Continuum Models and Discrete Systems (NATO Science Series II: Mathematics, Physics and Chemistry, 158)

The Tenth International Symposium on Continuum Models and Discrete Systems (CMDSIO) took place at the Shoresh Holiday Complex in Shoresh, Israel, near the Capital City Jerusalem, from 30 June until 4 July 2003. The previous symposia in this series were: CMDS 1 (Kielce, Poland, 1975) CMDS2 (Mont Gabriel, Canada, 1977) CMDS3 (Freudenstadt, German Federal Republic, 1979) CMDS4 (Stockholm, Sweden, 1981) CMDS5 (Nottingham, England, 1985) CMDS6 (Dijon, France, 1989) CMDS7 (Paderborn, Germany, 1992) CMDS8 (Varna, Bulgaria, 1995) CMDS9 (Istanbul, Turkey, 1998) As in the previous symposia, participation was by invitation from the Inter­ national Scientific Committee. Participants were chosen from a list of recom­ mendations of the committee members, as well as from applications following advertisement of the symposium on the internet and in email messages to po­ tential participants. The members of the International Scientific Committee were: Karl-Heinz Anthony CMDS7 Chairman (University ofPaderborn, Germany) David J. Bergman, Conference Chairman (Tel Aviv University, Israel) Bikas K. Chakrabatii (Saha Institute of Nuclear Physics Calcutta, West Bengal, India) Hans Jurgen Herrmann (University of Stuttgart, Germany; and ESPCI, Paris, France) Esin Inan, CMDS9 Chairwoman (Istanbul Technical University, Istanbul, Turkey) Dominique Jeulin (ENSMP, Fontainebleau, France) Mark Kachanov (Tufts University, Boston, MA, USA) David Kinderlehrer (Carnegie-Mellon University, Pittsburgh, PA, USA) Arnold M. Kosevich (B. Verkin Institute for Low Temperature Physics, Khat"kov, Ukraine) Valery M. Levin (Petrozavodsk State University, Petrozavodsk, Russia) Konstantin Z.

Contents

Dedication v

Preface xiii

In Memoriam of Ekkehart Kroener xv

In Memoriam of Konstantin Zdravkov Markov xvii

Acknowledgment xx

Part 1 Thermodynamics, transport theory, and statistical mechan ics

GL Noise in non-Ohmic regimes of disordered systems (abstract) 3

Kamal K. Bardhan and Chandidas Mukherjee

RC Coupled tent and logistic maps: Lyapunov exponents, stability and bifur

cations of invariant set belonging to the map diagonal 5

Vladimir A. Dobrynskiy

RC Self-assembied 2D dipole clusters (abstract) 13

M. Golosovsky Y Saado, Y Neve-Oz and D. Davidov

RC Transforming to chaos by forma! forms 15

Avadis Hacinliyan Nazim Ziya Perdahci, Gokhan Sahin, H. Ahmet Yildirim

RC Representative volume element: A statistical point of view (not presented) 21 Dominique Jeulin Toufik Kanit, and Samuel Forest

RC Diffusion mediated transport and the Brownian motor 29

David Kinderlehrer

RC A phase field system with memory 37

Amy Novick-Cohen

RC Pattern formation, reconstruction, and roughening on a catalytic surface

(abstract) 43

M. Monine and L. M. Pismen

viii CONTINUUM MODELS AND DJSCRETE SYSTEMS

Part II Continuum mechanics of complex fluids and deformable solids with microstructure

RC The special electrical properties and the corresponding applications of car

bon black-polymer composites 47

1. Balberg

RC Continuum field model of defect-induced heterogeneities in a strained thin

layer 55

Mikhail Belogolovskii Gennadij Akimov, Yurii Komysa, Paul Seidel

OL The effective conductivity of densely packed high contrast composites 63

Yuliya Gorb and Leonid Berlyand

RC Simple algebraic approximations for the effective elastic moduli of a cubic

array of spheres 75

Israel Cohen and David J. Bergman

RC Geometrical factors affecting the bulk electrical properties of soils and rocks: Measurements and continuum mean field computations (abstract) 81

Shmulik 1’. Friedman Scott B. Jones, and David A. Robinson

RC Information theoretical sliding window optimization applied to discretiza

tion of continuous signals (abstract) 83

Huseyin Goksu and Donald C. Wunsch

RC Dispersive durable systems: The technology of synthesis with given prop

erties 85

Ramiz A. Hasanov

RC Artificial "magnetic atoms" for microwave composite materials 99

E. 0. Kamenetskii R. Shavit, and M. Sigalov

RC Effective properties of matrix composite materials with high volume con-

centrations of inciusions (abstract) 105

Sergey K. Kanaoun

RC On the effective constants of inhomogeneous poroelastic medium 107

v M. Levin and J. M. Alvarez-Tostado

RC On the solution of the inhomogeneous Helmholtz wave equation for ellip

soidal sources 115

T M. Michelitscj J. Wang, H. Gao, and V M. Levin

RC Computational mesomechanics of materials 123

Leon Mishnaevsky Jr

Contents ix

RC Non-homogenization approach to the analysis of periodic elastic systems:

Applications to fracture mechanics and topological optimization 129

Michael Ryvkin Moshe Fuchs, Fabian Lipperman, and Eyal Moses

RC Plasmonic nanoantennas (abstract) 135

Andrey K. Sarychev and Vladimir M. Shalaev

RC Effective conductivity of non-linear composites and electrical breakdown 137 A. Snarskii and M. Zhenirovsky

