Random Heterogeneous Materials

A heterogeneous material consists of domains of different materials or the same material in different states. This book provides graduate students and researchers in applied mathematics, physics, chemistry, materials science and engineering with a unified approach of treating the microstructure and effective properties of heterogeneous media. Although it covers the latest advances in the field, it is written in an accessible style and will be sufficiently well-contained for the non-expert wishing to learn the field.

A unified approach of treating the microstructure and effective properties of heterogeneous media Written in an accessible style Sufficiently well-contained for the non-expert wishing to learn the field Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
1 Motivation and Overview.- 2 Microstructural Descriptors.- 3 Statistical Mechanics of Many-Particle Systems.- 4 Unified Approach to Characterize Microstructure.- 5 Monodisperse Spheres.- 6 Polydisperse Spheres.- 7 Anisotropic Media.- 8 Cell and Random-Field Models.- 9 Percolation and Clustering.- 10 Some Continuum Percolation Results.- 11 Local Volume Fraction Fluctuations.- 12 Computer Simulations, Image Analyses, and Reconstructions.- 13 Local and Homogenized Equations.- 14 Variational Principles.- 15 Phase-Interchange Relations.- 16 Exact Results.- 17 Single-Inclusion Solutions.- 18 Effective-Medium Approximations.- 19 Cluster Expansions.- 20 Exact Contrast Expansions.- 21 Rigorous Bounds.- 22 Evaluation of Bounds.- 23 Cross-Property Relations.- A Equilibrium Hard-Disk Program.- B Interrelations Among Two- and Three-Dimensional Moduli.- References.