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 dimensionspartial 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