Continuum Models and Discrete Systems

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Series II: Mathematics, Physics and Chemistry – Vol. 158

Continuum Models and Discrete Systems edited by

David J. Bergman School of Physics and Astronomy, Raymond & Beverley Sackler Faculty of Exact Sciences , Tel Aviv University, Israel and

Esin Inan Department of Mathematics, Faculty of Art and Sciences, Isik University, Istanbul, Turkey

Springer-Science+Business Media, B.V.

ofthe Proceedings of the NATO Advanced Research Workshop on Continuum Models and Discrete Systems Shoresh, Israel 30 June–4 June-4 July 2003

c.1.P. Catalogue record for this book is available from the Library of of Congress. A C.I.P.

Additional Additional material material to to this this book book can can be be downloaded downloaded from from http://extras.springer.com http://extras.springer.com ISBN 978-1-4020-2315-6 ISBN 978-1-4020-2316-3 (eBook) DOI 10.1007/978-1-4020-2316-3

Printed on acid-free paper

All Rights Reserved © 2004 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 2004 Softcover reprint of the hardcover 1st edition 2004

No part of this work may be reproduced, stored in a retrieval system, or transmitted ofthis in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of of being entered of and executed on a computer system, for exclusive use by the purchaser of the work. ofthe

This book is dedicated to the memories of Ekkehart Kroener and Konstantin Z. Markov. The first passed away in the time between CMDS9 and CMDSIO, after playing a major role in the initiation and continuation of the CMDS sequence of symposia. The second passed away shortly after CMDSIO; he too played a major role in the planning and execution of many of the CMDS symposia, including the latest one CMDSIO.

Contents

Dedication

v

Preface

xiii

In Memoriam of Ekkehart Kroener In Memoriam of Konstantin Zdravkov Markov

xv xvii

Acknowledgment

xx

Thermodynamics, transport theory, and statistical mechanics in the context of continuum modeling of discrete systems

Part I

GL Noise in non-Ohmic regimes of disordered systems (abstract) Kamal K. Bardhan and Chandidas Mukherjee Coupled tent and logistic maps: Lyapunov exponents, stability and bifurcations of invariant set belonging to the map diagonal Vladimir A. Dobrynskiy

3

RC

RC Self-assembled 2D dipole clusters (abstract) made of magnetic particles: experiment, modeling and aplication for tunable photonic crystals M. Golosovsky, Y. Saado, Y. Neve-Oz and D. Davidov RC Transforming to chaos by normal forms Avadis Hacinliyan, Nazim Ziya Perdahci, Gokhan Sahin, H. Ahmet Yildirim

5

13

15

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 David Kinderlehrer

29

RC A phase field system with memory Amy Novick-Cohen

37

RC

Pattern formation, reconstruction, and roughening on a catalytic surface (abstract) 43 M. Monine and L. M. Pismen

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CONTINUUM MODELS AND DISCRETE SYSTEMS

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

The special electrical properties and the corresponding applications of carbon black-polymer composites 47 I. Balberg Continuum field model of defect-induced heterogeneities in a strained thin 55 layer Mikhail Belogolovskii, Gennadij Akimov, Yurii Komysa,Paul Seidel RC

The effective conductivity of densely packed high contrast composites with inclusions of optimal shape Yuliya Gorb and Leonid Berlyand GL



RC

Simple algebraic approximations for the effective elastic moduli of a cubic 75 array of spheres Israel Cohen and David J. Bergman Geometrical factors affecting the bulk electrical properties of soils and rocks: Measurements and continuum mean field computations (abstract)  Shmulik P. Friedman, Scott B. Jones, and David A. Robinson RC

RC

Information theoretical sliding window optimization applied to discretization of continuous signals (abstract)  Huseyin Goksu and Donald C. Wunsch RC

Dispersive durable systems: The technology of synthesis with given prop erties Ramiz A. Hasanov RC Artificial "magnetic atoms" for microwave composite materials E.O. Kamenetskii, R. Shavit, and M. Sigalov



RC

Effective properties of matrix composite materials with high volume concentrations of inclusions (abstract)  Sergey K. Kanaoun RC

On the effective constants of inhomogeneous poroelastic medium

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



RC

On the solutions of the inhomogeneous Helmholtz wave equation for ellip soidal sources T. M. Michelitsch, J. Wang, H. Gao, and V. M. Levin RC Computational mesomechanics of materials Leon Mishnaevsky Jr



ix

Contents 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) Andrey K. Sarychevand Vladimir M. Shalaev

135

RC Effective conductivity of non-linear composites and electrical breakdown 137 A. Snarskii and M. Zhenirovsky Exact relations between macroscopic moduli of composite media in n dimensions 143 Yakov M. Strelnikerand David J. Bergman RC

