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Seminar Abstracts

Max Morini

Geometrically constrained walls in two dimensions.

Abstract

We address the effect of extreme geometry on a non-convex variational problem motivated by recent investigations of magnetic domain walls trapped by thin necks. The main purpose is to extend the results of Kohn&Slastikov to the two-dimensional case. The analysis turns out to be significantly more complicated and requires different methods. In particular, the purely variational point of view adopted in the paper by Kohn&Slatikov is here replaced by a more direct approach based on PDE techniques. The existence of local minimizers representing geometrically constrained walls is proven under suitable symmetry assumptions on the domain and an asymptotic characterization of the wall profile is given. The asymptotic behavior, which depends critically on the scaling of length and width of the neck, turns out to be qualitatively different from the higher-dimensional case and a richer variety of regimes is shown to exist.

TUESDAY, December 1, 2009
Time: 1:30 P.M.
Location: PPB 300