Continuum Models and Discrete Systems: NATO Science Series II: Mathematics, Physics and Chemistry, cartea 158

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