DTIC ADA276298: Mathematical Research in Materials Science: Opportunities and Perspectives. Part 2

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AD-A276 298
RESEARCH
MATHEMATICAL
IN
MATERIALS SCIENCE
Opportunities and Perspectives
":.,C
Board on Mathematical Sciences
National Research Council
94-06152 -..- "
I"
94 2 24 115
The National Research Council
established the Board on
Mathematical Sciences in 1984.
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of Scientific Research, Army
Research Office, Department of
Energy, IBM, National Science
Foundation, National Security
Agency, and Office of Naval
Research.
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1 26 October 1993 Final: 1 February 1992-31 October 1993
4. TITU AND SUBTITLE S. FUNDING NUMBERS
Mathematical Research in Materials Science: DAALO3-92-G-0013
Opportunities and Perspectives Part II
6. AUTHOR(S)
Committee on Mathematical Sciences Applied to Materials Science
Board on Mathematical Sciences
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National Academy of Sciences
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13. ABSTRACT (Maximum 200 words)
This National Research Council report from the Board on Mathematical Sciences documents and presents
technical details of fruitful collaborations between the mathematical sciences and materials science, and
indicates areas of mathematical sciences research holding the most promise for advancing materials science.
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, it focuses on directions for potentially promising collaboration between materials scientists and
mathematical scientists, and encourages both communities to increase such collaborations. It emphasizes that
both the mathematical sciences and materials science communities have much to gain from an increase in
cross-disciplinay collaborations, and presents 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. It seeks to encourage research directions in the mathematical sciences that
complement vital materials science research, and raise awareness of the value of quantitative methods in
materials science. It is available through National Academy Press.
14. SUBJECT TERMS 15. NUMBER OF PAGES
Mathematical Sciences, Materials Science, Cross-Disciplinary -,I"
Research, biomaterials, ceramics, complex fluids, composites, fracture, metals, 16. PRCE CODE
volvmers, processina. synthesis
17. SECURITY CLASSIFICATION 16. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. -LMITATION OF ABSTRACT
OF REPORT OF THIS PAGE OF ABSTRACT
UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL
NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89,
PtV Oabdy ANSI SW.Z 3l*.1
290-102
MATHEMATICAL RESEARCH
IN MATERIALS SCIENCE
Opportunities and Perspectives
Committee on the Mathematical Sciences Applied to Materials Science
Board on Mathematical Sciences
Commission on Physical Sciences, Mathematics, and Applications
National Research Council
National Academy Press
Washington, D.C. 1993
NOTICE: The project that is the subject of this report was approved by the Governing Board of the National
Research Council, whose members are drawn from the councils of the National Academy of Sciences, the
National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible
for the report were chosen for their special competences and with regard for appropriate balance.
This report has been reviewed by a group other than the authors according to procedures approved
by a Report Review Committee consisting of members of the National Academy of Sciences, the National
Academy of Engineering, and the Institute of Medicine.
The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars
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Dr. Bruce Alberts is president of the National Academy of Sciences.
The National Academy of Engineering was established in 1964, under the charter of the National
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The National Research Council was organized by the National Academy of Sciences in 1916 to
associate the broad community of science and technology with the Academy's purposes of furthering knowledge
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respectively, of the National Research Council.
Support for this project was provided by the Department of the Army, Army Research Office, and the
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Library of Congress Catalog Card Number 93-84439
International Standard Book Number 0-309-04930-X
Copyright 1993 by the National Academy of Sciences. All rights reserved.
Additional copies of this report are available from:
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B-157
?rinted in the United States of America
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
Accesion For
NTIS CRA&I
DTIC TAB
Unannounced E5
Justification _..-......-....................
By ----------------------------
Dist ib,ýtion I
AvaiklbihtY Codes
Avail and / or
Dist Special
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. KETITENRING, 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
iv
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
v
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 ,ollaborations. 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
vii
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.
NOTES
1. National Research Council. 1991. Applications of the MathematicalS ciences to Materials Science.
Board on Mathematical Sciences. Washington, D.C.: National Academy Press. 36 pp.
2. See, for example, National Research Council, 1989, Materials Science and Engineeringf or the 1990s,
Board on Physics and Astronomy, and National Materials Advisory Board, Washington, D.C.: National
Academy Press.
3. Federal Coordinating Council for Science, Engineering and Technology. 1992. Advanced Materials
and Processing: The Fiscal Year 1993 Progranm Committee on Industry and Technology. Washington,
D.C.: Office of Science and Technology Policy.
viii