Graduate Student / Postdoc Seminar
Energy-Driven Pattern Formation: A New Frontier for the Calculus of Variations
Speaker: Robert Kohn, Courant
Location: Warren Weaver Hall 1302
Date: Friday, April 22, 2011, 1 p.m.
Energy-driven pattern formation examines how energy minimization leads to the formation of defects and microstructure in a variety of physical systems. Examples include the wrinkling of a stretched elastic membrane, the formation of domains in a magnetic material, and the twinning produced by martensitic phase transformation. These systems can be described by "Landau theories" -- essentially, nonconvex variational problems regularized by higher-order singular perturbations. I will show in various examples -- some old, some new -- how one can identify the scaling law of the minimum energy; how this sheds light on the underlying patterns; and how the investigation of such issues leads to new types of questions in the calculus of variations.