Phase Separation in Heterogeneous Media

Explore a 44-minute lecture on phase separation in heterogeneous media presented by Irene Fonseca at the International Mathematical Union. Delve into a variational model within the gradient theory for fluid-fluid phase transitions, focusing on small-scale heterogeneities. Examine two regimes: one where heterogeneities and diffuse interfaces occur at the same scale, leading to anisotropic interfacial energy, and another where phase separation happens at a smaller scale than homogenization. Learn about the establishment of bounds on homogenized surface tension, identification of zeroth and first order Γ-limits, and the characterization of large-scale limiting behavior in viscosity solutions to non-degenerate and periodic Eikonal equations in half-spaces. Access accompanying presentation slides for visual support of the complex mathematical concepts discussed.