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.