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Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
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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

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
×

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 engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. 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 Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Robert M. White is president of the National Academy of Engineering.

The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine.

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 and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council.

Support for this project was provided by the Department of the Army, Army Research Office, and the National Science Foundation. The content of this report does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.

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:
National Academy Press
2101 Constitution Avenue, N.W. Washington, D.C. 20418

B-157

Printed in the United States of America

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
×

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

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
×

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

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
×

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

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
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Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
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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

Page viii Cite
Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
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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 Mathematical Sciences 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 Engineering for 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 Program. Committee on Industry and Technology. Washington, D.C.: Office of Science and Technology Policy.

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
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Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
×

5

 

DEFECTS, DEFORMATION, AND INTERFACES

 

52

   

Introduction

 

52

   

Development of Mesoscale Statistical Mechanics of Solids

 

54

   

Mechanics of Defects and Interfaces

 

54

   

Plasticity and Fracture

 

55

   

Large Local Field-Induced Instability in Random Systems

 

57

   

Dynamic Fracture

 

58

   

Liquid Crystals

 

59

   

Equilibrium and Nonequilibrium Surface Structure

 

62

   

Development of a Lattice Model of Microemulsions

 

63

   

Grain Boundaries

 

64

   

Statistical Issues

 

64

   

Statistical Mechanics Models

 

65

   

Computer Simulation

 

65

6

 

AGGREGATES AND DISORDERED MATERIAL

 

66

   

Introduction

 

66

   

Colloidal Suspensions

 

66

   

Stokesian Dynamics

 

67

   

Computational Microhydrodynamics

 

68

   

Nonequilibrium Statistical Mechanics

 

68

   

Variational Techniques

 

69

   

Self-Consistent Field Theories

 

69

   

Equilibrium Structure

 

69

   

Effective Moduli of Composites

 

70

   

Future Directions

 

72

   

Optimal Composites

 

74

   

Glasses and Other Amorphous Solids

 

75

7

 

PROCESSING, FABRICATION, AND EVALUATION

 

77

   

Introduction

 

77

   

Processing of Semiconductor Chips

 

77

   

Amorphous Semiconductors

 

79

   

Casting

 

79

   

Polymer Processing

 

80

   

Other Processing

 

80

   

Mixing

 

80

   

Mathematical Modeling in Quantitative Nondestructive Evaluation

 

81

   

Functionally Gradient Materials

 

82

   

Nonlinear Optical Materials

 

83

Suggested Citation:"FRONT MATTER." National Research Council. 1993. Mathematical Research in Materials Science: Opportunities and Perspectives. Washington, DC: The National Academies Press. doi: 10.17226/2206.
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This book describes fruitful past collaborations between the mathematical and materials sciences and indicates future challenges. It seeks both to encourage mathematical sciences research that will complement vital research in materials science and to raise awareness of the value of quantitative methods. The volume encourages both communities to increase cross-disciplinary collaborations, emphasizing that each has much to gain from such an increase, and it presents recommendations for facilitating such work.

This book is written for both mathematical and materials science researchers interested in advancing research at this interface; for federal and state agency representatives interested in encouraging such collaborations; and for anyone wanting information on how such cross-disciplinary, collaborative efforts can be accomplished successfully.

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