ANALYSIS OF A FOURTH-ORDER EXPONENTIAL PDE ARISING FROM A CRYSTAL SURFACE JUMP PROCESS WITH METROPOLIS-TYPE TRANSITION RATES

We analytically and numerically study a fourth-order PDE modeling rough crystal surface diffusion on the macroscopic level. We discuss existence of solutions globally in time and long-time dynamics for the PDE model. The PDE, originally derived by Katsevich is the continuum limit of a microscopic model of the surface dynamics, given by a Markov jump process with Metropolis-type transition rates. We outline the convergence argument, which depends on a simplifying assumption on the local equilibrium measure that is valid in the high-temperature regime. We provide numerical evidence for the convergence of the microscopic model to the PDE in this regime.

Duke Scholars

Author Anya Katsevich Statistical Science

Author Jianfeng Lu Mathematics

Author Jian-Guo Liu Physics