Brian Spencer, Department of Mathematics, University at Buffalo
"Anisotropic crystal shapes: corner energy regularizations and elastically-induced shape transitions in solid films"
We consider two variations of the "Wulff shape" problem for the equilibrium shape of a solid particle in two dimensions.
The first part of the talk considers the effect of a corner-energy regularization which rounds sharp corners of the crystal. We consider the limit of small regularization, and use matched asymptotic expansions to construct solutions to the free boundary problem. It is shown that the regularized solutions approach the Wulff shape as the regularization goes to zero.
The second part of the talk discusses equilibrium crystal shapes ("islands" or "quantum dots") in strained solid films. Here numerical results on the interaction of anisotropic surface energy and elastic energy generates interesting bifurcation behavior in the shape of quantum dots.
TUESDAY, February 3, 2004