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