RC Local fields effects and optical susceptibility of composite media Gregory Surdutovich

151

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 Yuriy K. Tovbin

165

RC Computation of ground bearing capacity from shear wave velocity Ergun Turker

173

RC Boundary element method applied to some multiphase flows (abstract) D. V. Yevdokymov

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

Part IV

Dislocations and plasticity

RC Annealing of dislocations in two dimensions—partial universality Nathan Argaman

209

RC Elasto-plastic models with dislocations based on configuration with torsion215 Sanda Cleja-Tigoiu

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CONTINUUM MODELS AND DISCRETE SYSTEMS

RC Spin Effects in Plasticity (abstract) V. Fleurov and M. Molotskii

221

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 screw dislocations in copper 231 D. Mordehai, I. Kelson, G. Makov

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

Part V

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

The generation of non-trivial fracture surface in the dynamic fracture of brittle materials (extended abstract) 241 Jay Fineberg , Amir Sagy, Ariel Livne, and Gil Cohen RC Prediction possibility in the fractal overlap model of earthquakes Srutarshi Pradhan, Pinaki Choudhuri, and Bikas K. Chakrabarti

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 fractions 253 M. A. Tasdemir, S. Akyuz, F. Bayramov, A. S. Agar

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

Analysis of stochastically heterogeneous microbeams by a functional perturbation method 261 Eli Altus RC

Modeling infiltration during soil seal formation: Effects of seal 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

xi

Contents 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 discrete model for DNA elasticity that accounts for the dependence of the mechanical properties of DNA on nucleotide sequence (abstract) 279 Bernard D. Coleman RC

Integral representations for solutions of some nonclassical one dimensional pseudoparabolic problems 281 Esin Inan, Seyidali S. Akhiev

RC

Phononic band gap properties of doubly periodic arrays of coated inclusions 287 S. B. Platts and N. V. Movchan

RC Adaptation of autocatalytic reactants to discrete catalysts (abstract) Nadav Shnerb

295

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 Peng Yu, Shlomo Ta’asan Part VII

299

Granular material: Statics and dynamics

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

313

GL Elasticity and force chains I. Goldhirsch, C. Goldenberg

315

GL Restructuring of force networks Hans J. Herrmann , R. Cruz Hidalgo, F. Kun

327

RC Hydrodynamics of “thermal” granular convection Evgeniy Khain

341

RC Force chains and stress in granular materials (abstract) Dov Levine

347

Part VIII RC

Percolation problems

Exact relations between critical exponents for elastic stiffness and electrical conductivity of percolating networks David J. Bergman

351

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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. Senand 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 Ohad Levy

379

GL Patterns in drying water films S. G. Lipson

387

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

405

Alphabetical list of conference participants with addresses

419

Author Index

425

Preface 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 CMDS5 CMDS6 CMDS7 CMDS8 CMDS9

(Stockholm, Sweden, 1981) (Nottingham, England, 1985) (Dijon, France, 1989) (Paderborn, Germany, 1992) (Varna, Bulgaria, 1995) (Istanbul, Turkey, 1998)

As in the previous symposia, participation was by invitation from the International Scientific Committee. Participants were chosen from a list of recommendations of the committee members, as well as from applications following advertisement of the symposium on the internet and in email messages to potential 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. Markov, CMDS8 Chairman (University of Sofia, Bulgaria) Amy Novick-Cohen, (Technion-Israel Institute of Technology, Haifa, Israel) Ping Sheng (University of Science and Technology, Kowloon, Hong Kong) Robin Stinchcombe (Oxford University, England) Catmine Trimarco (University of Pisa, Italy)

Altogether there were 63 active participants from 13 different countries, who presented 13 "general lectures (GL)" and 50 "research communications (RC)", of which 37 were oral presentations and 13 were posters. Each GL was 50 minutes long, including questions and discussion, while each oral RC was 25 minutes long, including questions and discussion. The posters were exhibited throughout the 5 days of the symposium. There was ample time and opportunity for private discussions. Many private scientific meetings and interactions took place. Hopefully these will lead to new collaborations and other

