationdynamics, and protein dynamics will be presented.

Xiantao LiDepartment of MathematicsPennsylvania State Universityxli@math.psu.edu

MS132

Stochastic Modeling Through the Mori-ZwanzigFormalism

The Mori-Zwanzig formalism tells us that if we project adynamical system onto a subset of its degrees of freedom,the resulting process will generally exhibit memory effects.Unfortunately, the associated memory kernels, which areneeded for dimension reduction, are typically difficult toobtain directly from the formalism itself. In this talk, wepropose an empirical approach based on statistical estima-tion and apply it to certain prototypical models of spa-tiotemporal chaos.

Alexander J. ChorinUniversity of California, BerkeleyMathematics Departmentchorin@math.berkeley.edu

Kevin K. LinDepartment of MathematicsUniversity of Arizonaklin@math.arizona.edu

MS132

MZ-PDF Methods for Stochastic Analysis in Non-linear Dynamical Systems

We propose a new framework for stochastic analysis in non-linear dynamical systems based on goal-oriented probabil-ity density function (PDF) methods. The key idea stemsfrom techniques of irreversible statistical mechanics, and itrelies on deriving reduced-order PDF equations for quanti-ties of interest, e.g., functionals of the solution to systems ofstochastic ordinary and partial differential equations. Theproposed approach is useful to many disciplines as it leadsto new and more efficient computational algorithms.

Daniele VenturiDivision of Applied MathematicsBrown University

124 AN14 Abstracts

daniele venturi@brown.edu

MS133

A Predator-prey-disease Model with Immune Re-sponse in Infected-prey

This talk presents a predator-prey-disease model with im-mune response in the infected prey. The basic repro-duction number of the within-host model will be definedand it is found that there are three equilibria: extinc-tion equilibrium, infection-free equilibrium and infection-persistent equilibrium. The stabilities of these equilibriaare completely determined by the reproduction number ofthe within-host model. Furthermore, a basic reproductionnumber of the between-host model and two predator inva-sion numbers exists along with a predator invasion numberin the absence of disease and predator invasion numberin the presence of disease. There also exists a predatorand infection-free equilibrium, infection-free equilibrium,predator-free equilibrium and a coexistence equilibrium.The local stabilities of these equilibria under certain con-ditions depending on the basic reproduction and invasionreproduction numbers shall be explained in this talk. Fi-nally the global stability of the predator-free equilibriumwill be explained in this talk.

Souvik BhattacharyaNorth Dakota State UniversityVisiting Assistant Professorouvik.bhattacharya@unitn.it

MS133

Modeling the Spread of Bacterial Infections in aHospital with Environmental Contamination

Nosocomial infections, i.e. hospital-acquired infections,have become a major concern for public health officialsas the amount of antibiotic-resistant bacterial infectionsincreases. One important mechanism for bacterial persis-tence is the ability of bacteria to contaminate hospital sur-faces and survive in this environment for extended periodsof time. In this talk, I discuss a differential equation modelof bacterial infections in a hospital with environmental con-tamination. The basic reproduction number of the modelis proved to be a global threshold under certain conditions.In addition, simulations of the deterministic model and astochastic version of the model provide insight into an out-break of bacterial infections in a hospital. This is jointwork with Glenn Webb.

Cameron BrowneVanderbilt Universitycameron.j.browne@vandebilt.edu

MS133

Model of Spontaneous HIV Infection Control Fol-lowing Cessation of Antiretroviral Therapy

Reports suggest that HIV antiretroviral therapy initiatedearly may permit post-treatment control (PTC) of HIV(undetectable viral load) after treatment termination. Wehypothesize that early treatment induces PTC by restrict-ing the latent reservoir size, allowing immune responses tocontrol infection post-treatment. ODE model analysis re-veals a range in immune response-strengths where a patientmay show viral rebound or PTC. In this bistable regime,we predict a latent reservoir size threshold below which

PTC is achievable.

Jessica M. ConwayLos Alamos National Laboratoryconway@lanl.gov

Alan S. PerelsonTheoretical Biology and BiophysicsLos Alamos National Labn/a

MS133

Dyanamics of Low and High Pathogenic Avian In-fluenza in Wild and Domestic Bird Populations

An earlier infection with low pathogenic avian influenza(LPAI) provides a partial immunity towards infection withhigh pathogenic avian influenza (HPAI). We consider atime-since recovery structured model to study the dynam-ics of LPAI and HPAI in wild and domestic bird popula-tions. The system has a unique disease-free equilibriumwhich is locally and globally stable when the reproduc-tion number is less than one. There are unique LPAI-onlyand HPAI-only equlibria, which are locally asymptoticallystable as long as the other pathogen can not invade theequilibrium. There exist a coexistence equilibirum whenthe invasion number of both pathogens are greater thanone. We show that both pathogen can coexist in the formof sustained oscillations.

Necibe TuncerUniversity of Tulsanecibe-tuncer@utulsa.edu

Maia Martcheva, Juan TorresUniversity of Floridamaia@ufl.edu, gatorcha@ufl.edu

MS134

Inverting for Maritime Environments Using Em-pirical Eigenfunction Bases from Radar Imagery

Radar wave front arrival times and spatial energy depo-sition, associated with propagation through a given ma-rine atmospheric boundary layer, may be described usingproper orthogonal modes, and subsequently represented aspoints on the compact Stiefel manifold. By exploiting theRiemannian structure of Stiefel, interpolation within thecloud of manifold points is possible when solving inverseproblems aimed at uncovering in situ maritime conditionsaffecting radar propagation on a given day.

Vasileios Fountoulakis, Christopher J. EarlsCornell Universityvf59@cornell.edu, cje23@cornell.edu

MS134

Optimal Filters for General-Form Tikhonov Regu-larization

In this work, we use training data in an empirical Bayesrisk framework to estimate optimal regularization parame-ters for the general-form Tikhonov problem and the multi-parameter Tikhonov problem. We will show how estimatesof the optimal regularization parameters can be efficientlyobtained and present several numerical examples from sig-nal and image deconvolution to demonstrate their perfor-

AN14 Abstracts 125

mance.

Julianne ChungVirginia Techjmchung@vt.edu

Malena I. EspanolDepartment of MathematicsUniversity of Akronmespanol@uakron.edu

MS134

Reproducible Kernel Hilbert Space Modeling andComputing in Imaging

Regularization ensures uniqueness and smoothness in var-ious inverse problems arisen in imaging science. Most ofthe existing regularization methods can not efficiently in-terpolate or extrapolate image intensity. They are thusnot effective in solving image super-resolution and inpaint-ing problems that both need to extend intensity informa-tion at one region to another. We use reproducible kernelHilbert space (RKHS) to model these two problems. RKHSmethod is more flexible, adaptive to data and involves sim-ple computation.

Weihong GuoDepartment of Mathematics, Case Western ReserveUniversitywxg49@case.edu

Liangjian Deng, Si WangUniversity of Electronic Science and Technology of Chinaliangjian1987112@126.com, uestcsiwang@163.com

MS134

Improved Image Reconstruction by StatisticallyEstimating Near-Optimal Parameters for SpectralFilters

Spectral Filters improve the reconstruction of images cor-rupted by blur and unknown noise. We compute in thiswork the near-optimal parameters for general filters suchas a hybrid method that combines the Tikhonov filter andthe truncated SVD. Using the discrete Picard condition,we provide an algorithm for computing a Picard parame-ter, a cut-off for the singular values beyond which the ob-servations are predominantly noise. The method comparesfavorably against other reconstruction methods.

