Sixth Workshop

on

Mathematical Modelling

of

Environmental and Life Sciences Problems

Constanta, 5–9 September 2007

ACADEMIA ROMANA

INSTITUTUL DE STATISTICA MATEMATICA SI MATEMATICAAPLICATA ,,GHEORGHE MIHOC-CAIUS IACOB”

SECTIA DE MATEMATICA APLICATA

UNIVERSITATEA OVIDIUS DIN CONSTANTA

FACULTATEA DE MATEMATICA SI INFORMATICACENTRUL DE MATEMATICI APLICATE

sponsorizata de

SOFTWIN Bucuresti si Ministerul Educatiei si Cercetarii

Comitetul Acad. Lazar DragosStiintific Prof. Dr. Dorel Homentcovschi

Acad. Marius IosifescuProf. Dr. Alexandru MoregaProf. Dr. Ulirch RudeProf. Dr. Harry Vereeken

Comitetul Prof. Dr. Marius Craciunde Organizare Dr. Stelian Ion

Dr. Gabriela MarinoschiProf. Dr. Constantin Popa

Secretariatul drd. Elena BautuConferintei Felicia Grigore

drd. Elena Pelican

PROGRAMUL GENERAL AL CONFERINTEI

MIERCURI 5 SEPTEMBRIE

16.00-18.00 Inregistrarea participantilor

JOI 6 SEPTEMBRIE

9.00-10.20 Deschiderea conferintei10.20-11.20 Comunicari11.20-11.40 Pauza11.40-13.00 Comunicari13.00-14.30 Pauza de masa14.30-15.30 Comunicari15.30-15.45 Pauza15.45-16.45 Comunicari16.45-17.00 Pauza17.00-18.00 Comunicari

VINERI 7 SEPTEMBRIE

9.30-11.10 Comunicari11.10-11.30 Pauza11.30-12.30 Comunicari12.30-12.50 Pauza12.50-13.50 Comunicari13.50-14.30 Pauza de masa14.30-15.30 Comunicari19.00-23.00 Banchet