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research developments in the coming years. All participants were encouraged to submit a short manuscript to this volume, summarizing their presentation at the symposium. Many did so-those who did not have only the abstract of their presentation published here. The chapters in this proceedings volume which only include an abstract are marked as such in the Table of Contents (TOC). Also indicated in the TOC is the character of each presentation, i.e., GL or RC. In the case of more than one author, the name of the presenting author is underlined, both in the TOC and in the article by line. At the end of this volume there appears a list of all the presenting participants, along with addresses, both postal and e-mail. An Author Index (AI) also appears at the end of this volume-all the manuscript authors appear in it along with the page number(s) where their article(s) begins. The presenting author is always indicated by underlining that page number. Authors not actually participating in or present at the symposium are marked in the AI by an asterisk *. The CMDS 10 Symposium was chaired by David J. Bergman (DJB). The undersigned (DJB and Esin Inan) were co-directors of the NATO Advanced Research Workshop (ARW), under the umbrella of which this symposium was conducted. They are also co-editors of this Conference Proceedings volume. The Organizing Committee of the NATO ARW included, besides the two codirectors, also Karl-Heinz Anthony, Hans Jurgen Herrmann (HJH), and the late Konstantin Z. Markov, all of whom were also members of the International Scientific Committee (ISC). Special thanks to Amy Novick-Cohen are in order: She and DJB were coorganizers of the Israel Science Foundation (lSF) Research Workshop, under the umbrella of which part of this symposium also resided. The Scientific Committee of this ISF Research Workshop included, besides the two coorganizers, also the ISC members HJH and David Kinderlehrer. Special thanks to Chava Balson, the administrative assistant to the symposium organizers, are also in order: Without her help and hard work the conference would not have run as smoothly as it did. In summary, without the active cooperation of all of these devoted people, the conference could not have taken place. It would also not have been possible to hold this workshop without the material support provided by the Scientific Research Division of NATO, by the Israel Science Foundation, by the Ministry of Science and Technology of the State of Israel, by Tel Aviv University, and by the Sackler Institute of Solid State Physics. All of these agencies/institutions deserve our deep gratitude. The next symposium in the CMDS series is planned to take place in France in the year 2006. David J. Bergman and Esin Inan, Tel Aviv, February 2004

xv

IN MEMORIAM

Ekkehart Kroener 1919-2000 Prof. Dr. Dr. h.c. mult. Ekkehart Kroener, one of the promoters of the CMDS conference series, passed away in April 2000, following an unexpected serious illness. Due to his excellent and extensive scientific competence, as well as to his kind and charming nature, he had been an outstanding personality in the CMDS symposia from their very beginning in 1975. He was a man of high culture and benevolence; he was an attractive personality for people of any age and status. Especially the CMDS community will keep him in pleasant and grateful remembrance. Ekkehart Kroener was born in Berlin in the year 1919 to a physician's family. In 1937, just after his school-leaving examination in Potsdam, he was called up for military service which took away eleven years of his youth: He

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CONTINUUM MODELS AND DISCRETE SYSTEMS

became involved in the horror of the second world war, winding up as a prisoner of war in the Soviet Union until 1948. In 1948 he settled in Stuttgart, where he married Gertrud Hartmann. They had two daughters. During 1948-1954 Ekkehart Kroener studied physics at the Technical University of Stuttgart. His dissertation on "Kontinuumstheorie der Versetzungen und Eigenspannungen (Continuum Theory of Dislocations and EigenStresses)" appeared as a monograph, and immediately attracted much attention. Today, 50 years later, this work is still highly regarded in the relevant scientific community. After a short period as Associate Professor at the University of Stuttgart, and a one-year research stay at the Massachusetts Institute of Technology, he was offered professorships simultaneously at three universities-in Aachen, Hannover, and Clausthal-Zellerfeld. Clausthal-Zellerfeld, a small town in the middle of Germany, famous for its venerable Bergakademie (Academy of Mines), was his choice. There, from 1963 until 1969, he was Professor of Theoretical Physics at the Technical University. In 1969 he got an appointment at the University of Stuttgart, where he was Director of the Institute for Theoretical and Applied Physics until 1985. Ekkehart Kroener retired in 1985. However, as a Professor Emeritus he remained untiringly active in this institute, in seminars, in conferences, and as a researcher who until the last days of his life was full of new ideas. Ekkehart Kroener became a scientist of worldwide reputation. He was a pioneer in dislocation theory and thus in the theory of plastic deformation of solids and in non-linear theory of elasticity of structured media. These topics led naturally to his contributions to non-local continuum theories, to his fundamental research on non-Euclidean geometry as applied to physical structures in material systems, and to contributions in gauge field theory for dynamical material systems. Being aware, early-on, of the coarse-grained structure of real materials, he also became a pioneer of statistical continuum theories. Ekkehart Kroener had a broad outlook on theoretical physics: Analogies between different physical disciplines was his passion, e.g., between the non-euclidean geometry of topological defects in crystalline structures and space-time structures in general relativity. In 1965 his scientific achievements were honored by the award of the Physics Prize of the German Physical Society. He was member of the Braunschweig Academy of Sciences, of the Polish Academy of Sciences, and of the German Max Planck Society. He was awarded honorary doctorates by the Universities of St. Petersburg and of Metz. Karl-Heinz Anthony and Valentin Popov, December 2003

xvii

IN MEMORIAM

Konstantin Z. Markov 1945-2003 Prof. Dr. Konstantin Z. Markov, who was Chairman of the Eighth International Symposium on Continuum Models and Discrete Systems (CMDS8), passed away in Varna on 7th August 2003, after suffering from failing health during the last three years. During that period, even though he was forced to set aside many of his University duties in favor of medical treatments, Konstantin Markov continued to devote every available moment of time to his research pursuits. His deep devotion to learning has been a consistent source of inspira-

