PDEs and Continuum Models of Phase Transitions
Proceedings of an NSF-CNRS Joint Seminar Held in Nice, France, January 18-22, 1988
1st Edition
Published on 8. November 1989
Book
Hardback
VII, 232 pages
978-3-540-51617-0 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Illustrations
64 s/w Abbildungen
Dimensions
Height: 24.2 cm
Width: 17 cm
Weight
515 gr
ISBN-13
978-3-540-51617-0 (9783540516170)
DOI
10.1007/BFb0024930
Schweitzer Classification
Other editions
Additional editions
Michel Rascle | Denis Serre | Marshall Slemrod
PDEs and Continuum Models of Phase Transitions
Proceedings of an NSF-CNRS Joint Seminar Held in Nice, France, January 18-22, 1988
Book
08/2014
Springer
€106.99
Shipment within 7-9 days
Content
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.