SAMBATA 8 SEPTEMBRIE

Program Social

DUMINICA 9 SEPTEMBRIE

9.30-11.30 Masa rotundaStrategii de cercetare in domeniul biomatematicii

11.30-12.30 Inchiderea lucrarilor conferintei

3

Lucrarile conferintei

JOI 6 SEPTEMBRIE, 2007

10.20-13.00 Comunicari

Moderatori Gabriela Marinoschi, Gheorghe Albeanu

1 Gabriela Marinoschi

Periodic solutions for underground flows

2 Neculai Andrei

Another hybrid conjugate gradient algorithm for molecular formation un-

der pairwise minimization3 Corneliu I. Oprea and Mihai A. Gırtu

Density functional theory calculations of metal-tetracyanoethylene com-

plexes——————Pauza————————

4 Stefania Petra and Christoph Schnorr

Tomographic Image Reconstruction in Experimental Fluid Dynamics

5 Tiberius Duluman, Constantin Popa, and Ulrich Rude

Algebraic multigrid interpolation strategies with application in image re-

construction6 Adrian Moncea and Crenguta Bogdan

Romanian Optical Characters Recognition Application Using Artificial

Neural Networks7 Katsumi Moriwaki

Modelling and Control of the Guide Robot for Visually Handicapped Per-

sons and Aged Persons14.30-18.00 Comunicari

Moderatori Nicolae Pop, Katsumi Moriwaki, Alexei Leahu

8 Nicolae Pop

Analysis of the nonlinear inexact Uzawa algorithms for saddle-point in

elastic contact problems9 Eduard Marius Craciun and Adrian Carabineanu

Mathematical modelling of the incremental fields in a cracked composite

4

10 D.M. Popovici, D. Sopu, M. Gırtu

ScientView - a Virtual Reality based platform for scientific visualisation

———————-Pauza———————11 Christian Mancas

Mathematic and Computer Science Modeling of Endangered Species Data

12 Beatrice Mihaela Macri

Cholesterol effect on the insertion of coumarin-3-carboxylic acid effect

into model lipid bilayers13 Dumitru Popescu and A. G. Popescu

Dynamics of Pulsatory Liposome

———————-Pauza———————14 Grigore Albeanu and Manuela Ghica

Bootstrap simulation models for probabilistic approaches in environmental

economics15 Alexei Leahu and Carmen E. Lupu

Renewal processes with two-parameter exponentially distributed renewal

lifetimes16 Elena Carmen Lupu

Analysis of the different censored sampling schemes from a new lifetime

distribution

VINERI 7 SEPTEMBRIE 2007

9.30-11.10 Comunicari

Moderatori Stelian Ion, Constantin Popa

17 Cristina Elena Asaftei and Elena Pelican

On a simulation of hydraulic system with applications to Nuclear Power

Plant Cernavoda18 Andrei Bautu and Elena Bautu

Designing telescope arrays with PSO

19 Daniel Draghicescu and Crenguta Bogdan

Using Web Services, J2ME, A* Algorithm and .NET Framework to Con-

struct Mobile Phone Software Applications20 Robu Octavian and Popescu Elena

Development of a vertical intelligent sonar

21 Robu Octavian and Popescu Elena

Propagation of the sound in marine environment. Development of a model

5

11.30-13.30 Comunicari

Moderatori Marius Craciun, Nicolae Andrei

22 Stelian Ion

Unsaturated water flow through stratified soil

23 Gheorghe Juncu, Aurelian Nicola, Constantin Popa and Tudor

UdrescuNonlinear Multigrid Methods for Groundwater Flow problems in Hetero-

geneous Prous media24 Gheorghe Juncu, Aurelian Nicola, Constantin Popa and Tudor

UdrescuMultigrid Based Preconditioning Algorithms for Diffusion-Convection-

Reaction Equations25 Daniel Mocanu, Alexandru M. Morega and Andrei Negoias

DNA Hybridization in Microfluidics Systems - Transport Mechanisms

26 Florin A. Radu

Numerical simulation of bio-reactive contaminant transport in soil

27 N. Suciu, P. R. Kramer, F. A. Radu and C. Vamos

Lagrangian-Eulerian statistics and numerical modeling of transport in ho-

mogeneous random media

6

Rezumate

7

Bootstrap simulation models for probabilistic approaches inenvironmental economics

byGrigore Albeanu and Manuela Ghica

Computer-intensive methods for estimation assessment provide valuableinformation concerning the adequacy of applied probabilistic models. Thebootstrap method is an extensive computational approach for understand-ing empirical data and is based on resampling and statistical estimation. Itis a powerful tool, especially when only a small data set is used to predictthe behaviour of systems or processes. This paper describes the usage ofthe bootstrap approaches for modelling loss distributions and for generaldynamic financial analysis. The research is based on previous developmentsin accuracy assessment, reliability estimation and risk exchange modeling.The same techniques will be illustrated for some distributions used in envi-ronment modelling for business.

Another hybrid conjugate gradient algorithm for molecular formationunder pairwise minimization

byNeculai Andrei

Another hybrid conjugate gradient algorithm is proposed and analyzed.The parameter βk is computed as a convex combination of βHS

kcorrespond-

ing to Hestenes-Stiefel and of Dai-Yuan conjugate gradient algorithms, i.e.βCk= (1− θk)β

HSk

+ θkβDYk

. The parameter θk in the convex combination iscomputed in such a way that the direction corresponding to the conjugategradient algorithm is equating the Newton direction. The algorithm uses thestandard Wolfe line search conditions. Numerical comparisons with conju-gate gradient algorithms for molecular formation under pairwise minimiza-tion show that this hybrid computational scheme outperforms the Hestenes-Stiefel and the Dai-Yuan conjugate gradient algorithms, as well as someother known hybrid conjugate gradient algorithms.

8

On a simulation of hydraulic system with applications to NuclearPower Plant Cernavoda

byCristina Elena Asaftei and Elena Pelican

In this paper we shall present some practical considerations when dealingwith hydraulic systems, along with a module which simulates the liquid zoneprocess, its motors and valves. As the liquid zone control is one of severalreactivity control systems, which purpose is to provide a tool for controlingthe neutron flux and thus reactor power, it is important to have a real timesimulator for it.The liquid zone control system is composed of a dematerialized water sys-tem (which provides a means for neutron absorption) and a helium covergas circuit. We shall briefly present theoretical base of the simulation of thehydraulic system based on the physics principles and its due mathematicequations.

