Random Heterogeneous Materials Review

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Random Heterogeneous Materials ReviewI had the opportunity to use this text while taking Prof. Torquato's material science course at Princeton. The classnotes were a condensed version of the book, while the book describes all the concepts in more details. The book presents a unified treatment of the basic equations of continuum mechanics (flow, elasticity, conduction, diffusion) from a statistical mechanical viewpoint (heavy use of probability models is made), in composite materials (for example, a material with 'spherical inclusions' of a different physical electrical conductivity from the surrounding medium are added) characterized by effective properties (conductivity, permeability, stiffness, trapping constant). The effective properties are calculated from first principles via various correlation functions (Section I describes the probability functions required for dealing with random media; Section II deals with actual calculations of effective properties). To my knowledge, it is the first comprehensive book on the subject; other texts deal with smaller subsections. In some cases, these techniques were previously available only in the specialized literature. I found the many examples provided in the text to be very helpful. I also enjoyed the section on variational principles in the second half of the book; it provides further examples of how variational calculus can be applied to solve relevant problems (in this case, dealing with the optimization of material properties). Most of the theorems are proved and the proofs are short and so shouldn't be much of a burden. The chemist should know this is mostly a book on mathematics, and so does not provide numerical examples with numbers and units (however, all one needs to do is plug in numbers in the formulas), and doesn't present too many actual real-life physical examples you are likely to deal with in the laboratory. Prerequisites are simple: a bit of linear algebra, tensor calculus (but only in orthogonal euclidean spaces), familiarity with basics of probability theory (you should know what a probability density is). Knowledge of statistical mechanics is helpful but not required. There is, of course, a section on hard sphere packing for which the author is well-known for. The chapter on homogenization theory is one of the most accessible I've seen (no knowledge of functional analysis is required-- so it is perfect for the beginner). This book does not have exercises or problems for the reader (it is not for the undergraduate student-- but rather for researchers in the cross-disciplinary fields), and so requires a certain degree of maturity to absorb the material.Random Heterogeneous Materials Overview

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