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.

Format:

Book

Author/Creator:

National Research Council (U.S.). Committee on the Mathematical Sciences Applied to Materials Science.

Language:

English

Subjects (All):

Materials science--Research.

Materials science.

Mathematics--Research.

Mathematics.

Physical Description:

1 online resource (141 p.)

Edition:

1st ed.

Place of Publication:

Washington, DC : National Academy Press, 1993.

Language Note:

English

Summary:

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.

Contents:

MATHEMATICAL RESEARCH IN MATERIALS SCIENCE

Copyright

PREFACE

NOTES

Contents

1 SUMMARY AND OVERVIEW

2 ATOMIC SCALE

3 MACROMOLECULAR STRUCTURES

INTRODUCTION

SINGLE-CHAIN CONFORMATIONS

MODELING PROTEIN STRUCTURE AND DYNAMICS

ENTANGLEMENTS, REPTATION, AND ELASTICITY

Constitutive Equations

Existence, Well-Posedness

Numerical Methods and Singularities

Sharkskin and Spurt Flow

Flow Instabilities

Micromechanics

THEORY OF THE LIQUID STATE OF POLYMERS

INTERFACES IN POLYMER SYSTEMS

BLOCK COPOLYMERS

STIFF POLYMERS AND LIQUID CRYSTALS

OTHER PROBLEMS

4 EVOLUTION OF MICROSTRUCTURES

SPINODAL DECOMPOSITION AND NUCLEATION

GRAIN GROWTH AND OTHER INTERFACE MOTION CONTROLLED BY INTERFACE KINETICS

Computer Algorithms

SHAPE EVOLUTION CONTROLLED BY SURFACE DIFFUSION

MORPHOLOGICAL STABILITY

Phase Transformations and Pattern Formation

Dendritic Growth

MUSHY ZONES

PRECIPITATION AND COARSENING

Evolution of Microstructures

Stress and Current Effects

MARTENSITE AND SHAPE-MEMORY MATERIALS

MAGNETIC MATERIALS

SUPERCONDUCTIVITY

5 DEFECTS, DEFORMATION, AND INTERFACES

DEVELOPMENT OF MESOSCALE STATISTICAL MECHANICS OF SOLIDS

MECHANICS OF DEFECTS AND INTERFACES

PLASTICITY AND FRACTURE

LARGE LOCAL FIELD-INDUCED INSTABILITY IN RANDOM SYSTEMS

DYNAMIC FRACTURE

LIQUID CRYSTALS

EQUILIBRIUM AND NONEQUILIBRIUM SURFACE STRUCTURE

DEVELOPMENT OF A LATTICE MODEL OF MICROEMULSIONS

GRAIN BOUNDARIES

Statistical Issues

Statistical Mechanics Models

Computer Simulation

6 AGGREGATES AND DISORDERED MATERIAL

COLLOIDAL SUSPENSIONS

Stokesian Dynamics

Computational Microhydrodynamics

Nonequilibrium Statistical Mechanics

Variational Techniques

Self-Consistent Field Theories.

EQUILIBRIUM STRUCTURE

EFFECTIVE MODULI OF COMPOSITES

Future Directions

OPTIMAL COMPOSITES

GLASSES AND OTHER AMORPHOUS SOLIDS

7 PROCESSING, FABRICATION, AND EVALUATION

PROCESSING OF SEMICONDUCTOR CHIPS

AMORPHOUS SEMICONDUCTORS

CASTING

POLYMER PROCESSING

OTHER PROCESSING

MIXING

MATHEMATICAL MODELING IN QUANTITATIVE NONDESTRUCTIVE EVALUATION

FUNCTIONALLY GRADIENT MATERIALS

NONLINEAR OPTICAL MATERIALS

8 MATHEMATICAL AND NUMERICAL METHODS

MICROSCOPIC SCALE

MACROSCOPIC SCALE

MESOSCOPIC SCALE

POTENTIALLY APPLICABLE MATHEMATICAL SCIENCES DEVELOPMENTS

9 RECOMMENDATIONS

Acknowledging Obstacles to Collaboration

Fostering Increased Collaboration

RECOMMENDATIONS

Universities

Federal and State Government

Industry

Universities, Government, and Industry Together

Professional Societies

Bibliography

APPENDIX Contributors to Mathematical Research in Materials Science.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 103-125).

ISBN:

9786610195954

9781280195952

1280195959

9780309585651

0309585651

9780585153957

0585153957

OCLC:

43477216