论文标题
分析由大都市型转变速率的晶体表面跳跃过程产生的第四阶PDE
Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
论文作者
论文摘要
我们通过分析和数值研究了第四阶PDE在宏观水平上建模粗糙的晶体表面扩散。我们在全球范围内的解决方案的存在和PDE模型的长时间动力学讨论。 PDE最初是由第二作者得出的，是表面动力学的微观模型的连续限制，该模型由Markov跳跃过程带有Metropolis类型过渡速率。我们概述了收敛参数，该参数取决于在高温方向上有效的局部平衡度量的简化假设。我们提供了微观模型在此制度中与PDE收敛的数值证据。
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 the second author, 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.
