Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids: A Collection of Reprints of 14 Seminal Papers

ISBN-13: 9783642641886 / Angielski / Miękka / 2011 / 474 str.

John M. Ball; David Kinderlehrer; Paulo Podio-Guidugli

Opis

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."

Spis treści

Introduction: Fifty Years of Research on Evolving Phase Interfaces.- I. Papers on Materials Science.- Surface Tension as a Motivation for Sintering.- Two-Dimensional Motion of Idealized Grain Boundaries.- Morphological Stability of a Particle Growing by Diffusion or Heat Flow.- Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics.- The Interactions of Composition and Stress in Crystalline Solids.- II. Papers on Continuum Mechanics.- Multiphase Thermomechanics with Interfacial Structure. 1. Heat Conduction and the Capillary Balance Law.- The Effect of Surface Stress on Crystal-Melt and Crystal-Crystal Equilibrium.- Multiphase Thermomechanics with Interfacial Structure. 2. Evolution of an Isothermal Interface.- On the Driving Traction Acting on a Surface of Strain Discontinuity in a Continuum.- The Nature of Configurational Forces.- III. Papers on Mathematics.- Solutions for the Two-Phase Stefan Problem with the Gibbs-Thomson Law for the Melting Temperature.- Motion of Level Sets by Mean Curvature.I.- Uniqueness and Existence of Viscosity Solutions of Generalized Mean Curvature Flow Equations.- Convergence of the Phase-Field Equations to the Mullins-Sekerka Problem with Kinetic Undercooling.- Papers Reprinted.

Blurb

This book addresses the physics of phase transitions in chemical compositions and crystal or molecular structures. It deals with the control of the scale and distribution of microstructural features that are associated with different phases. Here a mathematical framework is presented with the capacity to describe and predict the evolution of phase interfaces. Some of the relevant developments are summarized, with emphasis being placed on the contributions made by those researchers whose works are printed in this volume.