November 6: Robert Kohn, CIMS
Energy-Driven Pattern Formation
Energy-driven pattern formation is difficult to
define, but easy to recognize. I'll discuss two examples:
(a) surface-energy-driven coarsening of two-phase mixtures.
(b) cross-tie wall patterns in magnetic thin films.
The two problems are rather different -- the first is dynamic, the
second static. But they share certain features: in
each case nature forms complex patterns as it attempts to
minimize a suitable "free energy". The task of modeling and
analyzing such patterns is a rich source of challenges -- many
still open -- in the nonlinear PDE and the calculus of variations.