<p>This IMA Volume in Mathematics and its Applications MICROSTRUCTURE AND PHASE TRANSITION is based on the proceedings of a workshop which was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." We thank R. Fosdick, M.E. Gurtin, W.-M. Ni and L.A. Peletier for organizing the year-long program and, especially, D. Kinderlehrer, R. James, M. Luskin and J. Ericksen for organizing the meeting and editing these proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, and the National Science Foun dation. A vner Friedman Willard Miller. Jr. PREFACE Much of our traditional knowledge of materials and processes is achievf'd by observa tion and analysis of small departures from equilibrium. Many materials, especially modern alloys, ceramics, and their composites, experience not only larger but more dramatic changes, such as the occurrence of phase transitions and t.he creation of defect structures, when viewed at the microscopic scale. How is this observed, how can it be interpreted, and how does it influence macroscopic behavior? These are the principle concerns of this volume, which constitutes the proceedings of an IMA workshop dedicated to these issues.</p>

Microstructure and Phase Transition (The IMA Volumes in Mathematics and its Applications)

Science & Math

JAMES, RICHARD

Kinderlehrer, David

Luskin, Mitchell

Ericksen, Jerry L.

Mathematics

Secaucus, New Jersey, U.S.A.: Springer Verlag, 1993

<p>This unabridged republication of the 1980 text, an established classic in the field, is a resource for many important topics in elliptic equations and systems and is the first modern treatment of free boundary problems. Variational inequalities (equilibrium or evolution problems typically with convex constraints) are carefully explained in An Introduction to Variational Inequalities and Their Applications. They are shown to be extremely useful across a wide variety of subjects, ranging from linear programming to free boundary problems in partial differential equations. Exciting new areas like finance and phase transformations along with more historical ones like contact problems have begun to rely on variational inequalities, making this book a necessity once again.</p>

An Introduction to Variational Inequalities and Their Applications (Classics in Applied Mathematics, Series Number 31)

Stampacchia, Guido

Society for Industrial and Applied Mathematics

This volume contains articles based on recent research and experiments concerning microstructure and phase transition, collected by the Institute for Mathematics and its Applications. The book provides a critique of current progress in some of the powerful new methods introduced to study questions on the behaviour of crystalline solids, as well as recent experimental results. These articles utilize nonlinear theory as a way to understand and control this behaviour. Many potentially relevant technological applications are addressed, including shape memory materials, non-linear dielectrics and ferroelectrics, magnetostrictive materials, composites or other materials fabricated or devised to promote special properties.

Microstructure and phase transition (The IMA volumes in mathematics and its applications)

Springer, Verlag

Hans Lewy Selecta

Lewy, Hans

Birkhauser

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