Heterogeneous Materials I Linear Transport and Optical Properties
This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal, electrical, magnetic), elastic moduli, dielectrical constant, optical properties, mechanical fracture, and ele
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Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: interdisciplinary Ap p lied Mathematics. The purpose of this series is to meet Ihe current and future needs for the interaction between various science and technology areas on Ihe one hand and mathematics on Ihe other. This is done, firstly, by encouraging the ways thai mathematics may be applied in traditional areas, and well as point towards new and innovative areas of applications; and, secondly, by encouraging other scientific disciplines lo engage in a dialog with mathematicians outlining their problems to both access new methods and suggest innovative developments within mathematics itself. The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology.
Interdisciplinary Applied Mathematics Volumes published are listed al the end o f Ihis bo o k.
Springer New York
Berlin Heidelberg Hong Kong
London Milan Parti Tokyo
Muhammad Sahimi
Heterogeneous Materials I
Linear Transport and Optical Properties
With 145 Illustrations
Springer
Muhammad Sahimi Department of Chemical Engineering University of Southern California Los Angeles. CA 90089-1211 USA and Institute for Advanced Studies in Basic Sciences Gava Zang. Zanjan 45195-159 Iran [email protected] Editors S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742
J.E. Marsden Control and Dynamical Systems Mail Code 107-81 California Institute of Technology Pasadena. CA 91125 USA [email protected]
[email protected] USA
L. Sirovich University of Bristol Division of Applied Mathematics Bristol BS8 1TW Brown University K U Providence, Rl 02912 [email protected] USA [email protected] Mathematics Subject Classification (2000); 82-02, 65M Library of Congress Cataloging- in- Publication Data Sahimi, Muhammad, Heterogeneous materials/ Muhammad Sahimi. p. cm, — (Interdisciplinary applied mathematics : 22-23) Includes bibliographical references and indexes. Contents: [1] Linear transport and optical properties — [2] Nonlinear and breakdown properties and atomistic modeling. ISBN 0-387-00167-0 (v. 1 : alk. paper) — ISBN 0-387-00166-2 (v. 2 : alk. paper) 1. InhomogenecHis materials. 2- Composite materials. I. Title. II. Interdisciplinary applied mathematics ; v. 22-23. TA418.9.153S24 2003 620, 1'l— dc21 2002042744 ISBN 0-387-00167-0
Printed on acid-free paper.
6 2003 Springer- Verlag New York. Inc. All righis reserved. This work may not be translated or copied in whole or in part without the writ ten permission of The publisher (Springer- Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010,USA), except for brief excerpts i
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