Designing telescope arrays with PSOby

Andrei Bautu and Elena Bautu

The optimal placement of telescope array stations with respect to the uv

coverage is a crucial importance problem in ground-based radio astrology.The main objective is to design an array that allows several distributed smalltelescopes to achieve the resolution of a costly single large telescope by cor-relating data to create a synthesized beam. The complexity of this problemincreases when other objectives, related to economical and technologicalfactors (e.g. distance between stations, transmission delays, materials, etc.)are considered. In this paper we tackle this problem in a multiobjectiveenvironment with the Particle Swam Optimization (PSO) technique. Theexperimental results and discussion indicate that PSO designs competitivetelescope arrays.

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Mathematical modelling of the incremental fields in a crackedcomposite

byEduard Marius Craciun and Adrian Carabineanu

Mathematical modelling of the incremental fields in a pre-stressed elasticcomposite in plane and antiplane states is done using the theory of complexanalysis. We formulate and solve the crack problem in all three classi-cal modes in complex potentials. Following Guz and using the theory ofRiemann-Hilbert problem, Cauchy’s integral, Plemelj’s functions we obtainthe assimptotic behavior of the incremental fields in the vecinity of the cracktip. The critical values of the incremental stresses which are producing crackpropagation are obtained.

Using Web Services, J2ME, A* Algorithm and .NET Framework toConstruct Mobile Phone Software Applications

byDaniel Draghicescu and Crenguta Bogdan

In the last years, the mobile software acquired an increasingly attentionfrom both developers and users. The mobile applications are divided intoseveral categories: games, multimedia, and utility applications. In the lastcategory, we can place the applications for guidance in a city, which offerservices like path finding, area information, and so on. Today, these applica-tions are mainly developed using the GPS technology. The main objective ofour study was to use different software technologies, like web services, J2ME,heuristic algorithms, and .NET framework to develop a complex mobile ap-plication. This paper presents the MPF (Mobile Path Finder) applicationfor the guidance of the user in a city. The application uses all the abovetechnologies and the A* algorithm to allow a mobile phone user to find theoptimal path between two intersections of a city. MPF is a distributed andn-tier application, modularized in four subsystems: server, administration,client, and data storing. Each one provides different functionalities neededfor the application functioning. MPF is based on the client-server archi-tecture. The client subsystem runs on a mobile phone, but all of the dataprocessing is done remotely on a dedicated server, in order to bypass thephones small computing power. The server, administration and persistence

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subsystems run on one or more regular PC’s. The MPF application pro-vides all of the mobile phones advantages, like mobility, ease usability andlow costs for developing and using, costs sometimes even lower than the GPStechnology.

Algebraic multigrid interpolation strategies with application in imagereconstruction

byTiberius Duluman, Constantin Popa, and Ulrich Rude

In this paper, we are focussing on the design and analysis of some versionsof algebraic multigrid interpolation operators, as well as an extended matrixapproach for least squares problems arising after the mathematical mod-elling and discretization of image reconstruction from projections problemsin computerized tomography. All the empirical and theoretical considera-tions are included on numerical experiments on model problems arising inelectromagnetic geotemography and CT medical applications.

Unsaturated water flow through stratified soilby

Stelian Ion

In this paper we report some numerical results concerning the Richards’equation. The physical problem refers to the unsaturated water flow throughhorizontal layered soil. In the case of stratified soil the different mechanicalproperties of the soils require different constitutive functions which in turnlead to a partial differential equation with discontinuous coefficient. On aninterface of two different strata one must impose some compatible conditionsto have a well defined problem. A new numerical algorithm to solve theequation is proposed and some numerical tests are also presented.

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Nonlinear Multigrid Methods for Groundwater Flow problems inHeterogeneous Prous media

byGheorghe Juncu, Aurelian Nicola, Constantin Popa and Tudor

Udrescu

A nonlinear multigrid method for the solution of the Richards’ equation(RE) with discontinuous coefficients is the focus of this work. Written inits saturation - based form, this nonlinear parabolic equation models waterflow into unsaturated heterogeneous porous media. The numerical approachis based on an implicit time second - order accurate discretization combinedwith a nonlinear multigrid algorithm. The test problems simulate variableinflows and outflows (e.g. infiltration of water into and evaporation from)in a 2D heterogeneous unsaturated porous medium. The result is the soilwater content at any required time and depth.

