Research Activities >
Nonequilibrium Interface and Surface Dynamics 2007
Continuum modeling of surface relaxation
below the roughening temperature
CSIC Building (#406),
Seminar Room 4122.
Continuum modeling of surface relaxation below the
New York University
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.