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Robert Kohn


Speaker: Robert Kohn
Title: Energy-Driven Pattern Formation: A New Frontier for the Calculus of Variations
Affiliation: Courant Institute, New York University
Date: Friday, April 15, 2011
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. 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, and how this sheds light on the underlying patterns.