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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.
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."
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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