Back to Departmental Colloquium: Spring 2000
Departmental Colloquium
Date: Thursday, Feb 17, 2000
Time: 4:15PM
Location: JWB 335
Stephan Luckhaus
Leipzig)
Title |
Phase changes, evolution of varifolds and the second law of thermodynamics |
Abstract |
In continuum physics phase transitions are modelled by a change in the constitutive laws coupling the thermodynamic quantities. In systems with heat and mass diffusion this law may be taken to be the entropy as a function of energy and mass density (for isothermic systems entropy is replaced by free energy). The overall entropy is then the convex hull of the entropies of all the phases. The equations of evolution are degenerate parabolic systems of Stefan type and exhibit regions of phase mixtures, so called mushy regions. Following Gibbs, mesoscopic models include terms proportional to the area of the phase interface in the entropy, thus avoiding mushy regions. The evolution equations for these models are parabolic in the bulk coupled to either mean curvature or mean curvature flow equations on the phase interface. A notion of solution is discussed which is closed under weak convergence. This is a slight variation of the one introduced by Brakke for mcf and extended by Soner to the Mullins Sekerka problem. In this context the phase interface becomes an integer varifold. |
Mathematical Biology