Multigrid Based Preconditioning Algorithms forDiffusion-Convection-Reaction Equations

byGheorghe Juncu, Constantin Popa, Aurelian Nicola and Tudor

Udrescu

Diffusion-convection-reaction equations are used for modelling many im-portant practical problems (as e.g. convective heat transfer or convectivemass transfer with or without chemical reaction). They are usually dis-cretized by finite element or finite differences schemes, that give rise to bigand sparse linear systems of equations, for which the iterative solvers aremore appropriate. Unfortunately, when the convection term dominates andthe discretization mesh-size is not enough small to equilibrate it, instabilitiescan appear in the computed solution. In order to eliminate this situations wepropose in this paper two preconditioning techniques, based on a multiplelevels discretization of the problem. Numerical experiments and compar-isons between our methods and classical iterative solvers are presented fora convection - diffusion - reaction problem that models the transport of aneffluent through a porous medium.

12

Renewal processes with two-parameter exponentially distributedrenewal lifetimes

byAlexei Leahu and Carmen E. Lupu

In our paper we approach distribution of n-th renewal moment, distributionof counting process and renewal function for renewal processes with two-parameter exponentially distributed renewal lifetimes. Analytical resultswill be compared with corresponding results of statistical simulation.

Analysis of the different censored sampling schemes from a newlifetime distribution

byElena Carmen Lupu

In this paper it is considered the maximum likelihood estimation procedureof the parameters when data are Type I, Type II and interval censored fora new lifetime distribution proposed by Coscun Kus (2007). The maximumlikelihood estimators of the unknown parameters and the Fisher informa-tion matrix are obtained. Simulation studies are carried out to observe theperformance of the estimators in small sample.

Mathematic and Computer Science Modeling of Endangered SpeciesDataby

Christian Mancas

Plants and animals hold medicinal, agricultural, ecological, commercial andaesthetic / recreational value; endangered species must be protected andsaved so that future generations can experience their presence and value.Lot of unstructured data on them is available worldwide, either electroni-cally or not. This paper is aimed at offering rigorous both mathematical andIT data models for it, covering not only their taxonomy (including photosand videos), but also reasons for protecting them, causes of endangerment(habitat destruction, pollution, introduction of exotic species, overexploita-tion, disease, etc.), protection ways (generally causes’ duals), correspondinglegislation and organizations, as well as references. Three data model types

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are used: the Elementary Mathematical, the Entity-Relationship, and theRelational one (for which a plausible, valid, and interesting instance is alsoprovided). These models are not only structuring existing data, but are alsoa solid theoretical basis for designing and implementing a database softwareapplication to store, maintain, and query this data.

Periodic solutions for underground flowsby

Gabriela Marinoschi

This work deals with the study of periodic solutions underground flows mod-eled by a fast diffusion equation with a highly nonlinear convective term,according to van Genuchten hydraulic model. The existence of a solution toan intermediate problem restraint to a period T will be proved and then theresult will be extended by periodicity to all time real space. The approachwill involve an appropriate approximating problem and next, compactnessresults and a pass to the limit technique will ensure the existence of a weaksolution to the original problem. Under the considered hypotheses this willbe not unique, but supplementary properties of the solution, uniqueness in-cluded, are presented in the case of a globally Lipschitz convective function.Also, results upon the solution asymptotic behavior at large time are pro-vided. The theoretical results will be illustrated at the end by numericalapplications to a real problem of water infiltration in nonlinear soils.

Cholesterol effect on the insertion of coumarin-3-carboxylic acid effectinto model lipid bilayers

byBeatrice Mihaela Macri

Coumarins comprise a very large class of phenolic substances found in plantsand are made of fused benzene and 03b1-pyrone rings. In view of the estab-lished low toxicity, relative cheapness, presence in the diet and occurrencein various herbal remedies of coumarins, it appears an interesting topic toevaluate their physico-chemical properties and their interaction with lipidbilayers. A few studies from the literature discuss the interaction betweencoumarinic derivatives and lipid membranes: (i) TAMAC and DTMACdetect the surface hydrophobicity increase as the bilayer approaches the

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hexagonal phase transition temperature; (ii) 7-acetoxy-4-methylcoumarinderivative insert deeply within the DMPC bilayers; (iii) no effect of DOPCunilamellar vesicles bilayer curvature on solvent relaxation was detected byDTMAC fluorescence. The goal of our study was to identify the mecha-nism of incorporation into model lipid bilayers of coumarin-3-carboxylic acid,and the effect of cholesterol presence on this compound insertion, using thetechnique of black lipid membranes. Electrical capacitance increases uponcoumarin-3-carboxylic acid application for PC, PC:CHOL 3/1, PC:CHOL4/1, and decreases for PC:CHOL 2/1 bilayers. In PC:CHOL 2/1 bilayers,coumarin-3-carboxylic acid determines a high ionic permeability. We be-lieve that this compound promotes the formation of lipid rafts and thus weexplain the ubiquitary effect on several ion channels and receptors. Thus,the ratio between phospholipids and cholesterol in a model bilayer, stronglyinfluence the insertion of coumarin-3-carboxylic acid. Our study can beextended to other relevant coumarins.

