Coarse graining results in crystal surface relaxation

Jonathan Weare, University of Chicago
April 18th, 2012 at 4PM–5PM in 939 Evans Hall [Map]

I will present recent results on the coarse graining of two models of crystal surface relaxation. First, I will discuss joint work with Hala Al Hajj Shehadeh and Robert V. Kohn on an ODE model of a 1D monotone crystal surface. We prove that the slope of a finite size crystal in this setting converges (in the long time limit) to a similarity solution. We also give an informal derivation of a fully nonlinear fourth order PDE (large crystal) limit of the ODE's as well as analogues of our similarity results in the continuum. Next, I'll discuss current work with Jeremy Marzuola investigating certain scaling limits of a general family of Kinetic Monte Carlo models of crystal surface relaxation. We informally derive two fully non-linear fourth order PDE in two different scaling limits. Both PDE's are similar to (but not exactly the same as) PDE's that have been proposed as large-scale limits for the models in question. Our aim is to clarify how each arises as well as to establish the limits rigorously.