Victoria TaroudakiUniversity of Marylandvicttar@math.umd.edu

Dianne P. O’LearyUniversity of Maryland, College ParkDepartment of Computer Scienceoleary@cs.umd.edu

MS135

Considerations in the Design of Numerical Schemesfor Geophysical Flows

Long-term simulations of geophysical flows, e.g. in pre-dicting the climate change for the next century, requirenumerical schemes that conserve key quantities and accu-rately represent internal wave propagations, all at reason-able computational costs. In this talk, we will briefly re-

view the classical staggering-grid techniques proposed byArakawa et al almost forty years ago. Some recent devel-opments will be presented, and ideas for future work willalso be discussed.

Qingshan ChenClemson Universityqsc@clemson.edu

MS135

Finite Volume Approximation of the Inviscid Prim-itive Equations in a Complex Domain

We construct the cell-centered Finite Volume discretizationof the two-dimensional inviscid primitive equations in a do-main with topography. To compute the numerical fluxes,the so-called Upwind Scheme (US) and the Central-UpwindScheme (CUS) are introduced. We verify, with our numer-ical simulations, that the US (or CUS) is a robust first (orsecond) order scheme, regardless of the shape or size ofthe topography and without any mesh refinement near thetopography.

Gung-Min GieIndiana UniversityUSAgugie@umail.iu.edu

MS135

Approximation of the Singularly Perturbed Equa-tions of Parabolic Type in a Circular Domain

In this talk, I will present convergence results of singularlyperturbed problems in a circular domain and provide aswell approximation schemes, error estimates and numericalsimulations. To resolve the oscillations of classical numer-ical solutions due to the stiffness of our problem, we con-struct, via boundary layer analysis, the so-called boundarylayer elements which absorb the boundary layer singular-ities. Using a P1 classical finite element space enrichedwith the boundary layer elements, we obtain an accuratenumerical scheme in a quasi-uniform mesh.

YoungJoon HongIndiana Universityhongy@umail.iu.edu

MS135

POD Reduced-order Models of Complex FluidFlows

The proper orthogonal decomposition (POD) method hasbeen commonly applied to generate reduced-order mod-els for turbulent flows. However, to achieve a balance be-tween the low computational cost required by a reduced-order model and the complexity of the targeted turbulentflows, appropriate closure modeling strategies are needed.In this talk, we present several new nonlinear closure meth-ods for the POD reduced-order models, which synthesizeideas originating from large eddy simulation. We designefficient discretization algorithms for the new models andperform the numerical validation and verification in chal-lenging computational settings.

Zhu WangIMA, University of Minnesota

126 AN14 Abstracts

wangzhu@ima.umn.edu

MS136

Distribution of Directional Change as a Signatureof Complex Dynamics

Analyses of random walks traditionally use the meansquare displacement (MSD) as an order parameter char-acterizing dynamics. We show that the distribution of rel-ative angles of motion between successive time intervals ofrandom walks in two or more dimensions provides infor-mation about stochastic processes beyond the MSD. Weillustrate the behavior of this measure for common modelsand apply it to experimental particle tracking data. Fora colloidal system, the distribution of relative angles re-ports sensitively on caging as the density varies. For trans-port mediated by molecular motors on filament networks invitro and in vivo, we discover self-similar properties thatcannot be described by existing models and discuss pos-sible scenarios that can lead to the elucidated statisticalfeatures.

Stas BurovUniversity of Chicagotba

MS136

Honeybee Nest Bentilation: A Bio-robotic Studyof Collective Flapping Wing Fluid Mechanics

Honeybee workers ventilate their hive by collectively fan-ning their wings. The fluid mechanics of this phenomena—in which wings continuously operate in unsteady oncomingflows (i.e. the wake of neighboring worker bees) and nearthe ground—are unstudied and may play an important rolein the physiology of colony life. We perform field and lab-oratory observations of nest ventilation wing kinematics.Through recent advances in micro-robotics we constructat scale micro-mechanical models of honeybee ventilationswarms to explore the fluid mechanics of collective ventila-tion.

Nick GravishHarvard Universitynick.gravish@gmail.com

MS136

Propagating Waves Structure Spatiotemporal Ac-tivity in Visual Cortex of the Awake Monkey

Propagating waves have recently been found in the neocor-tex of anesthetized animals. Whether propagating wavesappear during awake and conscious states, however, re-mains unclear. To address this, we apply a phase-basedanalysis to single-trial voltage-sensitive dye imaging data,which captures the average membrane potential of neu-ronal populations over large cortical areas with high spa-tiotemporal resolution. With this approach, we detect andcharacterize spontaneous and stimulus-evoked propagatingwaves in visual cortex of the awake monkey.

Lyle MullerCNRS UNICmuller@unic.cnrs-gif.fr

Alexandre ReynaudCNRS & Aix-Marseille Universite, Marseille, Francetba

Frederic ChavaneCNRSInstitut de Neurosciences de la Timonefrederic.chavane@univ-amu.fr

Alain DestexheCNRS UNICdestexhe@unic.cnrs-gif.fr

MS137

A Novel Higher Order ETD Scheme for System ofCoupled Semi-linear PDEs

We introduce a novel version of the ETD3RK scheme basedon (1, 2)−Pade approximation to exponential function. Inaddition, we develop its extrapolation form to improve tem-poral accuracy to the fourth order. The scheme and its ex-trapolation are seen to be strongly stable and have abilityto damp spurious oscillations. We demonstrate the perfor-mance of the schemes on system of nonlinear Schrodingerequations and problem from biochemistry which containsdiscontinuity between initial and boundary condition.

Harish BhattMiddle Tennessee State Universityhpb2e@mtmail.mtsu.edu

MS137

Local Discontinuous Galerkin Method with aFourth Order Exponential Time DifferencingScheme for System of Nonlinear Schrodinger Equa-tions

This paper studies a local discontinuous Galerkin (LDG)approximation combined with fourth order exponentialtime differencing Runge-Kutta (ETDRK4) method forsolving the N-coupled nonlinear Schrodinger equation(NLSE). The numerical method is proven to be highly effi-cient and stable for long-range soliton computations. Nu-merical examples with periodic boundary conditions areprovided to illustrate the accuracy, efficiency and reliabil-ity of the proposed method.

Xiao LiangMiddle Tennessee State Universityxl2h@mtmail.mtsu.edu

MS137

A New Family of Discontinuous Galerkin Methodsfor Linear and Nonlinear Partial Differential Equa-tions

In this talk, we discuss a discontinuous Galerkin (DG) fi-nite element differential calculus theory for approximat-ing weak derivatives of Sobolev functions and piecewiseSobolev functions. By introducing numerical one-sidedderivatives as building blocks, various first and second or-der numerical operators such as the gradient, divergence,Hessian, and Laplacian operator are defined, and their cor-responding calculus rules are established. We show thatseveral existing DG methods can be rewritten compactlyusing the proposed DG framework, and that new DGmeth-ods for linear and nonlinear PDEs are also obtained.

Michael J. NeilanUniversity of PittsburghDepartment of Mathematics

AN14 Abstracts 127

neilan@pitt.edu

MS137

Application of the Laplace Transform Method toSolving Evolution Problems

We are interested in the highest-possible order time dis-cretization for solving parabolic problems. Recently themethod of Laplace transform has been drawing an increas-ing attention. Instead of solving parabolic problems us-ing time-marching algorithms, we attempt to solve theLaplace-transformed complex-valued elliptic equations inparallel. The inverse Laplace transform then gives thetime-domain solutions by using exponentional convergentquadrature rules on carefully-chosen contours. We will givea short review on this approach and generalize the methodto solving parabolic equations with time-dependent coef-ficients. The method will be shown to converge exponen-tially under suitable assumptions. We will discuss a coupleof directions to generalize this approach.