DNA Hybridization in Microfluidics Systems - Transport Mechanismsby

Daniel Mocanu, Alexandru M. Morega and Andrei Negoias

This study aims at developing a theoretical framework for the analysis oftransport effects on DNA hybridization reaction in microfluidic-based assays.We present a simple, Cartesian, yet efficient mathematical model aimedat assessing physicochemical phenomena associated with DNA hybridiza-tion. The coupled convection, diffusion transport processes of a species(free, target DNA suspension) and its consumption through the reactionwith a second species (probe DNA) at one of the confining channel sidewalls are investigated. The forced flow of the working fluid is laminar, atlow Reynolds number. The reaction between the target and probe DNAmolecules is assumed reversible, of second order, with known characteristicparameters. The numerical results provide for a better understanding ofthe influence that the transport phenomena have on the hybridization, andsuggest optimization criteria for microarray systems.

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Romanian Optical Characters Recognition Application Using ArtificialNeural Networks

byAdrian Moncea and Crenguta Bogdan

In the last few years, Romanian business companies want to give up theclassical paper documents, in order to keep their information in electronicformat. A solution is that some employees edit and format their documentsas they were on the paper. Another solution is the using of a softwareapplication that automatically carries out these functionalities using theOCR (Optical Character Recognition) procedure. The purpose of our studywas to use the mechanisms offered by the multilayer artificial neural networksand the back-propagation training algorithms in the characters recognitionprocess, including the Romanian diacritical marks.

Modelling and Control of the Guide Robot for Visually HandicappedPersons and Aged Persons

byKatsumi Moriwaki

The problem of modelling and control of the guide robot for visually hand-icapped persons and aged persons is considered. The guide robot, proposedhere, can play the role of a guide dog as the aid of a visually handicappedperson. This paper presents the cognition system, which finds out the lineof a series of Braille blocks (guide blocks) on the sidewalk by a CCD cam-era, and the tracking control system, with which the guide robot can tracesalong a series of Braille blocks and guides an accompanied person to walkoutdoors safely.

Density functional theory calculations of metal-tetracyanoethylenecomplexes

byCorneliu I. Oprea and Mihai A. Gırtu

The M[TCNE]x y(solvent) family of molecule-based magnets (M = V, Fe,Mn, Ni, Co, TCNE = tetracyanoethylene) has been one of the most ex-tensively studied due to the large Curie temperature of these compounds.

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Despite detailed magnetic, spectroscopic and conductivity studies the mech-anism for the strong exchange coupling in the family of metal-TCNE systemshas remained an open question, the difficulty being related to the absenceof structural data for these amorphous compounds. We report density func-tional theory (DFT) calculations on various vanadium-TCNE model sys-tems, providing the geometry optimization and the electronic structure. Wecompare and contrast the results and discuss the relevance of the modelsused to the real systems.

Analysis of the nonlinear inexact Uzawa algorithms for saddle-pointin elastic contact problems

byNicolae Pop

The Uzawa-type algorithms are widely used in the engineer community be-cause they are efficient and have minimal numerical computer memory re-quirements. For this reason, the Uzawa-type algorithms could be importantin large-scale scientific applications implemented for the computing archi-tecture. On this paper we focus on the transformation of the generalizedSignorini elastic contact problems into a discretized saddle-point problemby finite element methods, using some augmented Lagrangian functional.The unique existence of the discrete saddle-point problem and the equiva-lence of saddle point formulation to the discrete variational inequality wereestablished via a discrete inf-sup condition. As well, we propose a newUzawa-type algorithm, in the non-symmetrical case, which consists on im-proving the condition numbers of stiffness matrix, by splitting of the normalstress and tangential stress and which leads to a better convergence of thesolution. After finite element discretization of the elastic contact problemswith friction, we obtain a big sparse non-symmetric and non-linear systemsof equations, which are in many cases ill-conditioned. Solving these systemsby direct methods or classical iterative methods are non efficient and theyhave bad convergence properties. One way to overcome these difficultiesis to use the Uzawa-type algorithms. After linearization of the generalizedSignorini elastic contact problems with Newton’s method, an Uzawa-typealgorithm can be applied in which Lagrange multipliers are introduced innormal and tangential directions, respectively ΛN and ΛT . The global it-eration procedure with an inner Newton and outer augmentation loop ispresented and due to the fact that in the inner Newton loop the update

17

formulas used for the frictional forces, the tangent matrix is non-symmetric.Computational results are going to be reported for several contact problems.

