Stochastic Modeling of Microstructures

A major challenge in applied mathematics and mechanics of materials is to describe various types of material microstructures. The details of the microstructure of most natural and engineered materials are usually obscure; uncertainty and randomness are the inherent features. This complexity due to material heterogeneity has not been adequately described by current classical models and theories. Stochastic Modeling of Microstructures presents a concise and unified presentation of the basic principles and tools for the modeling of real materials, natural and man-made, that possess complex, random heterogeneity. The book uses the language and methods of random field theory combined with the basic constructs of stochastic geometry and geometrical/spatial statistics in order to give the reader the knowledge necessary to model various types of material microstructures. In addition, the book provides a link between the theoretical constructs and physical microstructures via statistical inference from empirical data and the analysis of selected applied problems. Topics and Features: * The first comprehensive introduction to the new field of stochastic modeling of material microstructures * Basic tools required from the diverse subjects of random field theory, stochastic geometry, and spatial statistics are provided * Background concepts from probability theory and stochastic processes are provided * Applications from various fields are discussed, including stochastic wave propagation and the mechanics of porous media flow * The clear and integrated exposition guides the reader from the basics through problems of contemporary research interest * A familiarity with basic probability theory and the most common techniques of applied mathemathics is the only assumed prerequisite. All other concepts required for the stochastic modeling of material microstructures are provided. This book is ideal for a general scientific and engineering audience needing an in-depth guide to current ideas, methods, and models for the stochastic modeling of microstructures. It is an essential reference for practitioners, researchers, and professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.