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 -- INTRODUCTION -- 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 -- INTRODUCTION -- 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 -- INTRODUCTION -- 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 -- INTRODUCTION -- 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 -- INTRODUCTION -- MICROSCOPIC SCALE -- MACROSCOPIC SCALE -- MESOSCOPIC SCALE -- POTENTIALLY APPLICABLE MATHEMATICAL SCIENCES DEVELOPMENTS -- 9 RECOMMENDATIONS -- INTRODUCTION -- 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.