Dynamics of Pulsatory Liposomeby

D. Popescu and A. G. Popescu

There are a lot of methods to induce a mechanical tension in the lipid bilayerof a unilamellar vesicle or a cell. Here we will consider that the inductionof mechanical tension is due to a transmembranar osmotic gradient. Oneconsiders a giant lipid vesicle filled with aqueous solution of an imperme-able solute, inserted into an aqueous hypotonic medium. Initially the vesiclemembrane is smooth and unstressed. Due to water osmotic influx, the vesi-cle is growing until a critical dimension, simultaneously with increases ofmechanical tension in membrane. This tension increases the pressure insidethe cell. In such conditions either the cellular membrane may be rupturedand the cell dies, or one pore may appear through its lipid matrix. The mem-brane recovery happens only if a part of the intracellular material comes outof the cell through this transient pore, which, firstly, increases up to a max-imum radius, then decreases and, finally, it disappears. When the pore isclosed, the vesicle is reached at its initial size. From this state the vesicleswells again and a new cycle begins. The liposome experiences a periodicprocess.

Tomographic Image Reconstruction in Experimental Fluid Dynamicsby

Stefania Petra and Christoph Schnorr

Particle Image Velocimetry (PIV) denotes an prevailing technique for imag-ing turbulent fluids with high-speed cameras. Corresponding image se-quences provide the basis for estimating such flows and corresponding flowpatterns through image processing. While this technique has been applied intwo dimensions (2D) so far in terms of an illuminated plane intersecting thevolume, recent research focuses on imaging fluids directly in 3D. This talkaddresses the corresponding basic problems involved and first steps towardstheir solution for reconstructing scalar-valued particle functions from few

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tomographical measurements. The results of this work provide an essentialprocessing step prior to the estimation of 3D flows.

ScientView - a Virtual Reality based platform for scientificvisualisation

byD.M. Popovici, D.Sopu, M. Girtu

In the following we present our virtual reality based software, ScientView,that allows the immersion within the simulated virtual environment, in par-ticular the evolution of the degradation of the physical properties of thematerials under the conditions of the irradiation-induced defect formationin various metals and metal alloys. Based on the positions and kinetic en-ergies of each particle of the system, ScientView leads to an interactive 3Dstereoscopic visualisation of the experiment, by easily displaying large sys-tems and using the color coding (or the grayscale) that visually indicate thekinetic energy of each particle.

Numerical simulation of bio-reactive contaminant transport in soilby

Florin A. Radu

Pollution of soil by organic contaminants is nowadays a serious and widespreadproblem. A comprehensive active remediation often is not feasible fromtechnical or financial reasons. Alternatively, in situ bioremediation (naturalattenuation) has been recognized as a promising approach to restore sitescontaminated with organic pollutants because it is less costly than activeremediation strategies, the contaminants can ultimately be transformed toinnoucous by-products with the help of microorganisms (not just transferredto another phase or place) and it can operate in situ. However, the decisionto apply natural attenuation at a specific site depends essentially on thereliable prediction of the fate of the contaminant plume. Together with lab-oratory and field experiments, mathematical models can be used to predictthe evolution of a site over long time periods. We present a general model todescribe the simultaneous reactive transport in porous media of an arbitrarynumber of organic substances in the presence of some microbial populations.The model includes the effects of advection, dispersion, sorption and degra-dation. The groundwater movement, taking into account the unsaturated

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subregions near the surface, is described by the Richards equation. The in-teraction of the relevant components (species) via sensitive, highly nonlinearreactive processes stresses the need for very accurate numerical schemes. Ar-tificial numerical diffusion leads to erroneous reactive processes and thus tofalse predictions of the contaminant fate by overestimating the availability ofthe reactants [1]. The need of an adequate approximation of the fluid flow bymixed Finite Element Methods has been recognized in the water resourcesliterature since several decades, see, e.g., [2]. These methods offer the advan-tage of local mass conservation and continuous flux approximations over theelement faces. However, for associated solute transport problems normallyconventional methods are applied, e.g. conforming FEM or Finite Volumeschemes. Consequently, to seize the aforementioned advantages, the mixedhybrid FEM is used also for the multicomponent transport equations. Theresulting nonlinear algebraic equations are solved by a damped version ofNewton’s method, while for the linear systems a W-cycle multigrid methodis used. The algorithmic solution process is presented. Illustrative numeri-cal studies, including a real case study concerning natural attenuation, areshown.

