April 2: Al Hajj Shehadeh, CIMS
The relaxation of a crystal surface: Step ODE's, PDE's, and
self-similarity
In the first part of the talk, we will give a brief overview of
the subject of crystal relaxation. Below the roughening temperature, the
surface of a crystal consists of steps, terraces, and flat regions called
facets. The microscopic physics involves the attachment and detachment of
atoms at steps, and the diffusion of atoms across terraces. The
macroscopic consequences of these mechanisms are still poorly understood.
We will introduce some widely used discrete and continuum models that
describe the relaxation phenomena.
Then we'll discuss our recent progress (with Robert Kohn and Jonathan
Weare) on a one-dimensional step train separating two facets in the
"attachment detachment regime". Here, we prove that the evolution is
asymptotically self-similar, and that the continuum limit is associated
with a fourth order PDE.
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