ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology...

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Computa(onal Science at the Università della Svizzera italiana Lugano November 18, 2014 Ins6tute of Computa6onal Science Faculty of Informa6cs Università della Svizzera italiana R. Krause M. Bronstein, I. Horenko, V. Limongelli, M. Parrinello, I. Pivkin, M. Potse, O. Schenk,

Transcript of ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology...

Page 1: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

Computa(onal  Science  at  the  

Università  della  Svizzera  italiana  

Lugano  November  18,  2014

Ins6tute  of  Computa6onal  Science  Faculty  of  Informa6cs  

Università  della  Svizzera  italiana

R.  Krause  

M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk,

Page 2: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�2R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk 4

Theory Physical Experimentation

Computational   Science

 21st  Century  Science

Computational  Science

2005  Report  of  the  US  President's  Information  Technology  Advisory  Committee  „Computational  Science:  Ensuring  America's  Comptetitiveness“    

Page 3: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�3R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk 3ICS,  wetterjournal.wordpress.com,  lbl.gov,  research.nokia.com    

The  21st  century’s  first  great  scientific  breakthrough  was  a  triumph  of  large-­‐scale  computational  science..    PITAC  Report

Engineering  and  Manufacturing

Meteorology/Climatology  and  Geosciences

Finance

Biology

Physical  Sciences

Political  and  Social    Sciences

Neuroscience

Medicine

Page 4: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�4R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Science    (physics,  chemistry,  

Mathematics

Informatics

Computational  Science  

Computational science, may be defined as the intellectual discipline concerned with the study, development, and use of algorithms, methods and simulations tools implemented on computing devices for scientific discovery and applications in science, engineering,

medicine, and technology.

Page 5: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�5R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Numerical Simulation in Science, Medicine, and Engineering (Krause)

Computational Shape Analysis (Bronstein)

Computational Fluid Dynamics (Pivkin)

Advanced Computing Laboratory (Schenk)

Cardiac Electrophysiology (Potse)

Computational Time Series Analysis (Horenko)

Computational Biology & Material Science (Parrinello)

8  Research  Groups  >  60  members  

Master  Program  "Computa(onal  Science”  PhD  in  “Computa(onal  Science”  

PhD  Program  FOMICS

Medicinal Chemistry & Drug Design (Limongelli)

Page 6: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�6R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Center for Computational Medicine in Cardiology CCMCInstitute of Computational Science ICSFaculty of Informatics

UniversitàdellaSvizzeraitaliana

!

Center for Computational Medicine in Cardiology Auricchio (CCT), Krause (ICS/USI), Potse (ICS/USI)

Page 7: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�7R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

CSCS

Engineering

MedicineHealth

VisualData

EnvironmentClimateSociety

Energy

BiologyDrugs

DataAnalysisShape &

ImageAnalysis

Solid and Fluid

Mechanics

Geo Science

EngineeringOptimization

Material Science

Biology

Medicinal Chemistry

& Drug design

MedicineCardiology

EconomicsSocial

Sciences

Life Sciences

HPC

ICSApplied Mathematics

Master and PhD inComputational Science

Computational Science

Simulation tools and software

Graduate School FOMICS

Numerical Methods

CCMCCenter for

Computational Medicine in Cardiology

Page 8: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�8R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

CSCS

Engineering

MedicineHealth

VisualData

EnvironmentClimateSociety

Energy

BiologyDrugs

DataAnalysisShape &

ImageAnalysis

Solid and Fluid

Mechanics

Geo Science

EngineeringOptimization

Material Science

Biology

Medicinal Chemistry

& Drug design

MedicineCardiology

EconomicsSocial

Sciences

Life Sciences

IRBIOR

Cardiocentro Ticino

EPFL

EPFL

U Basel

ETH

U Bern

ETH

EPFL

HS Luzern

ETH

ETH

FU Berlin

CSIROU Tel-Aviv

TechnionDuke

KIT

U Bern

USI Eco

U BernISTB

U MaastrichtPolitecnico

HPC

ICSApplied Mathematics

Master and PhD inComputational Science

Computational Science

Simulation tools and software

Graduate School FOMICS

Numerical Methods

ETH

U Chicago

FZ JÜLICH

CCMCCenter for

Computational Medicine in Cardiology

SPP 1748

SCCER SoE

SPP SPPEXASCCER FURIESNCCR MARVEL

PASC

PASC

ERC

ERCPASC

NFP 70

Page 9: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�9R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Designed  for  Computa6onal  Science

Interdisciplinary  educa6on  is  more  than  just  pu_ng  together  lectures  from  different  disciplines

Page 10: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�10R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  SchenkDickopf, Krause, Krause, Potse SISC Journal for Scientific Computing, 2014

Center for Computational Medicine in CardiologyComputational Electrophysiology

(Potse, Krause (USI) Auricchio (CCT))

