Colloquium: Homogenization of composite media with time-dependent microstructure
4:10 p.m. Neill Hall 5W
Abstract: Homogenization is a mathematical method for writing simplified effective equations of media with complicated microstructure such as composite materials, flows in porous media, bio-fluids flow etc. In the first part of the talk we present an overview of some basic ideas in homogenization theory. The second part is devoted to a recent result on homogenization of two-phase flows with moving interface. The emphasis is on the description of micro-geometry of non-periodic disordered media. In the talk we present and discuss explicit geometric conditions that allow homogenization. These conditions are more flexible than periodicity, and do not use probability theory. In addition to being useful in moving interface problems, they also provide a theoretical justification of multi-scale computational algorithms for non-periodic media.