This book approaches the concept of boundary, central in linguistic theory, and the related notion of phase from the perspective of the interaction between syntax and its interfaces. A primary notion is that phases are the appropriate domains to explain most interface linguistic phenomena and that the study of (narrow) interfaces helps to understand conditions on the internal structure of the Language Faculty. The first part of this volume is dedicated to introducing the notion of boundary, cycle and phase, and also the current debates regarding internal interfaces, in particular, the syntax-phonology, syntax-semantics, syntax-discourse, syntax-morphology and syntax-lexicon interfaces, in order to show how the notion of boundary/phase is related to (or even determines) most of their characteristics. The four sections of the second part deal with (morpho)phonology/ syntax and the role or boundaries/phases; the syntax-discourse and syntax-semantics interface; and the lexicon-syntax interface, while the notion of boundary/phase cross-cuts the main topics addressed.

This book approaches the concept of boundary, central in linguistic theory, and the related notion of phase from the perspective of the interaction between syntax and its interfaces. A primary notion is that phases are the appropriate domains to explain most interface linguistic phenomena and that the study of (narrow) interfaces helps to understand conditions on the internal structure of the Language Faculty. The first part of this volume is dedicated to introducing the notion of boundary, cycle and phase, and also the current debates regarding internal interfaces, in particular, the syntax-phonology, syntax-semantics, syntax-discourse, syntax-morphology and syntax-lexicon interfaces, in order to show how the notion of boundary/phase is related to (or even determines) most of their characteristics. The four sections of the second part deal with (morpho)phonology/ syntax and the role or boundaries/phases; the syntax-discourse and syntax-semantics interface; and the lexicon-syntax interface, while the notion of boundary/phase cross-cuts the main topics addressed.

An accessible yet rigorous discussion, featuring case studies and study problems to illustrate and reinforce key concepts.

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.

There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface. This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”

This IMA Volume in Mathematics and its Applications ON THE EVOLUTION OF PHASE BOUNDARIES 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". The purpose of the workshop was to bring together mathematicians and other scientists working on the Stefan problem and related theories for modeling physical phenomena that occurs in two phase systems. We thank M.E. Gurtin and G. McFadden for editing the proceedings. We also take this opportunity to thank the National Science Foundation, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE A primary goal of the IMA workshop on the Evolution of Phase Boundaries from September 17-21, 1990 was to emphasize the interdisciplinary nature of contempo rary research in this field, research which combines ideas from nonlinear partial dif ferential equations, asymptotic analysis, numerical computation, and experimental science. The workshop brought together researchers from several disciplines, includ ing mathematics, physics, and both experimental and theoretical materials science.