Titlebook: Random Heterogeneous Materials; Microstructure and M Salvatore Torquato Book 2002 Springer Science+Business Media New York 2002 Clustering.

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Cell and Random-Field Modelsfined shape in a matrix. This classification includes animal and plant tissue (which have a cellular structure), bone, foams, froths, polycrystals, block copolymers, and microemulsions, to mention but a few examples. In this chapter we will consider analytical methods to characterize the microstruct

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Percolation and Clusteringsimply a . group of elements. Roughly speaking, the ., or ., of the system is the point at which a cluster first spans the system, i.e., the first appearance of . connectivity. In the thermodynamic limit, the percolation threshold is the point at which a cluster becomes infinite in size. The percola

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Computer Simulations, Image Analyses, and Reconstructionsandom medium using a particular simulation method. Second, one must sample each realization for the correlation functions of interest and then average over all realizations to get the ensemble-averaged correlation functions. Similar sampling techniques can be used to extract correlation functions fr

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Phase-Interchange Relationse but with the phases interchanged as .. When such rigorous relations apply to a wide class of heterogeneous materials, they can provide useful tests of analytical and numerical estimates of the effective properties. We focus here on the effective conductivity and elastic moduli of two-phase composi

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Exact Resultsaterials exactly. Such rare results are nonetheless quite valuable as benchmarks to test theories and computer simulations. Exact results also provide useful insights into the mechanisms responsible for the effective behavior, insights that extend beyond the specific microstructures for which they a

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Single-Inclusion Solutions a single inclusion of one material in a matrix of another material. Such estimates include effective properties of dispersions in the dilute-concentration limit (Chapter 19), a variety of effective-medium type approximations (Chapter 18), and rigorous bounds on the effective properties (Chapter 21)