Dongwoo SheenSeoul National UniversityDepartment of Mathematicssheen@snu.ac.kr

MS138

Uncover Deep Learning: Assess Online LearnersCognitive Presence in Mooc

The study will investigate learners cognitive presence levelin a five-week MOOC data science course. Transcript anal-ysis, social network analysis, learning records (i.e. fre-quency of views, grades), survey of perceived learning andsatisfaction will be used to assess the learning process andoutcomes. The results will reveal the levels of cognitivepresence exhibited by learners, how their cognitive pres-ence evolves overtime, and how their levels of cognitivepresence correlate with their online behaviors and satisfac-tions.

Ye ChinSyracuse Universityychen129@syr.edu

MS138

Coalition for Undergraduate Computational Sci-ence and Engineering Education - Proof of Concept

This talk will present the project funded by NSF TUESto create a cluster of collaborating institutions that com-bine students into common classes and use cyberlearningtechnologies to deliver and manage instruction. As an ideaof scale-up project, we will discuss how to advance Under-graduate Computational Science Education through learn-ing analytics, deep learning assessment and massive openonline courses.

Hong LiuDepartment of MathematicsEmbry-Riddle Aeronautical Universityliuho@erau.edu

MS138

Undergraduate Exploration of Agent-Based Mod-eling

The final week of a modeling and simulation course in fall,

2013, students explored agent-based models (ABMs) withNetLogo. Initially, they completed tutorials to developmodels on unconstrained growth and average distance cov-ered by random walkers. Besides revealing their utility,these models provided an opportunity to compare agent-based modeling with previously considered techniquessys-tem dynamics modeling, empirical modeling, and cellularautomaton simulations. Improved test scores and positivequestionnaire results support the success of this approach.

Angela B. ShifletMcCalla Professor of Math. & CS, Dir. of ComputationalSci.Wofford Collegeshifletab@wofford.edu

George W. ShifletWofford Collegeshifletgw@wofford.edu

MS138

The Ingenious Project and Other Initiatives

This talk will focus on aspects of the INGenIOuS Mathe-matical Sciences Workforce Development project that re-late especially to computational applied mathematics ed-ucation. The NSF-funded project was a joint venture ofall the main professional societies (ASA, AMS, MAA andSIAM). The focus on workforce development led to a strongrole for applied mathematical science education. Thistheme continues for the upcoming CBMS forum, which willfocus on the first two years of college education.

Peter R. TurnerClarkson UniversitySchool of Arts & Sciencespturner@clarkson.edu

MS139

Mathematical Modeling and Discretization for Ex-ascale Simulation

In simulations, the choices of mathematical models andtheir discretization significantly influence the properties ofthe resulting discrete systems. The advent of exascale com-puting is an opportunity to re-think the formulation andimplementation of mathematical models and discretiza-tions in ways that are more favorable for numerical in-tegration on exascale machines. We will survey severalpromising research topics and the fundamental constraintsinvolved in the process of expressing physical phenomenaas fully discrete models.

Luis ChaconLos Alamos National Laboratorychacon@lanl.gov

MS139

Resilient Algorithms and Computing Models

Abstract not available at time of publication.

Michael A. HerouxSandia National Laboratories

128 AN14 Abstracts

maherou@sandia.gov

MS139

Discrete Solvers at the Exascale

Discrete solvers are crucial in scientific simulations. Mov-ing to the exascale will put heavier demands on these ker-nels due to the need for increasing amounts of data localityand to obtain much higher factors of fine-grained paral-lelism. Thus, parallel solvers must adapt to this environ-ment, and new algorithms and implementations must bedeveloped to capitalize on the capabilities of future hard-ware. We will discuss several key topics that are potentiallyrelevant in the exacale era.

Esmond G. NgLawrence Berkeley National Laboratoryegng@lbl.gov

MS139

Hierarchical Multilevel Methods for Exascale Un-certainty Quantification and Optimization

The sustained increase in computational capabilities willenable new possibilities at the intersection of optimiza-tion and uncertainty quantification (UQ), including modelcalibration, robust control and design under uncertainty.However, numerous changes in scientific computing atextreme scales are expected to challenge the currentUQ/optimization paradigm, wherein theses techniques aretypically wrapped around a black-box simulation. Thistalk will focus on several multi-fidelity, hierarchical approx-imations for UQ/optimization that exploit greater levels ofparallelism provided by emerging many-core architectures.

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

Stefan WildArgonne National Laboratorywild@mcs.anl.gov

MS140

The Behavior of a Quasi-Circular Vesicle DuringDrying Processes

A proposed method for the preservation of biological cellsis through desiccation. We consider a two-dimensional,quasi-circular vesicle, whose boundary is an inextensiblebilipid membrane wall but whose enclosed area varies ow-ing to the osmotic transport of water through the mem-brane. The evolution of the vesicle’s shape is computedand the effects of advection, diffusion and the membrane’spermeability are analyzed and compared with conclusionsdrawn from recent level-set simulations.

Maurice J. BlountCardiff Universityblountmj@cardiff.ac.uk

Stephen H. DavisDept. of Engineering Sciences and Applied MathNorthwestern Universitysdavis@northwestern.edu

Michael J. Miksis

Department of Engineering Sciences and AppliedMathematicsNorthwestern Universitymiksis@northwestern.edu

MS140

Electrohydrodynamics of Lipid Bilayer Vesicles inAC and DC Fields

Vesicles are closed, fluid-filled lipid bilayers which exhibitshape transitions in the presence of electric fields. Herewe model the vesicle membrane as an infinitely thin, ca-pacitive, area-incompressible interface with the surround-ing fluids acting as charge-advecting leaky dielectrics, thenuse the boundary integral method to numerically investi-gate the dynamics of a vesicle in various electric field pro-files. Finally, we present a comparison of our numericalresults with recent small deformation theory and experi-mental data.

Lane McConnellUniversity of New Mexicolmcconne@gmail.com

MS140

Field Theoretic Approaches for Non-SpontaneousDeformation of Bilayers under Surface DirectorEnergies

The shapes of membranes are continually changing in theiraqueous environment. Often, these shape changes involveproteins but the mechanistic coupling between proteins andbilayers is poorly understood. In this talk, we will discusssome classical and field theoretic calculations which havegiven insight into membrane shape changes away from equi-librium and allowed us to evaluate a path of deformationsleading to a least energy barrier between quasi-static mem-brane configurations.

Rolf RyhamFordham Universityrryham@fordham.edu

Fredric CohenDepartment of Molecular Biophysics and PhysiologRush Universityfredric cohen@rush.edu

Bob EisenbergDepartment of Molecular Biophysics and PhysiologyRush University Medical Centerbeisenbe@rush.edu

MS140

Deformation and Stability of Vesicles in Dc ElectricPulses

Electrohydrodynamics of vesicles are investigated understrong DC pulses. In an applied field, the membrane actsas a capacitor and the vesicle deforms into an oblate orprolate ellipsoid. If poration occurs, the membrane capac-itor becomes short-circuited and leads to non-ellipsoidalshape and vesicle collapse. The evolution of vesicle shapeis studied for DC pulses of different strength and duration.Membrane composition is varied to observe the effect ofmembrane viscosity, capacitance, and poration threshold.

Paul Salipante

AN14 Abstracts 129

Max Plank Institutepaul.salipante@gmail.com

Petia VlahovskaBrown Universitypetia vlahovska@brown.edu

MS142

Fast Iterative Methods for The Variable DiffusionCoefficient Equation in a Disk

Variable coefficient diffusion equation has widespread ap-plications in many areas of Physics, Engineering and Indus-trial research like the flow in porous media, tomography inimage processing to mention a few. We present here fast,efficient iterative methods to solve this equation in a diskwith applications to the Ginzburg Landau equation. Ourtechnique is based on the solution of the Poisson equationin a disk using fast Fourier transform and recursive rela-tions. The method takes advantage of scaling the originalproblem and using shifted iteration. This is an ongoingwork and our focus is to develop a fast solution for this non-seperable elliptic equation in arbitrary two-dimensional do-mains by the help of domain embedding method using theoptimal distributed control algorithm. The performance ofthis fast method is illustrated with some numerical exam-ples.

