Random Heterogeneous Materials Microstructure and Macroscopic Properties

ISBN-10: 0387951679

ISBN-13: 9780387951676

Edition: 2002

Authors: Salvatore Torquato

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Description:

The overall aim of this book is to provide a rigorous means to characterize the microstructure and properties of heterogeneous materials that can simultaneously yield results of practical utility. A unified treatment of both microstructure and properties is emphasized. The book is divided into two parts. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical, computer-simulation and imaging techniques. Emphasis is placed on theoretical methods. Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure. This is accomplished using rigorous methods. Wherever possible,… theoretical predictions for the effective properties are compared to available, experimental and computer-simulation data. This book will be of interest to graduate students and researchers in applied mathematics, physics, chemistry, materials science and engineering.FROM THE REVIEWS:This is an important book, which is recommended to all stochastic geometers as well as spatial statisticians, at least to learn what a leading physicist has to say about stochastic geometry . . . [Many] of the formulas in Part II are perfectly general and make no assumption about the type of microstructure, i.e., they are valid for foams, heterogeneous polymer phases, granular media, colloids, composites, etc. . . . [This] is a book which is very important and which merits great attention in the mathematical-statistical community.METRIKA"'Random Hetergeneous Materials' should become a standard reference for those beginning a study of random hetergeneous media."APPLIED MECHANICS REVIEWSThe book at hand has at least two aims: to bring to the literature the current state of the analytic theory of random heterogeneous structures and to expose the tools that have led to a resurgence of interest in these and related materials. The author is in a very good position to achieve these goals, since he is responsible for much of the recent progress in this subject area, and because of his interest in the study of complex systems. Furthermore, much of the material has not appeared in any previous book on the subject . . . This is a well-written monograph with a high degree of originality. The pedagogy is strong, with most of the mathematical derivations elaborated in detail and without excessive verbiage. Much of the book is written so as to be accessible to specialists and advanced students. The mathematical background required of the reader is not extensive. In fact, a number of open research questions are outlined in the course of presentation. Torquatos book does not contain any exercises, but on the other hand there are many carefully worked out examples and meticulous notes about the history and literature in the field . . . [This book] answers a demand for a long awaited textbook for those who wish to learn about this fascinating and still poorly understood area of condensed matter physics which is sure to remain a focus of intense research activity in the years to come. Torquatos monograph should make an excellent text for self-study or for a graduate course in disordered materials. It will be welcomed by the physical and materials science communities.OPTICS & PHOTONICS NEWS

Book details

Copyright year: 2002
Publisher: Springer
Publication date: 10/25/2005
Binding: Hardcover
Pages: 703
Size: 7.25" wide x 9.25" long x 1.50" tall
Weight: 2.948
Language: English



Motivation and overview



Microstructural characterization


Microstructural descriptors


Statistical mechanics of particle systems


Monodisperse spheres


Polydisperse spheres


Anisotropic media


Cell and random-field models


Percolation and clustering


Some continuum percolation results


Local volume fraction fluctuation


Computer simulation and image analysis



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



Equilibrium Hard disk program



Interrelations among 2-3D moduli


References


Index