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PDEs and Continuum Models of Phase Transitions

Proceedings of an NSF-CNRS Joint Seminar Held in Nice, France, January 18–22, 1988

  • Conference proceedings
  • © 1989

Overview

Editors:
  1. M. Rascle
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  2. D. Serre
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  3. M. Slemrod
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Part of the book series: Lecture Notes in Physics (LNP, volume 344)

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Table of contents (16 papers)

  1. Front Matter

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  2. Clusters of singularities in liquid crystals

    • Yves Bouligand
    Pages 1-9

  3. Stability analysis of flows of liquid crystal polymers exhibiting a banding structure

    • Maria-Carme Calderer
    Pages 10-21

  4. Coupled transverse-longitudinal solitons in elastic crystals

    • S. Cadet
    Pages 22-33

  5. The computation of the austenitic-martensitic phase transition

    • Charles Collins, Mitchell Luskin
    Pages 34-50

  6. Theory of diffusionless phase transitions

    • Richard James, David Kinderlehrer
    Pages 51-84

  7. Invariance properties of inviscid fluids of grade n

    • Pierre Casal, Henri Gouin
    Pages 85-98

  8. On diffusion in two-phase systems: the sharp interface versus the transition layer

    • Morton E. Gurtin
    Pages 99-112

  9. Instabilities in shear flow of viscoelastic fluids with fading memory

    • Bradley J. Plohr
    Pages 113-127

  10. Singularities of the order parameter in condensed matter physics

    • Maurice Kléman
    Pages 128-137

  11. Swelling and shrinking of polyelectrolyte gels

    • Ingo Müller
    Pages 138-145

  12. Adiabatic phase changes, fast and slow

    • Philip A. Thompson, Gerd E.A. Meier
    Pages 146-174

  13. The continuous structure of discontinuities

    • J. Glimm
    Pages 175-186

  14. Riemann problems involving undercompressive shocks

    • Michael Shearer, Stephen Schecter
    Pages 187-200

  15. The viscosity-capillarity approach to phase transitions

    • Marshall Slemrod
    Pages 201-206

  16. A version of the fundamental theorem for young measures

    • J. M. Ball
    Pages 207-215

  17. Very slow phase separation in one dimension

    • J. Carr, R. L. Pego
    Pages 216-226

  18. Back Matter

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Keywords

About this book

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.

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