Aditi Ghosh, JoungDong KimTexas A&M Universityamathematics@gmail.com, jdkim@math.tamu.edu

Prabir DaripaTexas A&M UniversityDepartment of Mathematicsprabir.daripa@math.tamu.edu

MS142

Subspace Iteration Randomization and Low-rankApproximation

A classical problem in matrix computations is the efficientand reliable approximation of a given matrix by a matrixof lower rank. The truncated singular value decomposi-tion (SVD) is known to provide the best such approxima-tion for any given fixed rank. However, the SVD is alsoknown to be very costly to compute. Among the differ-ent approaches in the literature for computing low-rankapproximations, randomized algorithms have attracted re-searchers’ recent attention due to their surprising reliabilityand computational efficiency in different application areas.Typically, such algorithms are shown to compute with veryhigh probability low-rank approximations that are withina constant factor from optimal, and are known to performeven better in many practical situations. In this paper, wepresent a novel error analysis that considers randomizedalgorithms within the subspace iteration framework andshow with very high probability that highly accurate low-rank approximations as well as singular values can indeedbe computed quickly for matrices with rapidly decayingsingular values. Furthermore, we show that the low-rankapproximations computed by these randomized algorithmsare actually rank-revealing approximations, and the spe-cial case of a rank-1 approximation can also be used tocorrectly estimate matrix 2-norms with very high proba-bility. Our numerical experiments are in full support ofour conclusions.

Ming Gu

University of California, BerkeleyMathematics Departmentmgu@math.berkeley.edu

MS142

Fast Algorithms for the Evaluation of Layer Poten-tials using ’Quadrature by Expansion’

Quadrature by Expansion, or ’QBX’, is a systematic, high-order approach to singular quadrature that applies to layerpotential integrals with general kernels on curves and sur-faces. This talk discusses algorithmic options for usingQBX within a variant of the Fast Multipole Method. Amethod is presented that preserves accuracy, generality andclose evaluation capability while only requiring a relativelymodest increase in computational cost in comparison to apoint-to-point FMM.

Andreas KloecknerCourant Institute of Mathematical SciencesNew York Universityandreask@illinois.edu

MS142

Stability and Accuracy of Structured DirectSolvers

Structured direct solvers are known to be very efficient insolving some integral equations and PDEs. Here, we showthat they are not only faster than standard direct solvers,but can also have much better stability. In particular,for hierarchically semiseparable (HSS) matrices, we firstshow how the approximation errors can be controlled bythe tolerance in either classical or randomized compression.We further demonstrate the backward stability of the di-rect solution. In fact, the growth of the numerical errorin the direct factorization is significantly slower than thatin standard LU factorization with pivoting. The growthfactors are derived.

Jianlin XiaDepartment of MathematicsPurdue Universityxiaj@math.purdue.edu

Yuanzhe XiPurdue Universityyxi@math.purdue.edu

MS143

Fictitious Domain Method with a Hybrid CellModel for Simulating Motion of Cells in Fluid Flow

This talk will consider a hybrid model to represent biologi-cal cells and the distributed-Lagrange-multiplier/fictitious-domain (DLM/FD) formulation for simulating thefluid/cell interactions. The hybrid model to represent thecellular structure consists of a continuum representationof the lipid bilayer, from which the bending force is cal-culated through energetic variational approach, a discretecytoskeleton model utilizing the worm-like chain to repre-sent network filament, and area/volume constraints. Forour computational scheme, a formally second-order accu-rate fractional step scheme is employed to decouple the en-tire system, and is solved by the projection method, levelset method, ENO reconstruction, and the Newton method.Numerical results compare favorably with previously re-ported numerical and experimental results, and show that

130 AN14 Abstracts

our method is suited to the simulation of the cell motionin flow.

Wenrui HaoDept. of Applied and Comp. Mathematics and StatisticsUniversity of Notre Damewhao@nd.edu

MS143

Modeling and Computation of a Precipitate in In-homogeneous Elastic Media

We present linear theory and nonlinear simulations tostudy the self-similar growth/shrinkage of a precipitate ina 2D elastic media. For given applied stress boundary con-ditions, we show that depending on the mass flux enter-ing/exiting the system, there exist critical flux and elastic-ity at which compact self-similar growth/shrinkage occursin the linear regime. Numerical results reveal that at longtimes there exists nonlinear stabilization that leads the pre-cipitate to evolve to compact limiting shape.

Shuwang LiDepartment of Applied MathematicsIllinois Institute of Technologysli@math.iit.edu

MS143

A Boundary Integral Method for Particles Movingin Viscoelastic Fluids

We present a boundary integral method for computingforces on interacting particles in an unsteady viscoelasticflow. Using a correspondence principle between Stokes flowand linear viscoelasticity in the Fourier domain, we providea simple boundary integral formulation for solid particlesmoving in a linear viscoelastic fluid. We present an ac-curate numerical method for finding the particle surfaceforces when the velocities are given or vice versa. Our nu-merical methods are validated against a known exact solu-tion and an existing asymptotic solution. The comparisonsare in excellent agreement.

Xiaofan LiIllinois Institute of Technologylix@iit.edu

MS143

Solving Interface Problems to High-order on a Reg-ular Cartesian Grid

In this talk I will present a regular Cartesian grid frame-work for solving two problem of central importance to in-terfacial dynamics. The first one is the solution of Poisson’sequation with interface jump conditions and the second oneis the evolution of the interface. The methods presentedare high order (4th order accurate), optimally local (com-pact stencil sizes), and easy to implement. I will presentapplications of these methods to solve the incompressibletwo-phase Navier Stokes equations for flows involving theinteraction of droplets with a membrane.

Jean-Christophe NaveMcGill Universityjcnave@math.mcgill.ca

MS144

Radial Basis Function Collocation Method in Block

Pseudospectral Mode

We numerically investigate radial basis function (RBF) col-location method in block pseudospectral (BPS) mode, amethod popularized by Driscoll and Fornberg for pseu-dospectral collocation method. The RBF implementationallows us to deal with irregular domain whereas match-ing solution and derivatives continuities are done in similarways as in BPS. Numerical experiments in solving simplecollocation problems will be shown.

Alfa HeryudonoUniversity of Massachusetts DartmouthDepartment of Mathematicsaheryudono@umassd.edu

MS144

Adaptive Trial Subspace Selection for Ill-Conditioned Kernel Collocation

Choosing data points is a common problem for researcherswho employ various meshless methods for solving partialdifferential equations. On the one hand, high accuracyis always desired; on the other, ill-conditioning problemsof the resultant matrices, which may lead to unstable al-gorithms, prevent some researchers from using meshlessmethods. In this talk, we will go over some adaptive trialsubspace selection algorithms that select basis to approxi-mate the true solution of the full problem.

Ling LeevanHong Kong Baptist UniversityDepartment of Mathematicslling@hkbu.edu.hk

MS144

Reproducing Kernel Hilbert Spaces Related toParametric Partial Differential Equations

Parametric partial differential equations often arise in com-plicated physical simulations. A recent source for high- andeven infinite dimensional problems is the modeling of un-certainties. For the efficient numerical treatment of thoseproblems it is crucial to have a decay in importance ofthe input parameters. Such a decaying ordering can beformally stated in terms of reproducing kernels. Such apoint of view also indicates numerical schemes which arewell-known in the kernel-based literature. We will providesome non-standard examples and discuss the resulting ap-proximation properties. This is partly based on joint workwith M. Griebel and B. Zwicknagl (both Bonn University).

