Oberseminar Numerische Mathematik / Scientific Computing
Axel Voigt
TU-Dresden
Phase field models - derivation, numerics and applications
Abstract:
Phase field equations are a convinient approach to solve interface problems. They are widely used in materials science to study pattern formation on mesoscopic length scales, typical examples are dendrite formation or grain growth. In this context the phase field model can directly be derived from classical density functional theory. We will use the phase field approach as a mathematical tool to solve PDEs on evolving surfaces. Thereby the surface is only implicitly represented as a level set of a phase field variable. The PDE to solve on the surface is e.g. a Cahn-Hilliard equation. Adaptive finite elements are used to discretize the system. Two applications are of interest: (i) thermal faceting of thin crystalline films, modeled by a diffusion equation on an evolving surface, where the evolution is governed by a 6th order equation (ii) budding of biomembranes, modeled by a Cahn-Hilliard equation on an evolving surface, where the evolution is governed by a 4th order equation.
| Datum: | 29.10.07 | Zeit: | 16:15 | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 032 im Erdgeschoss |