Ebook: Random Heterogeneous Materials: Microstructure and Macroscopic Properties

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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The book is divided into two parts. Part I describes basic concepts and recent advances in quantitatively characterizing the microstructure of random heterogeneous materials. Topics covered include the statistical mechanics of many-particle systems, the canonical n-point correlation function, lattice and continuum percolation theory, local volume-fraction fluctuations, computer-simulation methods, image analyses and reconstructions of real materials, and models of microstructures. Part II 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. Topics covered include homogenization theory, variational principles and rigorous bounds, phase-interchange relations, exact results, effective-medium approximations, cluster expansions, contrast expansions, and cross-property relations.

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The book is divided into two parts. Part I describes basic concepts and recent advances in quantitatively characterizing the microstructure of random heterogeneous materials. Topics covered include the statistical mechanics of many-particle systems, the canonical n-point correlation function, lattice and continuum percolation theory, local volume-fraction fluctuations, computer-simulation methods, image analyses and reconstructions of real materials, and models of microstructures. Part II 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. Topics covered include homogenization theory, variational principles and rigorous bounds, phase-interchange relations, exact results, effective-medium approximations, cluster expansions, contrast expansions, and cross-property relations.