A New Direction in Mathematics for Materials Science
This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials scienc
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Susumu Ikeda Motoko Kotani
A New Direction in Mathematics for Materials Science
SpringerBriefs in the Mathematics of Materials Volume 1
Editor-in-chief Motoko Kotani, Sendai, Japan Series editors Yasumasa Nishiura, Sendai, Japan Masaru Tsukada, Sendai, Japan Samuel M. Allen, Cambridge, USA Willi Jaeger, Heidelberg, Germany Stephan Luckhaus, Leipzig, Germany
More information about this series at http://www.springer.com/series/13533
Susumu Ikeda Motoko Kotani •
A New Direction in Mathematics for Materials Science
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Susumu Ikeda Advanced Institute for Materials Research Tohoku University Sendai, Miyagi Japan
Motoko Kotani Advanced Institute for Materials Research Tohoku University Sendai, Miyagi Japan
ISSN 2365-6336 ISSN 2365-6344 (electronic) SpringerBriefs in the Mathematics of Materials ISBN 978-4-431-55862-0 ISBN 978-4-431-55864-4 (eBook) DOI 10.1007/978-4-431-55864-4 Library of Congress Control Number: 2015954958 Springer Tokyo Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Japan KK is part of Springer Science+Business Media (www.springer.com)
Preface
This book is the first volume of SpringerBriefs in the Mathematics of Materials and a comprehensive guide to the interaction of mathematics with materials science. Until recently, the application of mathematics to materials science has progressed mainly to explain macroscopic phenomena by means of partial differential equations (PDE). Mathematics however, plays an important role in describing microscopic systems. Recently, direct observation and control of atoms and molecules have become possible and mathematics is expected to describe how macroscopic properties of materials emerge from microscopic structure, in particular, from geometrical structure. Furthermore, along with the development of computer technology, a global trend has developed where researchers are deriving important information from a large amount of
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