Christian RiegerUniversitat BonnHaussdorff Center for Mathematicsrieger@ins.uni-bonn.de

MS144

A Novel Radial Basis Function (RBF) Method forSolving Partial Differential Equations (PDEs) onLarge Point Clouds

Radial Basis Function (RBF) methods, with advantagessuch as mesh-free, simplicity of implementation, anddimension-independence, have been broadly employed forreconstructing arbitrary surfaces. However, there are stillmany challenge problems in the numerical solution of Par-tial Differential Equations (PDEs) on large point clouds. In

AN14 Abstracts 131

this talk, a novel RBF method will be briefly introduced.Several related topics, such as fast algorithms, treecode,will also be discussed. Numerical examples demonstratethat this method yields promising results.

Lei WangArgonne National Laboratorywang256@uwm.edu

Zeyun YuUniversity of Wisconsin, Milwaukee”zeyun yu” ¡yuz@uwm.edu¿

Emmanuel O. Asante-AsamaniDepartment of Mathematical SciencesUniversity of Wisconsin-Milwaukeeeoa@uwm.edu

MS145

Exponentially Decaying Error Rate in One-BitCompressive Sensing

In one-bit compressive sensing, s-sparse vectors x ∈ Rn

are acquired via extremely quantized linear measurementsyi = sgn〈ai,x〉, i = 1, . . . ,m. Several procedures to re-construct these sparse vectors have been shown to be ef-fective when a1, . . . ,am are independent random vectors.They typically yield an error decaying polynomially inλ := m/(s log(n/s)). This rate cannot be improved inthe measurement framework described above. However, weshow that a reconstruction error decaying exponentially inλ is achievable when thresholds τ1, . . . , τm are chosen adap-tively in the quantized measurements yi = sgn(〈ai,x〉−τi),i = 1, . . . ,m. Our procedure, which is robust to measure-ment error, is based on a simple recursive scheme involvingeither hard-thresholding or linear programming.

Richard G. BaraniukRice UniversityElectrical and Computer Engineering Departmentrichb@rice.edu

Simon FoucartMathematicsUniversity of Georgiafoucart@math.uga.edu

Deanna NeedellDepartment of MathematicsClaremont McKenna Collegedneedell@cmc.edu

Yaniv PlanDeaprtment of MathematicsUniversity of Michiganyplan@umich.edu

Mary WoottersUniversity of Michiganwootters@umich.edu

MS145

Compressed Subspace Matching on the Continuum

We consider the general problem of matching a subspaceto a set of (compressed) samples. We are interested in thecase where the collection of subspaces is continuously pa-rameterized, i.e. uncountably infinite. We present some

mathematical theory that shows that a random projectionembeds a collection of K-dimensional spaces if the num-ber of samples is on the order of K times a constant thatdescribes the geometry of the collection. We also showhow this embedding results in a guarantee on our abilityto choose the a subspace which is (almost) as good as theone computed from a full observation of the signal. This isjoint work with William Mantzel.

Justin RombergSchool of ECEGeorgia Techjrom@ece.gatech.edu

MS145

Constructing Matrices with Optimal Block Coher-ence

Block coherence of matrices plays an important role in an-alyzing the performance of block compressed sensing re-covery algorithms (Bajwa and Mixon, 2012). We presentbounds on worst-case block coherence and Kronecker prod-uct constructions which achieve these bounds. We alsoshow that random subspaces have optimal-order worst-caseblock coherence asymptotically. Finally, we present a flip-ping algorithm that can improve the average block coher-ence of a matrix, while maintaining the worst-case blockcoherence of the original matrix.

Andrew J. Thompson, Robert CalderbankMathematicsDuke Universitythompson@math.duke.edu, robert.calderbank@duke.edu

Yao XieIndustrial and Systems EngineeringGeorgia Institute of Technologyyao.xie@isye.gatech.edu

MS145

Compressed Sensing and Sigma-Delta Quantiza-tion: Decoding Via Convex Optimization

We introduce an alternative reconstruction method for sig-nals whose compressed samples are quantized via a Sigma-Delta quantizer. The method is based on solving a convexoptimization problem, and unlike the previous approaches,it yields a stable and robust estimate of the original sig-nal. Consequently, we can use Sigma-Delta quantizers forcompressible signals and when the measurements are noisy.Finally, our theory applies to ”fine” Sigma-Delta quantiz-ers and ”coarse” Sigma-Delta quantizers, e.g., 1-bit permeasurement.

Ozgur YilmazMathematicsUniversity of British Columbiaoyilmaz@math.ubc.ca

Rongrong WangUniversity of British Columbiarongwang@math.ubc.ca

MS146

Mori-Zwanzig Analysis of Brownian Motion in aConfined Molecular System

Brownian motion in molecular systems is one of the orig-

132 AN14 Abstracts

inal examples for which Mori-Zwanzig projection methodwas developed. Compared to the unbounded case, Brown-ian motion in a confined fluid exhibits interesting features,which are reflected on its memory kernel. By calculatingthe memory kernel from molecular dynamics simulationsand obtaining analytic results for the Rayleigh gas model,we investigate the effects of confinement.

Changho Kim, George E. KarniadakisBrown UniversityDivision of Applied Mathematicschangho kim@brown.edu, george karniadakis@brown.edu

MS146

Mori-Zwanzig and Adaptive Mesh Refinement forUncertainty Quantification

We employ the Multi-element generalized PolynomialChaos method to deal with stochastic equations involvingdiscontinuities in random space. We develop a new crite-rion through the model reduction and study the connectionbetween the variances of the outputs and the quantitieswhich are selected as the accuracy control parameters todetermine when to carry out the mesh refinement. TheKraichnan-Orszag three mode problem is used to illustratethe effectiveness of the algorithm for ODEs.

Jing LiUniversity of Minnesotalixxx873@umn.edu

MS146

Scale Dependence and Renormalization in ModelReduction

The problem of model reduction for complex systems isan active area of research. In this talk I want to discusshow the physics inspired concepts of scale dependence andrenormalization can be used to facilitate the constructionof accurate reduced models for complex problems.

Panos StinisUniversity of Minnesota, Twin Citiesstinis@umn.edu

PP1

A New Test for Exclusion Algorithm to Find theOptimum Value of Function in Rn

The problem of finding the global minimum of a vectorfunction is very common in science, economics and engi-neering. One of the most notable approaches to find theglobal minimum of a function is that based on intervalanalysis. In this area, the exclusion algorithms (EAs) area well-known tool for finding the global minimum of a func-tion over a compact domain. There are several choices forthe minimization condition In this paper, we introduce anew exclusion test and analyze the efficiency and compu-tational complexity of exclusion algorithms based on thisapproach.We consider Lipschitz functions and give a newminimization condition for the exclusion algorithm. Thenwe study the convergence and complexity of the method.

Ibraheem AlolyanKing Saud University

ialolyan@ksu.edu.sa

PP1

A Mesh Free Method for Numerical Simulation ofCalcium Dynamics In Ventricular Myocytes

We consider a coupled system of non-linear reaction-diffusion equations that model the spatio-temporal vari-ation of intracellular calcium concentration in ventricularmyocytes. We introduce a modified mesh free method andutilize exponential time differencing, to significantly reducethe simulation time. At the end we present numerical re-sults demonstrating the stability of the method when usedon uneven distribution of nodes.