Potse, 2014

Computations done at CSCS

Page 11: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�11R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk 5Computational  Science

Coupled Systems: Fluid Structure Interaction Fast solution methods and tailored discretization schemes

Computations done at CSCSSteiner, K’, 2014

Page 12: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�12R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Stochastic Platelet Model (more details) •  Platelets can be in three biological states: passive, triggered, activated •  The key component is an activation delay time – the time it takes for

platelet to go through the activation process ( Richardson, PD. (1973) Nature 245, 103–104)

•  The activation delay time was estimated from experimental data to be about 0.2 seconds

Pivkin, Richardson, Karniadakis PNAS 103, 17164–17169

PASSIVE non-adhesive

TRIGGERED non-adhesive

ACTIVATED adhesive

Exposure to high concentration of

activation chemicals

Activation delay time, chosen RANDOMLY

for each platelet

If not adhered after 5 s

Activation corona

High concentration of activation chemicals, time dependent region

Stochastic Platelet Aggregation Model Group Pivkin

Computations done at CSCS

Page 13: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�13R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Research  Highlight  2014  –    Real-­‐Fme  StochasFc  OpFmizaFon  of  Complex  Energy  Systems  on  High  Performance  Computers,  Leadership  CompuFng,  IEEE  Journal  CompuFng  in  Science  and  Engineering

Computations done at CSCS

Wave propagation and adjoint optimization with focus on numerical methods transfer of knowledge into the earth science community

Group Schenk

Page 14: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�14R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Parrinello Groupatomistic simulations of complex systems

Materials Biomolecules

Calculation of the unbinding rate of drug from protein:!!A!new!way!for!effec-ve!drug!design!

Characterisation of the self-assembly of complex materials:!

!Ra-onal!design!of!crystalliza-on!processes

Method Development

Rates from MetadynamicsWell Tempered Metadynamics

MetadynamicsCar-Parrinello Molecular Dynamics

Variational Approach to Enhanced Sampling

⌦[V ] =

1

�log

Rds e��[F (s)+V (s)]

Rds e��F (s)

+

Zds p(s)V (s)Sampling rare events

in complex molecular systems

Breaking the millisecond

barrier in fully atomistic

simulations

Computations done at CSCS

Page 15: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�15R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Binding mechanism to cellular membrane of the multiple sclerosis (MS) biomarker CSF114(Glc). Using these simulations, complemented by a number of experiments, we have elucidating its functional mechanism. Our findings provide the molecular tools to develop new MS diagnostic and therapeutic agents.

Investigating peptide/membrane binding Group Limongelli

Page 16: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�16R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Visual Shape Analysis Group Bronstein

Page 17: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�17R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Computations done at CSCS

Contact of soft elastic material with

rough hard substrate

Rigazzi, K’ 2014

Page 18: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�18R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

Group KrauseHigh Performance Methods for Numerical Simulation in

Science, Medicine and EngineeringConclusions and Outlook

Surface e�ects (Bio)mechanics

Coupled models Parallel computing

Models,Methods,Software

R. Krause Parallel Methods 41

Computations done at CSCS

Page 19: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�19R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

PASC - Swiss Platform for Advanced Scientific ComputingPASC is a structuring project jointly supported by the Swiss University Conference (SUC) and the ETH Board.

PASC is coordinated by USI in collaboration with CSCS and with the other Swiss universities and EPFL.

Physics Climate

Solid Earth

Material

Life Sciences

PASCICS

CSCSApplied Mathematics

Computational ScienceNumerical Methods

Co-Design

CADMOS

Social Sciences

ICS participates in 6 projects in 4 networkshttp://www.pasc-ch.org

ETHZ

ETHZ

Meteoswiss

EPFL

Geneva Basel

Fribourg

Zürich

USI

ETHZ

ETHZ

EPFLUSI

Geneva

Zürich

Zürich

EPFL

USIBasel Geneva

Bern

USI

ETHZ

Page 20: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

�20R.  Krause,  M.  Bronstein,  I.  Horenko,  V.  Limongelli,  M.  Parrinello,  I.  Pivkin,  M.  Potse,  O.  Schenk

• 2 ERC Grants (Bronstein, Parrinello) 2013• Participation in NCCR MARVEL (Parrinello) 2014• 18 snf projects at ICS since 2009• Participation in NFP 70 (K’) 2014• Participation via “Dachabkommen” in 2 SPPs and “Forschergruppe” (Horenko, K’)

2012,2013,2014• Mercator Professorship DFG (Horenko) 2014• Participation in “Energy Swiss Competence Center of Energy Research (SCCER)”

FURIES and SoE (Schenk, K’, Malek (ALARI)) 2014• Platform for Advanced Scientific Computing (PASC): Swiss National High

