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.

Klappentext

This volume emphasizes the interdisciplinary nature of contemporary research in the field of phase transitions, research which involves ideas from nonlinear partial differential equations, asymptotic analysis, numerical computation and experiment. Topics covered include the treatment of scaling laws that describe the coarsening or ripening behavior observed during the later stages of phase transitions; novel numerical methods for treating interface dynamics; the mathematical description of geometric models of interface dynamics; determination of the governing equations and interfacial boundary conditions in the context of fluid flow and elasticity. This volume should be valuable for any researcher pursuing modern developments in the theory and applications of phase transitions and interface dynamics.

Inhalt

Phase field equations in the singular limit of sharp interface problems.- A phase fluid model: Derivation and new interface relation.- Geometric evolution of phase-boundaries.- The approach to equilibrium: Scaling, universality and the renormalisation group.- Evolving phase boundaries in the presence of deformation and surface stress.- Effect of modulated Taylor-Couette flows on crystal-melt interfaces: Theory and initial experiments.- A one dimensional stochastic model of coarsening.- Algorithms for computing crystal growth and dendritic solidification.- Towards a phase field model for phase transitions in binary alloys.