Emmanuel O. Asante-AsamaniDepartment of Mathematical SciencesUniversity of Wisconsin-Milwaukeeeoa@uwm.edu

Bruce WadeDepartment of Mathematical Sciences, UW-MilwaukeeMilwaukee, Wisconsin 53201-0413wade@uwm.edu

Zeyun YuUniversity of Wisconsin-Milwaukeeyuz@uwm.edu

PP1

Gene Selection from Microarray Data : An Ex-ploratory Approach

The goal of microarray data analyses is often to identify thesmallest set of genes that can distinguish between classes ofsamples (e.g., from unhealthy samples to healthy ones). Inthis work, we explore current statistical learning techniqueson the discovery of informative genes from microarray ex-periments. In particular, several gene selection algorithmsare tested on a microarray data sets from samples in atype-1-diabetes (T1D) study. The results are comparedand discussed.

Sami CheongUniversity of Wisconsin-Milwaukeecheongs@uwm.edu

PP1

AWM Workshop: Confidence Sets for Geometricand Topological Distances

Distance measures arise in many contexts. Unfortunately,the most interesting distance is the one between an un-known ground truth object and an object created fromsampling. In this talk, we introduce the statistical boot-strap for the purpose of bounding the distance between areconstructed object and the original object. In particular,we derive confidence sets for persistence diagrams, persis-tence landscapes, road networks, and Reeb graphs.

Brittany FasyTulane Universitybfasy@tulane.edu

PP1

AWM Workshop: Fast Iterative Methods for TheVariable Diffusion Coefficient Equation in a Unit

AN14 Abstracts 133

Disk

Variable coefficient diffusion equation has widespread ap-plications in many areas of Engineering and Industrial re-search like the flow in porous media and Tomography. Wepresent here fast, iterative methods to solve this equationwith applications to the Ginzburg Landau equation. Ourtechnique is based on solution of Poisson and Helmholtzequation in a unit disc using fast FFT and recursive rela-tions. The performance of this fast method is illustratedwith some numerical examples.

Aditi GhoshTexas A&M Universityamathematics@gmail.com

PP1

Spatiotemporal Pattern of Temperature Changeover US Using Bounded-Variation Segmentation

In order to analyze low frequency variability of climate,the method of bounded-variation segmentation is appliedfor modeling temperature time series of US from 1184 sta-tions during 1900-2012. The method finds multiple lin-ear trends and locate times of significant changes. Im-portant attribute of this method is that it is not depen-dent on Gaussian or Markovian assumptions. Also multi-dimensional analysis used in this method eliminate the ef-fect of sensors relocation on the detected trends.

Mohammad Gorji SefidmazgiPhD StudentNorth Carolina A&T State Universitymgorjise@aggies.ncat.edu

Abdollah HomaifarNorth Carolina A&T State Universityhomaifar@ncat.edu

Mina Moradi KordmahallehNorth Carolina A&T State Unviersitymmoradik@aggies.ncat.edu

PP1

AWM Workshop: The Asymptotic Analysis of aThixotropic Yield Stress Fluid in Squeeze Flow

The partially extending strand convection model, com-bined with a Newtonian solvent, is investigated for a vis-coelastic fluid in biaxial extensional (squeeze) flow. For aprescribed tensile stress, the asymptotic analysis, while notsimple, is an essential tool for the physical interpretationof the distinct stages in evolution. The overall picture thatemerges captures a number of features that are associatedwith thixotropic yield stress fluids, such as delayed yieldingand hysteresis for up-and-down stress ramping.

Holly GrantVirginia Techhollygrant@vt.edu

PP1

Multiscale Decomposition and Modeling of Com-plex Networks

Statistical analyses of networks can provide critical in-sights into the structure, function, dynamics, and evolu-tion of many complex systems. Here, we introduce a flexi-

ble method for synthesizing realistic ensembles of networksstarting from a known network, through a series of map-pings that coarsen and later refine the network structureby randomized editing. The method, MUSKETEER, pre-serves structural properties with minimal bias, includingunknown or unspecified features, while introducing realis-tic variability at multiple scales.

Alexander GutfraindCornell Universityagutfraind.research@gmail.com

Ilya SafroClemson Universityisafro@g.clemson.edu

Lauren A. MeyersThe University of Texas at AustinSection of Integrative Biologylaurenmeyers@mail.utexas.edu

PP1

Pathways to Type 2 Diabetes with a MathematicalModel

We develop a mathematical model of how pancreatic betacells fail in the progression to type 2 diabetes. Insulin re-sistance by itself does not generally lead to diabetes unlessit is extreme. In contrast, typical degrees of insulin resis-tance do lead to disease if accompanied by an increasedpropensity to apoptosis, which impairs the ability to ex-pand beta-cell mass or function in response to insulin re-sistance. We have incorporated the dynamics of exocytosisof insulin granules. These enhancements allow us to lookat the mechanistic defects that underlie observed patholo-gies such as impaired fasting glucose (IFG) and impairedglucose tolerance (IGT). The model supports associationsin experiments between IFG and excess HGP and betweenIGT and peripheral insulin resistance.

Joon Ha, Arthur S. ShermanNational Institutes of Healthjoon.ha@nih.gov, asherman@nih.gov

PP1

Bayesian Statistics and Uncertainty Quantificationfor Safety Boundary Analysis in Complex Systems

The analysis of a safety-critical system often requires de-tailed knowledge of safe regions and their high-dimensionalnon-linear boundaries. We present a statistical approach toiteratively detect and characterize the boundaries, whichare provided as parameterized shape candidates. Usingmethods from uncertainty quantification and active learn-ing, we incrementally construct a statistical model fromonly few simulation runs and obtain statistically sound es-timates of the shape parameters for safety boundaries.

Yuning HeUC Santa Cruzyuning.he@nasa.gov

PP1

AWM Workshop: Traveling Fronts to the Combus-tion and the Generalized Fisher-Kpp Models

We show the nonexistence of traveling fronts in the com-bustion model with fractional Laplacian (−Δ)s when s ∈

134 AN14 Abstracts

(0, 1/2]. Our method can be used to give a direct andsimple proof of the nonexistence of traveling fronts for theusual Fisher-KPP nonlinearity. Also we prove the existenceand nonexistence of traveling fronts for different ranges ofthe fractional power s for the generalized Fisher-KPP typemodel.

Tingting HuanUniversity of Connecticuttingting.huan@uconn.edu

PP1

Which Conical Ant Mound is Optimal in Collectionof Solar Beams From Transient Sun

We optimize domes of ant nests, receiving energy from so-lar heating and losing it to a cold night air. Sun completesthe daily sky cycle with beams of radiation continuouslychanging their altitude and azimuthal angles. We calcu-late the incoming radiation at each exposed point of a con-ical dome surface and at each instance from dawn to sun-set. The daily energy serves as a criterion and the surfacearea of the cone, through which heat is lost during nighttime, serves as an isoperimetric constraint in the sense ofPolya-Szego, with the height to cones base ratio chosen as acontrol variable. For the simplest case, the instantaneousflux of the terrestrial solar power is explicitly expressedthrough the altitude Sun angle. Time-integration over theazimuthal angle and areal-integration over the illuminatedhalf-cone give the total solar day energy. This functional isthen optimized with respect to the size of the anthill thatanswers the question stated in the title.

Rouzalia KasimovaGerman University of Technology in Omanrouzalia.kasimova@gutech.edu.om

Denis Tishin, Yurii ObnosovKazan Federal University, Russiadenis.tishin@kpfu.ru, yurii.obnosov@gmail.com

Anvar KacimovSultan Qaboos Universityanvar@squ.edu.om

PP1

AWM Workshop: Competitive Geometric Flow OfNetwork Morphologies Under The FunctionalizedCahn-Hilliard (fch) Free Energy

The FCH is a higher order free energy which balances solo-vation energy of ionic groups against elastic energy of theunderlying polymer backbone, and describes the formationof solvent network structures which are essential to ionicconduction in polymer membranes. For the H -1 gradi-ent flow of the FCH energy, using functional analysis andasymptotic methods, we drive a sharp-interface geometricmotion which couples the flow of co-dimennsion 1 and 2network morphologies, through the far-field chemical po-tential.

