Abstract

Composite materials are important to modern technology as the mixing of two different material properties at fine scales can give rise to unexpected emergent behavior. Therefore, understanding the process of phase separation on such materials is crucial to leveraging these processes for technological applications.

A variational model for the interaction between homogenization and phase separation in a double-periodic material is considered. The focus of the talk is on the regime where the separation happens at a bigger scale than both micro-scales, and a phase separation for the homogenized functional is expected.

A mathematical introduction to the history of the phase separation functional will be given, and with it the tools needed to tackle the double-periodic case, such as Γ-convergence and the periodic unfolding operator.