Continuum Models and Discrete Systems

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.

Table of Contents:
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