Random Heterogeneous Materials
Subtitle: Microstructure and Macroscopic Properties
By: by Salvatore Torquato
Series: Interdisciplinary Applied Mathematics -- 16; Interdisciplinary applied mathematics -- 16.
Publisher: Springer New York
Published: 2002
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 703
ISBN-13: 9781475763577; 9781475763553
Subjects: Mathematical statistics; Mathematics; Surfaces (Physics); Distribution (Probability theory); Mechanical engineering
Description: The study of random heterogeneous materials is an exciting and rapidly growing multidisciplinary endeavor. This field demands a unified rigorous means of characterizing the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials that abound in nature and synthetic products. This book is the first of its kind to provide such an approach. Emphasis is placed on foundational theoretical methods that can simultaneously yield results of practical utility. The first part of the book deals with the quantitive characterization of the microstructure of heterogeneous materials. The second part of the book treats a wide variety of macroscopic transport, electromagnetic, mechanical, and chemical properties of heterogeneous materials and describes how they are linked to the microstructure of model and real materials. Contemporary topics covered include the statistical mechanics of many-partical systems, the canonical n-point correlation function, percolation theory, computer-simulation methods, image analyses and reconstructions of real materials, homogenization theory, exact property predictions, variational bounds, expansion techniques, and cross property relations. This clear and authoritative volume will be of particular interest to graduate students and researchers in applied mathematics, physics, chemistry, material sciences, engineering, geophysics, and biology. Moreover, the book is self-contained and approachable by nonspecialist. Salvatore Torquato is a professor in the Department of Chemistry and in the Materials Institute at Princeton University. He also holds affiliated appointments at Princeton University in applied and Computational Mathematics Program and in Chemical Engineering. Among other honors, he was a John Simon Guggenheim Fellow in 1998. He has published over two hundred journal articles across a variety of scientific disciplines.
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Table of contents: title: Part I. Microstructural characterization: Microstructural descriptors. Statistical mechanics of particle systems. Unified approach. Monodisperse spheres. Polydisperse spheres; title: Anisotropic media. Cell and random-field models. Percolation and clustering. Some continuum percolation results. Local volume fraction fluctuation. Computer simulation and image analysis; title: Part II. Microstructure property connections: Local and homogenized equations. Variational Principles. Phase-interchange relations. Exact results. Single-inclusion solutions. Effective medium approximations. Cluster expansions. Exact contrast expansions. Rigorous bounds. Evaluation of bounds. Cross-property relations.