Noa KraitzmanMichigan State Universitykraitzm1@msu.edu

PP1

On a Method for Approximation of the SingularityCurve of a Piecewise Constant Function of Two

Variables

We modify the method suggested earlier by us and over-come its main deficiency. The method enables the approx-imation of the singularity curve of a piecewise constantfunction of two variables by means of its Fourier-Jacobicoefficients. The method is based on the technique sug-gested by the author for recovering the locations of dis-continuities of a piecewise smooth function of one variable.The method could be generalized for functions of three ormore variables. In addition, some numerical examples arepresented.

George KvernadzeWeber State Universitygkvernadze@weber.edu

PP1

Stable Implementation of Complete RadiationBoundary Conditions in Finite Difference TimeDomain Solvers for Maxwell’s Equations

Complete Radiation Boundary Conditions (CRBCs) allowfor the efficient truncation of unbounded domains in wavepropagation problems. Unlike standard Perfectly MatchedLayer (PML) approaches, CRBCs allow for a weakly timedependent error estimate for both propagating and decay-ing waves. We demonstrate the how the CRBC can beimplemented in a Finite Difference Time Domain (FDTD)scheme and obtain an energy estimate using a summationby parts (SBP) argument to prove stability.

John Lagrone, Fritz JuhnkeSouthern Methodist Universityjlagrone@smu.edu, kjuhnke@smu.edu

Thomas HagstromDepartment of MathematicsSouthern Methodist Universitythagstrom@smu.edu

PP1

Regression in High Dimensions Via GeometricMulti Resolution Analysis

We present a framework for high-dimensional regressionusing the GMRA data structure. In analogy to classi-cal wavelet decompositions of function spaces, GMRA isa tree-based decomposition of data sets into local affineprojections. Moreover, GMRA admits a fast algorithmfor computing the projection coefficients on the already-learned dictionary. Within each node of the tree one canalso assign regression coefficients in any manner; here westudy the simple case of weighted linear regression.

David LawlorDepartment of MathematicsDuke Universitydjl@math.duke.edu

PP1

Two Projection Methods for Regularized TotalLeast Squares Approximation

We consider the Total Least Squares problems withTikhonov Regularization. Since the problem of finding theTotal Least Squares solution is equivalent to the solution ofthe two parameter linear system, our method derives twononlinear equations from the two parameter linear system,

AN14 Abstracts 135

applied a Newton method with a nonlinear Jacobian matrixthat is computed inexpensively. For large-scale problems,this is further combined with two projection methods, onebased on bidiagonal reduction, the other projecting onto ageneralized Krylov space.

Geunseop LeeThe Pennsylvania State Universitygxl174@cse.psu.edu

Jesse L. BarlowPenn State UniversityDept of Computer Science & Engbarlow@cse.psu.edu

PP1

Theoretical Analysis of Low-Energy ElectronDiffraction: New Results for Real Systems andNew Understanding for Model Ones

We describe our novel, first-principles approach to theoret-ical calculations of low-energy electron diffraction (LEED)spectra, and especially its expansion to off-normal inci-dence diffraction from few-layer-graphene systems. Wecompare our calculated off-normal incidence reflection in-tensities to conventional LEED calculations. We alsopresent an asymptotic investigation of electron scatteringin model systems, e.g., 2D square well potential, to betterunderstand the anomalous solutions that create difficultiesfor our wave-matching approach to this boundary valueproblem.

John F. McclainUniversity of New Hampshirejfi46@wildcats.unh.edu

Jiebing SunMichigan State Universityjsun@msu.edu

Karsten Pohl, Jian-Ming TangUniversity of New Hampshirekarsten.pohl@unh.edu, jmtang@mailaps.org

PP1

A Viscoelastic Model That Displays ThixotropicYield Stress Fluid Behavior

There are biological fluids such as the slime excreted byslugs, which are yield stress fluids. Among them, some arethixotropic. Typically, a model for yield stress fluids be-gins with inputting a measured value for the yield stress.On the other hand, our model does not assume any yieldstress behavior a priori. The relaxation time of the ma-terial is taken as a large parameter, and asymptotic solu-tions are obtained. These display some observed featuresof thixotropic yield stress fluids.

Yuriko RenardyVirginia TechDepartment of Mathematicsrenardy@vt.edu

PP1

AWM Workshop: Sexual Cannibalism As An Op-timal Strategy in Fishing Spiders

We consider a model, based on the aggressive spillover hy-

pothesis, where we link a females propensity to cannibalizea mate to her aggression towards prey. Higher levels of ag-gression lead to higher food consumption and lower matingrates, a trade-off in fitness. We find an optimal aggressionlevel and analyze its effects on the frequency and type ofsexual cannibalism. We then compare our results to exist-ing models of sexual cannibalism.

Sara ReynoldsUniversity of Nebraska-Lincolns-sreynol5@math.unl.edu

PP1

AWM Workshop: Time-Delayed Pdes withStochastic Boundary in Mathematical Modeling ofKidney

We consider nonlinear time-delayed transport equationswith stochastic boundary to study the stability of feed-back systems in the kidney. We prove the existence anduniqueness of the steady- state solution for deterministicand stochastic boundary cases with small delay, based onthe contraction mapping theorem. Model results revealedthat the system admits the stationary solution for smalldelay despite stochastic influences, whereas it exhibits os-cillatory solutions for large delay, resembling irregular os-cillations in spontaneously hypertensive rats.

Hwayeon RyuDuke Universityhwayeon@math.duke.edu

PP1

Analysis of a Camera-Based Model of Bar CodeDecoding

This work addresses the issue of the limited capability of acamera-based bar code decoding method. The question wewish to address is “What is the resolution needed in thecaptured image to unambiguously decode a bar code?” Forsimplicity, we consider the UPC bar code which consists ofblack and white bars of different widths. The width of theblack and white bars encode a 12-digit number accordingto a look-up table. The smallest element in the bar codeis assumed to be of width h. We further assume that thecamera pixels are lined up along the bars and they are ofsize d. The question now amounts to unique determinationof the digits for a fixed ratio of d to h. We show that thedigits are uniquely determined if the pixel size is no greaterthan twice the smallest element. Moreover, we show thatthis determination is stable. A decoding algorithm is pre-sented, along with numerical examples that illustrate themain ideas behind this work.

Madeline J. Schrier, Fadil SantosaUniversity of Minnesota-Twin Citiesschri051@umn.edu, santo002@umn.edu

PP1

Fully Nonlinear Model for Dispersive Wave Turbu-lence

The Majda-McLaughlin-Tabak (MMT) model describes aone-dimensional system exhibiting dispersive wave turbu-lence, and includes linear and nonlinear terms. I considera modified version of the model where the linear term isabsent. I discuss symmetry-based arguments, perturbativesolutions, and other methods for predicting the dispersion

136 AN14 Abstracts

relation and waveaction spectrum, and compare with nu-merical results. I consider both the case where driving anddamping are present and the case where they are absent.

