Fourth order models for crystal surface fluctations
We'll discuss derivations, dynamics, numerical approximations, recent analytical advances and open questions for a family of 4th order nonlinear PDEs that arise when modeling the fluctuations of a crystal surface. The microscopic problem follows from a continuous time jump Markov process where the jumps occur randomly with rates set from a generalized broken-bond Kinetic Monte Carlo model. The PDEs have a similar look to those of the thin film equations that have been studied by a large number of authors. We will discuss work with on this problem with Jonathan Weare, as well as Jian-Guo Liu, Jianfeng Lu and Dio Margetis; and Anya Katsevich.