Research Activities > Programs > Nonequilibrium Interface and Surface Dynamics 2007

Continuum modeling of surface relaxation below the roughening temperature

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Continuum modeling of surface relaxation below the roughening temperature

Professor Robert Kohn

New York University


Abstract:   I'll discuss the evolution of a crystalline surface as it relaxes to a facet under motion by surface diffusion. A widely-used continuum approach solves a fourth-order "steepest-descent" PDE with a singular surface energy. I'll discuss joint work with Irakli Odisharia and Henrique Versieux, concerning: (a) numerical aspects -- specifically, a new approach to time-stepping via implicit-in-time discretization, and the accuracy of nonlinear Galerkin schemes for spatial discretization; (b) analytical issues -- specifically, self-similarity of symmetric profiles in one space dimension. The correctness of the "steepest-descent" PDE model remains uncertain. While the PDE is correct away from the facet, the "steepest descent" viewpoint may not correctly model the free boundary condition at the edge of a facet. I'll explain why not.
[slides]

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