Development of a vertical intelligent sonarby

Robu Octavian and Popescu Elena

The developed vertical sonar is an important sensor for navigation of sub-mersed vehicles, realized in digital technology and it containes two distinc-tive elements: piezoceramic transducer and the electronic module. Con-structive, it is conceived according to the principle ”all in one”. The imple-mented software recommends it as included in category of intelligent sensors.In this paper is presented the structure of the hardware and the softwareasociated with signal processing and serial transfer on line of the informa-tion.

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Propagation of the sound in marine environment. Development of amodelby

Robu Octavian and Popescu Elena

The marine environment is a nonuniform environment separated verticallyin layers, according to the temperature. The speed of underwater prop-agation of the sound depends on the temperature, salinity and pressure.Consequently the sound will not propagate in stright line but it will un-dergo reflexion and refraction. Also the water surface and the sea bottomhave influence on the underwater propagation of the sound. As it is alreadyknown, the detection and observation in marine environment may be op-timally achieved only by using sounds (ultrasounds) and the knowledge ofthe propagation mode is of a major importance. The paper presents thealgorithms and the software which conducted to the development of thismodel.

Lagrangian-Eulerian statistics and numerical modeling of transport inhomogeneous random media

byN. Suciu, P. R. Kramer, F. A. Radu and C. Vamos

Relationships between statistical properties of Eulerian velocity (in a fixedreference frame) and Lagrangian velocity (i.e. the velocity of marked molecules)are examined for the case of diffusion in velocity fields described by randomspace functions. Assuming a constant diffusion coefficient and a divergence-free homogeneous Eulerian random field, we give simple proofs of the statisti-cal homogeneity of the Lagrangian velocity field and of the equality betweenthe Lagrangian and Eulerian one-point marginal probabilities. In general,these properties do not imply the translation invariance of the average overvelocity realizations of the transition probability of the advection-diffusionprocess. Further, we analyze numerical simulations using velocity fieldsgenerated with a classical randomization method. The numerical Eulerianvelocity is homogeneous within a reasonably small confidence interval. Sur-prisingly, at early times the Lagrangian mean velocity still depends on thestarting point of the trajectory and shows small oscillations which, however,are well beyond the confidence interval for the Eulerian mean velocity. Wedemonstrate that the lack of strict statistical homogeneity of the Lagrangian

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velocity induces a dependence on the initial concentration distribution of thesecond moment of the ensemble averaged concentration. At large times, thesimulated Lagrangian mean velocity tends to the Eulerian mean velocity,confirming an earlier conjecture, and the second moment of the mean con-centration loses the memory of the initial conditions.

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Autori

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Grigore Albeanu UNESCO Chair in Information Technologiesat University of Oradeae-mail:

Neculai Andrei Research Institute for Informatics, Center forAdvanced Modeling and Optimization 8-10,Averescu Avenue, Bucharest 1, Romaniae-mail: nandrei@ici.ro

Cristina E. Asaftei ”Ovidius” University of Constanta, Faculty ofMathematics and Computer Science, Roma-niae-mail:

Elena Bautu “Ovidius” University of Constantza, Romaniae-mail: erogojina@univ-ovidius.ro

Crenguta Bogdan e-mail: cbogdan@univ-ovidius.ro

Adrian Carabineanu Faculty of Mathematics and Informatics, Uni-versity of Bucharest, Romania,”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: acara@math.math.unibuc.ro

Tiberius Duluman Route 66 Brasov, Romaniae-mail: tiberius d@hotmail.com

Marius Craciun ”Ovidius” University of Constanta, Romaniae-mail: mcraciun@univ-ovidius.ro

Daniel Draghicescu e-mail:draghicescu daniel@yahoo.com

Manuela Ghica Faculty of Mathematics and Iformatics atSpiru Haret Universitye-mail:

Mihai A. Gırtu Department of Physics, Ovidius University ofConstanta, 900527, Romaniae-mail: girtu@univ-ovidius.ro