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tion to fellow researchers and students alike. Prof. Markov enjoyed exchanges with people from many disciplines, and his breadth of knowledge drew many people to him. Anyone who knew him could only hope that, one day, after completing his formal responsibilities at the University, he would have more time and freedom to pursue even more worldwide activities in the days ahead. Alas, those days never came. Konstantin Zdravkov Markov was born in Sofia, the capital city of Bulgaria, in the year 1945. He graduated from the University of St. Petersburg (then Leningrad) in Russia in 1968, thereafter pursuing studies in the same University until he got his PhD in Physico-Mathematical sciences in 1972. His dissertation was on "Group-theoretical Analysis of Constitutive Equations for Anisotropic Solids with Creep". He was awarded an advanced DSc degree (Doctor's Degree in Sciences-Mathematics) in 1983 from the Bulgarian Academy of Sciences and Sofia University for his thesis on "Mechanical and Mathematical Modeling of Micro-Heterogeneous Solids". From 1972 to 1977 he worked as a research associate in the Department of Continuum Mechanics, Institute of Mathematics and Mechanics, Bulgarian Academy of Sciences in Sofia. During that period he also visited the Department of Polymer Mechanics of the loffe Physico-Technical Institute, Soviet Academy of Sciences, St. Petersburg (Leningrad) and worked there as a research associate. From 1977 to 1989 he was Associate Professor in the Department of Continuum Mechanics, Faculty of Mathematics and Informatics, St. Kl. Ohridski University of Sofia, and from 1989 until he died he was Professor of Solid Mechanics and Mechanics of Continua in that same Department. He visited the Department of Engineering Sciences in Istanbul Technical University during the periods 9-12/1992 and 1-3/1994, presenting seminars on Damage Mechanics, Microstructural Theories of Elasticity, Random Media, and Mechanics of Composites. He also visited the School of Mathematical Sciences of the University of Bath in England during 4-8/1998, and the Department of Mathematics in Politecnico di Torino in May 1997. During his more than 30 years of scientific activity, Konstantin Markov made many contributions to the study of Mathematical Modeling of Continuum Mechanics, Microstructural Theories of Elasticity, Random Media, Damage Mechanics, Tensor Function Representations, and Mechanics of Composites. He published more than 80 research articles and many lecture notes of his undergraduate courses on Mathematical Modeling, Continuum Mechanics, Analytical Mechanics, and graduate courses on Mathematical Methods of Mechanics, Mechanics of Composites, Damage Mechanics, Rheology, and Tensor Calculus in Mechanics. He also was instrumental in guiding many promising young researchers, and he provided strong leadership for the establishment and organization of many research groups and meetings. He organized a Bulgarian-Greek Colloquium on Mathematical Modeling in Mechanics and

xix Techniques, in Gjuletchitza, Bulgaria, in October 1989, European Mechanics Colloquium No. 278 on Microstructure and Effective Properties of Random Composite Materials, in Shumen, Bulgaria, in June, 1991, and the Eighth International Symposium on Continuum Models and Discrete Systems (CMDS8) in Varna, Bulgaria, in June, 1995. He also helped to organize the Ninth International Symposium on Continuum Models and Discrete Systems (CMDS9) in Istanbul, Turkey, in June, 1998. He was a member of the International Scientific Committee of the Tenth International Symposium on Continuum Models and Discrete Systems (CMDS 10), which took place in Shoresh, Israel, in July 2003. We often consulted with him on the organization of this last symposium, and his advice was always thoughtful, kind, and very useful. Unfortunately, because of his health problems, he was unable to attend this symposium, and passed away very soon after it ended. Even though he lived through difficult times, he married and was a wonderfulloving father of three children, and he never stopped smiling and looking to the future with hope and optimism. Those who had the honor of knowing him personally will never forget his ever smiling face. Esin Inan and David J. Bergman, February 2004

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Acknowledgment Sponsors were: NATO Scientific Affairs Division, Israel Science Foundation, Science Ministry of the State of Israel, Tel Aviv University, Sackler Institute of Solid State Physics.