Performance Strategy (Parrinello, Pivkin, Schenk, K’) 2013• PhD School FOMICS 2012• PhD in Computational Science 2014• Master Program in Computational Science 2012• Center for Computational Medicine in Cardiology 2014• Local cooperations: CCT, SUPSI, ALARI, IDSIA, industry, … since 2009• (Inter-)national cooperations (PASC, SCCER, snf, CTI, snf/DFG,…) since 2009• More than 60% of annual salaries are third party funding since 2009• …

Page 21: ComputaonalScience at+the+ UniversitàdellaSvizzeraitaliana€¦ · Computational Electrophysiology (Potse, Krause (USI) Auricchio (CCT)) Potse, 2014 Computations done at CSCS. R.+Krause,’M.’Bronstein,’I.’Horenko,’V.’Limongelli,’M.’Parrinello,’I.’Pivkin,’M.’Potse,’O.’ScComputational’Science

Noisy Hegselmann-Krause Systems: Phase Transition and the ...chazelle/pubs/noisyHK-JSP.pdf · Noisy Hegselmann-Krause Systems: Phase Transition ... Noisy Hegselmann-Krause Systems

Noisy Hegselmann-Krause Systems: Phase Transition and the ...chazelle/pubs/noisyHK-JSP.pdf · Noisy Hegselmann-Krause Systems: Phase Transition ... Noisy Hegselmann-Krause Systems

KRAUSE GATEWAY CENTER

KRAUSE GATEWAY CENTER

kuhn krause PRODUCT RANGEFile/KuhnKrause_Brochure_LZ.pdfkuhn krause PRODUCT RANGE Tillage and Seeding INTRODUCING THE NEW KUHN KRAUSE PRODUCT LINE 2011 – 2012 The Company Located

kuhn krause PRODUCT RANGEFile/KuhnKrause_Brochure_LZ.pdfkuhn krause PRODUCT RANGE Tillage and Seeding INTRODUCING THE NEW KUHN KRAUSE PRODUCT LINE 2011 – 2012 The Company Located

Johannes Krause - Max Planck Society Vitae Johannes Krause, Page 1/13, December 13, 2017 Johannes Krause Born 1980 in Leinefelde, Thueringen, Germany Address Max Planck Institute for

Johannes Krause - Max Planck Society Vitae Johannes Krause, Page 1/13, December 13, 2017 Johannes Krause Born 1980 in Leinefelde, Thueringen, Germany Address Max Planck Institute for

Krause Gen2003 Press

Krause Gen2003 Press

Krause john vissual_resume_09_10_2012

Krause john vissual_resume_09_10_2012

Hypertension Krause

Hypertension Krause

About Brey-Krause Manufacturing Co. Brey-Krause Manufacturing Co. Brey-Krause manufactures a comprehensive line of commercial washroom accessories that are 100% made in the USA. Since

About Brey-Krause Manufacturing Co. Brey-Krause Manufacturing Co. Brey-Krause manufactures a comprehensive line of commercial washroom accessories that are 100% made in the USA. Since

Regina Krause - Mandalafestés

Regina Krause - Mandalafestés

Krause Fund

Krause Fund

Holly Krause Portfolio

Holly Krause Portfolio

kuhn krause PRODUCT RANGE · kuhn krause PRODUCT RANGE. Tillage and Seeding. INTRODUCING THE NEW KUHN KRAUSE PRODUCT LINE. 2011 – 2012

kuhn krause PRODUCT RANGE · kuhn krause PRODUCT RANGE. Tillage and Seeding. INTRODUCING THE NEW KUHN KRAUSE PRODUCT LINE. 2011 – 2012

R. Krause-Rehberg - Positron Annihilation in Hallepositron.physik.uni-halle.de/talks/Krause-Rehberg_APOSB... · 2010. 3. 23. · R. Krause-Rehberg Universität Halle, Inst. für Physik

R. Krause-Rehberg - Positron Annihilation in Hallepositron.physik.uni-halle.de/talks/Krause-Rehberg_APOSB... · 2010. 3. 23. · R. Krause-Rehberg Universität Halle, Inst. für Physik

Sustainable Energy - Martin Krause

Sustainable Energy - Martin Krause

Photographer Collection Reinhard Krause

Photographer Collection Reinhard Krause

Mike Krause

Mike Krause

Timothy Krause - ETF

Timothy Krause - ETF

Hybrid Particle Simulations: An approach to the spatial multiscale problem Guang Lin, PNNL Thanks: George Em Karniadakis, Brown University Igor Pivkin.

Hybrid Particle Simulations: An approach to the spatial multiscale problem Guang Lin, PNNL Thanks: George Em Karniadakis, Brown University Igor Pivkin.

(Krause 2004)

(Krause 2004)

Egon Krause Fluid Mechanics

Egon Krause Fluid Mechanics