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Copyright 1993 by the National Academy of Sciences. All rights reserved.
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COMMITTEE ON THE MATHEMATICAL SCIENCES APPLIED TO MATERIALS SCIENCE
AVNER FRIEDMAN,
University of Minnesota,
Chair
I.-WEI CHEN,
University of Michigan
MORTON M. DENN,
University of California at Berkeley
KARL F. FREED,
University of Chicago
JAMES E. GUBERNATIS,
Los Alamos National Laboratory
RICHARD D. JAMES,
University of Minnesota
ALEXANDER KAPLAN,
Johns Hopkins University
WILLIAM W. MULLINS,
Carnegie Mellon University
SOKRATES T. PANTELIDES,
IBM T.J. Watson Research Center
FRANK STILLINGER,
AT&T Bell Laboratories
JEAN E. TAYLOR,
Rutgers University
Staff
JOHN R. TUCKER, Senior Program Officer
BOARD ON MATHEMATICAL SCIENCES
SHMUEL WINOGRAD,
IBM T.J. Watson Research Center,
Chair
JEROME SACKS,
National Institute of Statistical Sciences,
Vice Chair
LOUIS AUSLANDER,
City University of New York System
HYMAN BASS,
Columbia University
LAWRENCE D. BROWN,
Cornell University
AVNER FRIEDMAN,
University of Minnesota
JOHN F. GEWEKE,
University of Minnesota
JAMES GLIMM,
State University of New York at Stony Brook
GERALD J. LIEBERMAN,
Stanford University
PAUL S. MUHLY,
University of Iowa
RONALD F. PEIERLS,
Brookhaven National Laboratory
DONALD ST. P. RICHARDS,
University of Virginia
KAREN K. UHLENBECK,
University of Texas at Austin
MARY F. WHEELER,
Rice University
ROBERT J. ZIMMER,
University of Chicago
Ex Officio Member
JON R. KETTENRING, Bell Communications Research Chair,
Committee on Applied and Theoretical Statistics
Staff
JOHN E. LAVERY, Director
RUTH E. O'BRIEN, Staff Associate
JOHN R. TUCKER, Senior Program Officer
BARBARA WRIGHT, Administrative Assistant
COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS
RICHARD N. ZARE,
Stanford University,
Chair
RICHARD S. NICHOLSON,
American Association for the Advancement of Science,
Vice Chair
JOHN A. ARMSTRONG,
IBM Corporation (retired)
SYLVIA T. CEYER,
Massachusetts Institute of Technology
GEORGE W. CLARK,
Massachusetts Institute of Technology
AVNER FRIEDMAN,
University of Minnesota
SUSAN L. GRAHAM,
University of California at Berkeley
ROBERT J. HERMANN,
United Technologies Corporation
NEAL F. LANE,
Rice University
HANS MARK,
University of Texas at Austin
CLAIRE E. MAX,
Lawrence Livermore National Laboratory
CHRISTOPHER F. MCKEE,
University of California at Berkeley
JAMES W. MITCHELL,
AT&T Bell Laboratories
JEROME SACKS,
National Institute of Statistical Sciences
A. RICHARD SEEBASS III,
University of Colorado at Boulder
CHARLES P. SLICHTER,
University of Illinois at Urbana-Champaign
ALVIN W. TRIVELPIECE,
Oak Ridge National Laboratory
NORMAN METZGER, Executive Director
PREFACE
This report is the product of the second phase of a two-phase study by the Committee on the Mathematical Sciences Applied to Materials Science, a committee convened by the Board on Mathematical Sciences (BMS). It builds on the committee's short phase-one survey,1 which (along with a briefing) was produced in response to a National Science Foundation (NSF) request. That report briefly described general mathematical theory and techniques that have been or show promise of being fruitful for ongoing and future materials science research. It was primarily aimed at and distributed to federal agencies that fund mathematical sciences and materials science research. This more comprehensive technical report documents and presents technical details of fruitful past collaborations between the mathematical sciences and materials science, and it indicates which particular areas of mathematical sciences research hold the most promise for advancing materials science.
Materials research is now undergoing a transformation into a quantitative science.2 Although interaction between the mathematical sciences and materials science is increasing, many researchers in both communities are unaware that fruitful collaborations are possible and that a broad mathematical theory of materials is already being developed. However, materials science has been a prominent theme of several recent mathematics professional society meetings. Also, materials and processing have become the focus of a major cross-government initiative3 because they are critical to the success of industries such as the aerospace, automotive, biomaterials, chemical, electronics, energy, metals, and telecommunications industries. In light of the subject's timeliness, and to follow up and build on the brief survey prepared for NSF, the BMS chose materials science as the focus for a BMS cross-disciplinary report. This is one of a series of BMS reports that highlight areas on the interface between the mathematical sciences and other fields.
The purpose of this report is not only to focus on directions for potentially promising collaboration between materials scientists and mathematical scientists, but also to encourage both communities to increase such collaborations. It is written primarily for mathematical and materials science researchers with an interest in advancing research at this interface, as well as for federal and state agency representatives interested in encouraging such collaborations. The opening and closing chapters (1 and 9) are intended for any persons wanting general information on how such cross-disciplinary, collaborative efforts can be successfully accomplished.
To articulate the many mathematical challenges faced by materials scientists, the committee asked a large number of researchers (see appendix) to provide short write-ups briefly describing materials science research areas and identifying mathematical challenges in those areas. The committee incorporated the information received into the committee's descriptions and perspectives presented here. This report emphasizes that both the mathematical sciences and materials science communities have much to gain from an increase in cross-disciplinary collaborations, and it presents the committee's recommendations for facilitating mathematical sciences research that bears on important issues in materials science, including recommendations on how to attract students and young
researchers to this area. These recommendations are general and are not intended to be a detailed "blueprint" for action. It is hoped that this report will encourage research directions in the mathematical sciences that complement vital materials science research, as well as raise awareness of the value of quantitative methods in materials science.
The committee is very grateful to the anonymous reviewers who provided excellent feedback in a short time, and to the many individuals who contributed information at the request of the committee. These colleagues strengthened this report significantly.