Mathematics of Multiscale Materials
Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, gels, foams, granular aggregates, sea ice, shape-memory metals, magnetic materials, and electro-rheological fluids are all examples of materials where an understanding of t
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Institute for Mathematics and its Applications IMA The Institute for Mathematics and its Applications was established by a grant from the National Science Foundation to the University of Minnesota in 1982. The IMA seeks to encourage the development and study of fresh mathematical concepts and quest ions of concern to the other seien ces by bringing together mathematicians and scientists from diverse fields in an atmosphere that will stimulate discussion and collaboration. The IMA Volumes are intended to involve the broader scientific community in this process. Avner Friedman, Director Robert Gulliver, Associate Director
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Continued at the back
Kenneth M. Golden Geoffrey R. Gritnmett Richard D. James Graeme W. Milton Pabitra N. Sen Editors
Mathematics of Multiscale Materials
With 75 Illustrations
Springer
Kenneth M. Golden Department of Mathematics University of Utah Salt Lake City, UT 84112, USA
Geoffrey R. Grimmett Statistical Laboratory University of Cambridge Cambridge, CB2 ISB, England
Richard D. James Department of Aerospace Engineering and Mechanics University of Minnesota Minneapolis, MN 55455, USA
Graeme W. Milton Department of Mathematics University of Utah Salt Lake City, UT 84112, USA
Pabitra N. Sen Schlumberger-Doll Research Center Old Quarry Road Ridgefield, er 06877, USA Series Editors: Avner Friedman Robert Gulliver Institute for Mathematics and its Applications University of Minnesota Minneapolis, MN 55455, USA Mathematics Subject Classifications (1991): 60K35, 62M4O, 73B27, 73B35, 73B4O, 73K20,73V30,76T05,78A30,82B43,82C43,82D25,82D30 Library of Congress Cataloging-in-Publication Data Mathematics of multiscaIe materials / Kenneth M. Golden ... [et al.]. p. cm. - (The IMA volumes in mathematics and its applications ; 99) Includes bibliographicaI references. ISBN 978-1-4612-7256-4 ISBN 978-1-4612-1728-2 (eBook) DOI 10.1007/978-1-4612-1728-2 I. MateriaIs-MathematicaI models. 2. Length measurement. 3. Continuum mechanics. I. Golden, Kenneth M. 11. Series: IMA volumes in mathematics and its applications; v. 99. TA405.M395 1998 98-18394 620.1 'I 'OI5118-dc21 Printed on aci
