Diffuse interface modeling of some interface problems involving elastic energy contributions
Qiang Du, Math, Penn State

In this talk, we report some recent works on the diffuse interface modeling and simulation of interface problems in materials science and biology. Particular examples include the studies of biomimetic vesicle membranes and homogeneous nucleation in anisotropic elastic solids. In both cases, elastic energy contributions are taken into account. We consider various theoretical and computational issues related to diffuse interface models and present some simulations results. We also discuss how to connect geometry, topology and analysis closely within a diffuse interface framework.