Continuum Models and Discrete Systems

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

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

cations of invariant set belonging to the map diagonal 5

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

RC Transforming to chaos by forma! forms 15

RC Representative volume element: A statistical point of view (not presented) 21 Dominique

RC Diffusion mediated transport and the Brownian motor 29

RC A phase field system with memory 37

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

(abstract) 43

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

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

layer 55

OL The effective conductivity of densely packed high contrast composites 63

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

array of spheres 75

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

RC Information theoretical sliding window optimization applied to discretiza

tion of continuous signals (abstract) 83

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

erties 85

RC Artificial "magnetic atoms" for microwave composite materials 99

RC Effective properties of matrix compositematerials with high volume con-

centrations of inciusions (abstract) 105

RC On the effective constants of inhomogeneous poroelastic medium 107

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

soidal sources 115

RC Computational mesomechanics of materials 123

Contents ix

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

Applications to fracture mechanics and topological optimization 129

RC Plasmonic nanoantennas (abstract) 135

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

RC Local field effects and optical susceptibility of composite media 151

RC On the approximation theorem for functionals and the asymptotic stability

for some classes of polynomial fluids 159

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

RC Computation of ground bearing capacity from shear wave velocity 173

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

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

Part IV Dislocations and plasticity

RC Annealing of dislocations in two dimensions-partial universality 209

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

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

crystalline polymer 223

RC A molecular dynamics and an elastic continuum study of serewdisloca

tions in copper 231

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

brittie materials (extended abstract) 241

RC Prediction possibility in the fractal overlap model of earthquakes 245

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

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

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

surface 271

Contents xi

RC Diffusion equation with fractional time derivative-physical sense and

practical realization (abstract) 277

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

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

sions 287

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

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

Sorin Solomon

GL Bridging micro and macro scales in fluids 299

Part VII Granular material: Statics and dynamics

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

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

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

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

RC Variable range hopping conduction in complex systems and a percolation

model with tunneling 367

RC The effective properties of macroscopically inhomogeneous ferromagnetic

composites (abstract) 375

Part IX Phase transitions and their applications

RC Switching transitions in confined liquid crystals 379

GL Patterns in drying water films 387

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

equation 399

GL A dynamical system approach to aridity and desertification 405

Alphabetical list of conference participants with addresses 419

Author Index 425