Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 18-CNA-026 A Note On Homogenization Effects On Phase Transition Problems Adrian HagertyDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PAahagerty@andrew.cmu.eduAbstract: In fluid-fluid phase transitions problems featuring small scale heterogeneity, we see that when the scale heterogeneity is sufficiently small, the periodic potential function $W(x,p)$ can be replaced with a homogenized potential function $W_H(p)$. This allows for a reduction to a problem already studied by Fonseca and Tartar [6]. In particular, we see an isotropic transition potential, in contrast with the case where the scales are roughly comensurate [4]. This note is intended as a prelude to a more complete analysis of the full range of scales.Get the paper in its entirety as  18-CNA-026.pdf