Heterogeneous Materials : Nonlinear and Breakdown Properties and Atomistic Modeling Volume II Volume II Characterization of Surface Morphology Characterization of Surface Morphology Effective Properties of Heterogeneous Materials with Constitutive Nonlinearities Nonlinear Conductivity and Dielectric Constant: The Continuum Approach Nonlinear Conductivity Dielectric Constant and Optical Properties: The Discrete Approach Nonlinear Rigidity and Elastic Moduli: The Continuum Approach Fracture and Breakdown of Heterogeneous Materials Electrical and Dielectric Breakdown: The Discrete Approach Fracture: Basic Concepts and Experimental Techniques Brittle Fracture: The Continuum Approach Brittle Fracture: The Discrete Approach Atomistic and Multiscale Modeling of Materials Atomistic Modeling of Materials Multiscale Modeling of Materials: Joining Atomistic Models with Continuum Mechanics. This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal electrical magnetic) elastic moduli dielectrical constant optical properties mechanical fracture and electrical and dielectrical breakdown properties. Both linear and nonlinear properties are considered. The nonlinear properties include those with constitutive nonlinearities as well as threshold nonlinearities such as brittle fracture and dielectric breakdown. A main goal of this book is to compare two fundamental approaches to describing and predicting materials properties namely the continuum mechanics approach and those based on the discrete models. The latter models include the lattice models and the atomistic approaches. The book provides comprehensive and up to date theoretical and computer simulation analysis of materials properties. Typical experimental methods for measuring all of these properties are outlined and comparison is made between the experimental data and the theoretical predictions. Volume I covers linear properties while volume II considers nonlinear and fracture and breakdown properties as well as atomistic modeling. This multidisciplinary book will appeal to applied physicists materials scientists chemical and mechanical engineers chemists and applied mathematicians. Muhammad Sahimi is Professor and Chairman of Chemical Engineering at the University of Southern California in Los Angeles and Adjunct Professor of Physics at the Institute for Advanced Studies in Basic Sciences in Zanjan Iran. His current research interests include transport and mechanical properties of heterogeneous materials: flow diffusion and reaction in porous media and large scale scientific complications. Among his honors are the Alexander von Humbodt Foundation Research Award and the Kapitza Gold Medal.