Graduate Student / Postdoc Seminar
The Relaxation of a Crystal Surface: Step ODE's, PDE's, and Self-Similarity
Speaker: Hala Al Hajj Shehadeh
Location: Warren Weaver Hall 1302
Date: Friday, April 2, 2010, 1 p.m.
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.