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" Evolution of material surfaces for highly anisotropic surface energy " Motion of material surfaces via atomic diffusion is an important aspect of semiconductor fabrication. It is well known that models for the time evolution of material surfaces can become mathematically ill-posed when the surface energy is highly anisotropic. In some cases, this ill-posedness has been associated with the formation of corners along the interface, the so-called Wulff shapes. In this talk, I consider a particular regularization of the ill-posedness which is implemented through the incorporation of higher order terms in the surface energy. Numerical solutions of the model equations for unstressed solids suggest that corners with Wulff angles form as the regularization tends to zero, in agreement with expectations. However, in the presence of elastic stresses the limiting corner angles are most often found to differ from angles on the (unstressed) Wulff shape, contrary to expectations. For large elastic stresses we also observe a novel filamenting instability, referred to as tipstreaming. This is joint work with Mike Miksis and Peter Voorhees at Northwestern University. |