MIT/HARVARD ANALYSIS SEMINAR

Speaker: Robert V. Kohn, Courant Institute, New York University

Title: Energy-Driven Pattern Formation

Date: April 28

Time: 4:15 pm

Location: MIT, 2-142

Abstract: Many physical systems can be modelled using a nonconvex bulk
energy regularized by higher-order terms or surface energy. Such
systems tend to form complex patterns of domains and walls.
It is natural to explore (a) the internal structures of walls, (b) the
overall patterns of domains, and (c) the nucleation of new domains and
walls due to thermal fluctuation. When a pattern is driven by energy
minimization we can "explain" it variationally, by showing that
no other pattern achieves a lower energy. I will discuss several examples
of this type, including (i) the branching of domains in a uniaxial ferromagnet (work with Choksi and Otto); (ii) the internal structure of a cross-tie wall (work by Alouges, Riviere, and Serfaty), and (iii) thermally-activated switching modelled by action minimization (work with Otto, Reznikoff, and Vanden-Eijnden).