PDEs and Continuum Models of Phase Transitions

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

Michel Rascle, Denis Serre, Marshall Slemrod (Herausgeber)

Buch | Softcover

VII, 232 Seiten

2014 | 1. Softcover reprint of the original 1st ed. 1989
Springer Berlin (Verlag)
978-3-662-13766-6 (ISBN)

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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.

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.

Erscheint lt. Verlag	23.8.2014
Reihe/Serie	Lecture Notes in Physics
Zusatzinfo	VII, 232 p. 64 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	427 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Analysis • Behavior • Compactness • Crystal • Diffusion • Dynamical system • Dynamical Systems • Energy • Equilibrium • Evolution • Oscillation • Phase • phase transition • Soliton • stability • Structure
ISBN-10	3-662-13766-6 / 3662137666
ISBN-13	978-3-662-13766-6 / 9783662137666
Zustand	Neuware