On the Evolution of Phase Boundaries

1. Front Matter

   Pages i-xiii

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2. Phase Field Equations in the Singular Limit of Sharp Interface Problems

   • Gunduz Caginalp, Xinfu Chen

   Pages 1-27

3. A Phase Fluid Model: Derivation and New Interface Relation

   • G. Caginalp, J. Jones

   Pages 29-50

4. Geometric Evolution of Phase-Boundaries

   • Yoshikazu Giga, Shun’ichi Goto

   Pages 51-65

5. The Approach to Equilibrium: Scaling, Universality and the Renormalisation Group

   • Nigel Goldenfeld

   Pages 67-76

6. Evolving Phase Boundaries in the Presence of Deformation and Surface Stress

   • Morton E. Gurtin

   Pages 77-80

7. Effect of Modulated Taylor-Couette Flows on Crystal-Melt Interfaces: Theory and Initial Experiments

   • G. B. McFadden, B. T. Murray, S. R. Coriell, M. E. Glicksman, M. E. Selleck

   Pages 81-100

8. A One Dimensional Stochastic Model of Coarsening

   • W. W. Mullins

   Pages 101-105

9. Algorithms for Computing Crystal Growth and Dendritic Solidification

   • James A. Sethian, John Strain

   Pages 107-125

10. Towards a Phase Field Model for Phase Transitions in Binary Alloys

    • A. A. Wheeler, W. J. Boettinger

    Pages 127-136

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.

• Phase Transition
• Phase Transitions
• algorithms
• differential equation
• numerical methods

• Department of Mathematics, Carnegie-Mellon University, Pittsburgh, USA

  Morton E. Gurtin

• NIST, Gaithersburg, USA

  Geoffrey B. McFadden

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