PDEs and Continuum Models of Phase Transitions

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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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.

• Oscillation
• behavior
• compactness
• crystal
• diffusion
• dynamical system
• dynamical systems
• energy
• equilibrium
• evolution
• phase
• phase transition
• soliton
• stability
• structure

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