RC Exact relations between macroscopic moduli of composite media in n di-

mensions 143

Yakov M. Strelniker and David J. Bergman

RC Local field effects and optical susceptibility of composite media 151

Gregory Surdutovich

RC On the approximation theorem for functionals and the asymptotic stability

for some classes of polynomial fluids 159

Victor Tigoiu

RC The lattice-gas model in micro- aero-hydrodynamics problems 165

Yuriy K. Tovbin

RC Computation of ground bearing capacity from shear wave velocity 173

Ergun Turker

RC Boundary element method applied to some multiphase fiows (abstract) 181

D. V Yevdokymov

Part III Continuum theory of living structures

GL Noisy reaction-diffusion models and their biological implications (abstract) 185 Herbert Levine

GL Engineered self-organization in natural and man-made systems 187

Nadav Raichinan, Tamir Gabay, Yael Katsir Yoash Shapira, and Eshel Ben-Jacob

Part IV Dislocations and plasticity

RC Annealing of dislocations in two dimensions―partial universality 209

Nathan A rgaman

RC Elasto-plastic models with dislocations based on configuration with torsion2l5 Sanda Cleja-Tigoiu

x CONTINUUM MODELS AND DISCRETE SYSTEMS

RC Spin Effects in Plasticity (abstract) 221

v Fleurov and M. Molotskii

RC Molecular model of rupture of a macromolecular chain of a loaded oriented

crystalline polymer 223

Ulmas Gafurov

RC A molecular dynamics and an elastic continuum study of serew disloca

tions in copper 231

D.Mordeh 1. Kelson, G. Makov

Part V Fundamentals of fracture, defect dynamics, fatigue, and crack dynamics on different microlevels

RC Damage mechanisms and fracture of glass at the nanometer scale (abstract)239 E. Bouc/ E Celarie, S. Prades, D. Bonamy, C. Guillot, C. Marliere

GL The generation of non-trivial fracture surface in the dynamic fracture of

brittie materials (extended abstract) 241

JayFineberg Amir Sagy, Ariel Livne, and Gil Cohen

RC Prediction possibility in the fractal overlap model of earthquakes 245

Srutarshi Pradhan, Pinaki Choudhuri, and Bikas K. Chakrabarti

GL Dynamical instabilities of quasi-static crack propagation under thermal

stress (abstract) 251

Itamar Procaccia

RC Inclusion based modeling of concrete with various aggregate volume frac

tions 253

M. A. Tasdçj S. Akyuz, E Bayrainov, A. S. Agar

Part VI New developmeuts in continuum theory, non-classical mathematical models, and discrete vs. continuum models

RC Analysis of stochastically heterogeneous microbeams by a functional per-

turbation method 261

Eli Altus

RC Modeling infiltration during soil sea! formation: Effects of sea! non-uniformity

in depth and soil heterogeneity in space (abstract) 269

S. Assouline Y Mualem

RC A fractal model for analyzing satellite-radar-altimetry images of the sea

surface 271

Doron E. Bar and Yehuda Agnon

Contents xi

RC Diffusion equation with fractional time derivative―physical sense and

practical realization (abstract) 277

E. M. Baskin and G. V Zilberstein

GL Theory of a naturally diserete model for DNA elasticity that accounts for the dependence of the mechanical properties of DNA on nucleotide sequence

(abstract) 279

Bernard Ii Coleman

RC Integral representations for solutions of some nonciassical one dimensional

pseudoparabolic problems 281

Esin man Seyidali S. Akhiev

RC Phononic band gap properties of doubly periodic arrays of coated inclu

sions 287

S. B. Platts and N. V Movchan

RC Adaptation of autocatalytic reactants to discrete catalysts (abstract) 295

Nadav Shnerb

GL How faithful are continuum models to discrete systems? Some strange rigorous results and their obvious real life applications (abstract) 297

Sorin Solomon

GL Bridging micro and macro scales in fluids 299

Peng Yu, Shiomo Ta ‘

Part VII Granular material: Statics and dynamics

RC What controls the rheology of granular materials? (abstract) 313

Einat Aharonov

GL Elasticity and force chains 315

LGo1dhfr C. Goldenberg

GL Restructuring of force networks 327

Hans J. Herrmann R. Cruz Hidalgo, F Kun

RC Hydrodynamics of "thermal" granular convection 341

Evgeniy Khain

RC Force chains and stress in granular materials (abstract) 347

Dov Levine

Part VIII Percolation problems

RC Exact relations between critical exponents for elastic stiffness and electri

cal conductivity of percolating networks 351

xii CONTINUUM MODELS AND DISCRETE SYSTEMS Davidf. Bergman

RC Mixed transfer-matrix method for computing the macroscopic conductivity of three-constituent extreme networks: Mixtures of normal conductor, perfect

insulator, and perfect conductor 359

Xiangting Li and David J. Bergman

RC Variable range hopping conduction in complex systems and a percolation

model with tunneling 367

Asok K. Sen and Somnath Bhattacharya

RC The effective properties of macroscopically inhomogeneous ferromagnetic

composites (abstract) 375

A. Snarskii and M. Zhenirovsky

Part IX Phase transitions and their applications

RC Switching transitions in confined liquid crystals 379

Ohad Levy

GL Patterns in drying water films 387

S. G. Lipson

RC Stability of stationary periodic solutions of the convective Cahn-Hilliard

equation 399

A. Podolny, A. A. Nepomnyashchy A. A. Golovin

GL A dynamical system approach to aridity and desertification 405

Erez Gilad, Jost von Hardenberg, Ehud Meron, Moshe Shachak, Yair Zarmi

Alphabetical list of conference participants with addresses 419

Author Index 425