SPRING 2021 Nonlinear Analysis Seminar Series
Professor Irene Fonseca, Carnegie Mellon University
Title: Phase Transitions in Heterogeneous Media: Equilibria and Geometric Flows
A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In the case where the scale of the small homogeneities is of the same order of the scale governing the phase transition, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial energy.
The underlying gradient flow provides unconditional convergence results for an Allen-Cahn type bi-stable reaction diffusion equation in a periodic medium. The limiting dynamics are given by an analog for anisotropic mean curvature flow, of the formulation due to Ken Brakke. As an essential ingredient in the analysis, an explicit expression for the effective surface tension, which dictates the limiting anisotropic mean curvature, is obtained.
This is joint work with Riccardo Cristoferi (Radboud University, The Netherlands), Adrian Hagerty, Cristina Popovici, Rustum Choksi (McGill), Jessica Lin (McGill), and Raghavendra Venkatraman (CMU).