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Stelian Ion ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: ro diff@yahoo.com

P. R. Kramer Rensselaer Polytechnic Institute, New Yorke-mail:

Gheorghe Juncu POLITEHNICA University of Bucharest,Catedra Inginerie Chimica, Polizu 1, 78126Bucharest, RomaniaFax: +40 21 345 05 96, Phone: + 40 21 34505 96e-mail: juncugh@netscape.net,

juncu@easynet.ro

Alexei Leahu “Ovidius” University of Constantae-mail: aleahu@univ-ovidius.ro

Carmen Elena Lupu Ovidius University of Constantae-mail: celenalupu@yahoo.com

Beatrice Mihaela Macri Department of Animal Physiology and Bio-physics, Faculty of Biology, University ofBucharest, Splaiul Independentei, 91-95, R-050095, Bucharest, Romaniae-mail: beatrice macri@yahoo.com

Christian Mancas ”Ovidius” University of Constanta, Romaniae-mail: cmancas@easynet.ro

Gabriela Marinoschi ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: gabimarinoschi@yahoo.com

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Daniel Mocanu Department of Bioengineering and Biotech-nology, University Politehnica of Buchareste-mail:

Adrian Moncea ”Ovidius” University of Constanta, Romaniae-mail: moncea adi@yahoo.com

Alexandru Morega POLITEHNICA University Bucharest, De-partment of Bioengineering and Biotechnol-ogy& Department of Electrical Engineering,Buchares 6, Romania,”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: amm@iem.pub.ro

Katsumi Moriwaki The University of Shiga Prefecture, Schoolof Engineering, Department of MechanicalSystems Engineering,

2500 Hassaka-cho, Hikone,Shiga, 522-8533, JAPANe-mail: moriwaki@mech.usp.ac.jp

Andrei Negoias POLITEHNICA University of Bucharest, De-partment of Electrical Engineering, Bucharest6, Romaniae-mail:

Aurelian Nicola ”Ovidius” University of Constanta, Romaniae-mail: anicola@univ-ovidius.ro

Corneliu I. Oprea Department of Physics, Ovidius University ofConstanta, 900527, Romaniae-mail:

Elena Pelican “Ovidius” University of Constanta, Faculty ofMathematics and Computer Science, Roma-niae-mail: epelican@univ-ovidius.ro

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Stefania Petra University of HeidelbergInstitute for Computer EngineeringGermanye-mail: petra@uni-mannheim.de

Nicolae Pop North University of Baia Mare, Faculty ofScience, Department of Mathematic andComputer Science, Victoriei, 76, 430121 BaiaMare, Romaniae-mail: nicpop@ubm.ro,

nic pop2002@yahoo.com

Constantin Popa “Ovidius” University of Constantza, Romaniae-mail: cpopa@univ-ovidius.ro

D.M.Popovici “Ovidius” University of Constantza, Romaniae-mail:

Alin G. Popescu Faculty of Automatics and Computer Sci-ence, Polytechnical University of Bucharest,Spl. Independentei nr. 213, Bucharest,Romania

Dumitru Popescu ”Gheorghe Mihoc–Caius Iacob” Institute ofStatistical Mathematics and Applied Math-ematics, Calea 13 Septembrie nr.13, 050711Bucharest, Romaniae-mail: popescu1947@yahoo.com

Popescu Elena ”Ovidius” University of Constanta, Romaniae-mail:

Florin Radu Max-Planck Institute for Mathematics in theSciences, Inselstr. 22, D-04103 Leipzig, Ger-manye-mail: fradu@mis.mpg.de

Robu Octavian ”Ovidius” University of Constanta, Romaniae-mail:

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Ulrich Rude Friedrich-Alexander Universitat Erlangen-Nurnberg, Germanye-mail: ruede@informatik.uni-erlangen.de

Christoph Schnorr University of HeidelbergInstitute for Computer EngineeringGermanye-mail: schnoerr@uni-mannheim.de

Daniel Sopu Department of Physics, Ovidius University ofConstanta, 900527, Romaniae-mail: daniel sopu@gmail.com

Nicolae Suciu Institute of Applied Mathematics I, Univer-sity of Erlangen-Nuremberg, Martensstr. 3,91058 Erlangen, Germanye-mail: suciu@am.uni-erlangen.de

Calin Vamos ”Tiberiu Popovici” Institute of NumericalAnalysis, Cluj-Napoca, Romaniae-mail: cvamos@ictp.acad.ro

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