Phase Field Modeling and Simulations of Interface Problems

Tuesday, July 16, 2013 - 8:40am - 9:30am
Keller 3-180
Qiang Du (The Pennsylvania State University)
We begin the tutorial by introducing a couple of interface
problems in various physical and biological applications as
motivating examples. We then present some basic ingredients
of phase field models and take a special example to illustrate
both analytical and computational aspects of the relevant
variational problems and associated gradient dynamics.
We discuss in particular dynamics related to the classical
Allen-Cahn model and Cahn-Hilliard models with various
mobilities. We next focus on a few phase field models for
selected applications in biology and materials science which
are developed for interface problems involving elastic energy
contributions and those involving the coupling with external fields.
Finally, we conclude the tutorial with discussions on other
issues related to phase field modeling and simulations such as
robust retrieval of statistical information, stochastic fluctuation
and effective multiscale modeling.
MSC Code: