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PDEs and Continuum Models of Phase Transitions - Proceedings of an NSF-CNRS Joint Seminar Held in Nice, France, January 18-22,... PDEs and Continuum Models of Phase Transitions - Proceedings of an NSF-CNRS Joint Seminar Held in Nice, France, January 18-22, 1988 (Paperback, Softcover reprint of the original 1st ed. 1989)
Michel Rascle, Denis Serre, Marshall Slemrod
R2,868 Discovery Miles 28 680 Ships in 10 - 15 working days

The study of phase transitions is one of the fundamental problems of physics. The goal of this seminar was to understand better the spectacular progress made recently in constructing continuum models. Concentrating on a few examples such as the microstructure of crystals, defects in liquid crystals and liquid-vapor interfaces, several key points are described, for example the structure and evolution of the interfaces, regularization via interfacial energy, and equilibrium theories. The mathematical treatment of these questions involves large-oscillation theories (Young's measures, compensated compactness), spectral theory, admissibility of shock waves, long-time behavior of dynamical systems, high-order perturbations, group actions, solitons, and others.

Shock Induced Transitions and Phase Structures in General Media (Paperback, Softcover reprint of the original 1st ed. 1993):... Shock Induced Transitions and Phase Structures in General Media (Paperback, Softcover reprint of the original 1st ed. 1993)
J.E. Dunn, Roger Fosdick, Marshall Slemrod
R2,866 Discovery Miles 28 660 Ships in 10 - 15 working days

This IMA Volume in Mathematics and its Applications SHOCK INDUCED TRANSITIONS AND PHASE STRUCTURES IN GENERAL MEDIA is based on the proceedings of a workshop that was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." The workshop focused on the thermodynamics and mechanics of dynamic phase transitions that are mainly inertially driven and brought together physicists, metallurgists, mathematicians, engineers, and molecular dynamicists with interests in these problems. Financial support of the National Science Foundation made the meeting pos sible. We are grateful to J .E. Dunn, Roger Fosdick, and Marshall Slemrod for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, .Jr. PREFACE When a body is subjected to a strong shock the material may suffer severe local structural changes. Rapid solidification, liquification, or vaporization can oc cur, and, moreover, complex structural heterogeneity is often left in the wake of the passing wave. Thus, inertially driven shock waves raise fundamental questions involving experiment, theory, and mathematics which bear on phase stability and metastability, as well as on reaction kinetics and appropriate measures of phase structure."

Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids - A Collection of Reprints of 14... Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids - A Collection of Reprints of 14 Seminal Papers (Paperback, Softcover reprint of the original 1st ed. 1999)
John M Ball; Introduction by E. Fried; Edited by David Kinderlehrer, Paulo Podio-Guidugli, Marshall Slemrod
R3,174 Discovery Miles 31 740 Ships in 10 - 15 working days

A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 ************************************************ 0 ***** 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 *********** 0 ******************* 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.

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