The interplay between discrete and continuum descriptions of physical systems and mathematical models is one of the more long lasting paradigms in the physical sciences as well as in the mathematical sciences. This is exemplified by the sequence of CMDS (Continuum Models and Discrete Systems) conferences, of which this volume summarizes the tenth such conference (CMDSIO), which took place in Shoresh, lsrael, in June 2003. It contains 65 articles, written by the various participants in this conference. These are scientists who are doing scientific research in a variety of disciplines in Physics, Mathematics, Mechanics, Engineering, Earth Sciences, etc. Topics covered inciude models for growth and evaporation of thin films, mechanical and electrical properties of composite media, defects and inhomogeneities in solids, mechanisms for mechanical and electrical failure of solids, earthquakes, dynamics of defects, fluid flow and rheology in porous soils and granular media, elasticity and force chains in granular media, percolation problems, models for desertification phase transition in and climates, the reliability and faithfulness of continuum models for discnete phenomena, etc. This Proceedings Volume is essential reading for anyone who wishes to remain up-to-date on developments in the areas and topics descnibed above, which keep changing and evolving from year to year, with new ideas and new results constantly being obtained.
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
