Analysis Seminar

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The Relaxation of a General Family of Broken Bond Crystal Surface Models

Speaker: Jeremy Marzuola, University of North Carolina

Location: Warren Weaver Hall 1302

Date: Thursday, September 22, 2016, 11 a.m.

Synopsis:

In work with Jon Weare (Chicago) that started when he was a Courant Instructor actually, we studied the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. With computational experiments and theoretical arguments we were able to derive several partial differential equation limits identified (or nearly identified) in previous studies and to clarify the correct choice of surface tension appearing in the PDE. These have the general form of fourth order nonlinear diffusion-type operators, though in certain cases they are degenerate. We will summarize these results, then discuss some properties of the derived PDEs and highlight some recent progress/interesting developments that have arisen in the study of these models.