Michael SchwarzRensselaer Polytechnic Institutemschwarz137@gmail.com

David CaiNew York UniversityCourant institutecai@cims.nyu.edu

Gregor KovacicRensselaer Polytechnic InstDept of Mathematical Scienceskovacg@rpi.edu

Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical Scienceskramep@rpi.edu

PP1

Ritz-Augmented Extended Krylov Subspaces forSequences of Lyapunov Equations

We consider the numerical solution of generalized Lya-punov equations occurring in bilinear model order reduc-tion. We proceed by splitting the operator and use a clas-sical stationary iteration, performing standard Lyapunovsolves with the extended Krylov subspace method. Thisenables reuse of computation via the use of augmentedKrylov subspaces. The resulting algorithm appears com-petitive with the existing state of the art on two benchmarkproblems.

Stephen D. ShankTemple Universitysshank@temple.edu

PP1

Numerical Investigation of Microfluidic DropletBreakup Using T-Junction Geometry

A critical analysis on the breakup of Microfluidic droplet ina T-junction is presented. A way by which droplets can beevenly distributed over multiple micro channels is to breakthem into many smaller droplets. Hence it is essential tounderstand the behavior of the breakup of droplet in amicro channel. Available theoretical and numerical dataare compared with simulations obtained using a modifiedversion of the interFoam solver of the OpenFOAM CFDpackage.

Olabanji Y. ShonibareDepartment of Mathematical SciencesMichigan Technological Universityoyshonib@mtu.edu

Kathleen FeiglMichigan Technological UniversityDept. of Mathematical Sciencesfeigl@mtu.edu

Franz TannerDepartment of Mathematical SciencesMichigan Technological University

tanner@mtu.edu

PP1

A Mathematical Model of Moisture Movement andBacterial Growth in a Two-Dimensional PorousMedium

Bacterial growth in sand is of concern in regard to thehealth of beaches. A mathematical model is presented thatrepresents the movement of moisture and the growth ofbacteria through a beach. Simulations were run by numer-ically solving Richard’s Equation using a Finite VolumeMethod. These simulations show that elevated bacteriacounts following rain events do not necessarily result frombacteria in the body of water, but can also be sourced fromthe sand.

Rachel E. TewinkelUniversity of Wisconsin - Milwaukeetewinke2@uwm.edu

PP1

A Guaranteed, Adaptive, Automatic AlgorithmFor Univariate Function Minimization

This algorithm attempts to provide an approximate mini-mum value of a one-dimensional function that differs fromexact minimum value by no more than an error tolerance.Besides guaranteed the error tolerance, this algorithm alsoconsiders the lengths tolerance of the subset containingpoint(s) where the minimum occurs.

Xin TongDepartment of Applied MathematicsIllinois Institute of Technologyxtong5@hawk.iit.edu

PP1

Iterative Functional Modification Method for Solv-ing a Transportation Problem

New method for solving transportation problems based ondecomposing the original problem into a number of two-dimensional optimization problems is proposed. Since thesolution procedure is integer-valued and monotonic in theobjective function, the required computation is finite. Asa result, we get not only a single optimal solution of theoriginal transportation problem but a system of constraintsthat can yield all optimal solutions. We give numericalexamples illustrating the constructions of our algorithm.

Vladimir I. TsurkovComputing Centre of RAStsur@ccas.ru

Alexander TizikCC RAStsurkov@gmail.com

PP1

A Multiscale Implementation for the PeridynamicModel of Mechanics

An investigation in continuous and discontinuous finite ele-ment methods for a peridynamics model of mechanics givesus a new view of the peridynamic model when dealing withsolutions with jump discontinuities. Peridyanmics can betransit between nonlocal and local models depending on

AN14 Abstracts 137

the size of horizon compared to the grid size. Therefore, amesh of good quality and an appropriate quadrature ruleto conform the multiscale setting need to be concerned. Wedeveloped a local grid refinement method that can be suit-able for the multiscale peridynamic model and also founda quadrature rule to estimate the weak formulation withhigh accuarcy.

Feifei XuFlorida State Universitywinterflyfei@gmail.com

PP1

AWM Workshop: Three Model Problems for 1-DParticle Motion with the History Force in ViscousFluids

Abstract. We consider various model problems that de-scribe rectilinear particle motion in a viscous fluid underthe influence of the history force. These problems includesedimentation, impulsive motion, and oscillatory slidingmotion. The equations of motion are integrodifferentialequations with a weakly singular kernel. We provide ana-lytical solutions using Laplace transforms and discuss themathematical relation between the sedimentation and im-pulsive start problems. We also compare several numericalschemes and benchmark them against the analytical re-sults.

Shujing XuCLAREMONT GRADUATE UNIVERSITYflora.xushujing@gmail.com

PP1

AWM Workshop: A Local Grid Mesh Reinementfor a Nonlocal Model of Mechanics

Nonlocal problems are based on integro-diferential equa-tions, which do not involve spatial derivatives. This makesit possible to deal with discontinuous solutions. We aremost interested in the numerical results for piecewise so-lutions with a jump discontinuity. A local grid reinementmethod is then investigated for two-dimensional nonlocalmodel, which would be suitable for the curve discontin-uous path. With the reine meshes, optimal convergencebehaviors are achieved.

Feifei XuFlorida State Universitywinterflyfei@gmail.com

PP1

Designing a Self-Propelled Hydrogel Microswim-mer

We use dissipative particle dynamics to design a new self-propelling bi-layered gel microswimmer. The gel consistsof one layer that swells in response to an external stimu-lus and one passive layer. When a periodic stimulus is ap-plied, the microswimmer undergoes a sequential expansion,bending, contraction, and straightening motions leading tonet propulsion at low Reynolds number. We probe howthe swimming speed can be enhanced by selecting mate-rial properties and geometry of the gel swimmer.

Peter Yeh, Svetoslav NikolovGeorgia Institute of Technologypyeh3@gatech.edu, snikolov3@gatech.edu

Alexander AlexeevGeorge W. Woodruff School of Mechanical EngineeringGeorgia Institute of Technologyalexander.alexeev@me.gatech.edu

PP1

Inverse Modeling and Prediction UncertaintyAnalysis of a Co2 Injection Pilot Test, Cranfield,Mississippi

The ensemble-based filtering algorithms and the null-spaceMonte Carlo approach are applied for characterizing theheterogeneity and quantifying model prediction uncer-tainty of a CO2 injection test, Cranfield, Mississippi. Anensemble of reservoir model conditioned to the observeddata is retained from both approaches and models predic-tion results are analyzed to evaluate the trade-off betweenmodel efficiency and model complexity to provide a com-putationally efficient and practically useful framework forpredictive uncertainty analysis of CO2 sequestration.

Hongkyu YoonGeoscience Research and ApplicationsSandia National Laboratorieshyoon@sandia.gov

Reza TavakoliUT-Austintavakoli@ices.utexas.edu

Bill ArnoldSandia National Laboratoriesbwarnol@sandia.gov

PP1

A Spatio-Temporal Point Process Model for Am-bulance Demand

We model spatio-temporal point processes as a time se-ries of spatial densities using finite mixture models. Wefix the mixture component distributions across time whileletting the mixture weights evolve over time. We captureseasonality by constraining mixture weights; we representlocation-specific temporal dependence by applying autore-gressive priors on mixture weights. To illustrate, we esti-mate ambulance demand in Toronto, Canada. Our methodaccurately captures the complex spatial and temporal dy-namics present in this large-scale dataset.

Zhengyi ZhouCenter for Applied MathematicsCornell Universityzz254@cornell.edu

David MattesonDepartment of Statistical ScienceCornell Universitydm484@cornell.edu

Dawn WoodardSchool of Operations Research and InformationEngineeringCornell Universitywoodard@cornell.edu

Shane HendersonCornell UniversitySchool of Operations Research and Industrial Engineering

138 AN14 Abstracts

sgh9@cornell.edu

Athanasios MicheasDepartment of StatisticsUniversity of Missouri-Columbiamicheasa@missouri.edu