PDEs and Continuum Models of Phase Transitions

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Beschreibung

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.

Inhalt
Clusters of singularities in liquid crystals.- Stability analysis of flows of liquid crystal polymers exhibiting a banding structure.- Coupled transverse-longitudinal solitons in elastic crystals.- The computation of the austenitic-martensitic phase transition.- Theory of diffusionless phase transitions.- Invariance properties of inviscid fluids of grade n.- On diffusion in two-phase systems: the sharp interface versus the transition layer.- Instabilities in shear flow of viscoelastic fluids with fading memory.- Singularities of the order parameter in condensed matter physics.- Swelling and shrinking of polyelectrolyte gels.- Adiabatic phase changes, fast and slow.- The continuous structure of discontinuities.- Riemann problems involving undercompressive shocks.- The viscosity-capillarity approach to phase transitions.- A version of the fundamental theorem for young measures.- Very slow phase separation in one dimension.

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Produktinformationen

Titel
PDEs and Continuum Models of Phase Transitions
Untertitel
Proceedings of an NSF-CNRS Joint Seminar Held in Nice, France, January 18-22, 1988
Editor
EAN
9783662137666
ISBN
978-3-662-13766-6
Format
Kartonierter Einband
Herausgeber
Springer, Berlin
Genre
Mathematik
Anzahl Seiten
232
Größe
H12mm x B245mm x T143mm
Jahr
2014
Untertitel
Englisch
Auflage
Softcover reprint of the original 1st ed. 1989
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