Robert V. Kohn, Courant Institute, NYU
Energy-Driven Pattern Formation

Nature is full of energy-driven patterns. Some represent local or global minimizers of a suitable free energy. Others are self-organized transients produced by energy-dissipating dynamics. Simulation can demonstrate the adequacy of a model, but it rarely explains "why" a pattern forms.
Nonlinear PDE and the calculus of variations can sometimes provide a more global understanding. I'll give four independent lectures on problems of this type, involving (a) bounds on coarsening rates; (b) the internal structure of a cross-tie wall; (c) motion by surface diffusion below the roughening temperature, and (d) thermally-activated transitions modeled by action minimization.