# Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates

@article{Gao2020AnalysisOA, title={Analysis of a fourth-order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates}, author={Yuan Gao and Anya Katsevich and Jian‐Guo Liu and Jianfeng Lu and Jeremy Louis Marzuola}, journal={Pure and Applied Analysis}, year={2020} }

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…

## 5 Citations

### Metropolis Crystal Surface Dynamics in the Rough Scaling Limit: From Local Equilibrium to Semi-Empirical PDE

- Multiscale Modeling & Simulation
- 2023

### The Local Equilibrium State of a Crystal Surface Jump Process in the Rough Scaling Regime

- MathematicsMultiscale Modeling & Simulation
- 2022

We investigate the local equilibrium (LE) distribution of a crystal surface jump process as it approaches its hydrodynamic (continuum) limit in a nonstandard, “rough” scaling regime introduced by…

### A proximal-gradient algorithm for crystal surface evolution

- Computer ScienceNumerische Mathematik
- 2022

This work develops a novel semi-implicit time discretization of the gradient flow, inspired by the classical minimizing movements scheme (known as the JKO scheme in the 2-Wasserstein case), and uses a primal dual gradient (PDHG) method to compute each element of the semi- Implicit scheme.

### A P ] 1 1 O ct 2 02 1 GLOBAL EXISTENCE OF A STRONG SOLUTION TO A FOURTH-ORDER EXPONENTIAL PDE MODELING CRYSTAL SURFACE GROWTH WITH METROPOLIS-TYPE RATES

- Mathematics
- 2021

Abstract. In this article we prove the global existence of a unique strong solution to the initial boundary-value problem for a fourth-order exponential PDE modeling crystal surface growth. The model…

### From local equilibrium to numerical PDE: Metropolis crystal surface dynamics in the rough scaling limit

- Mathematics
- 2021

This paper builds off of recent work in which we studied the local equilibrium (LE) distribution of a microscopic crystal surface jump process with Arrhenius transition rates, under the so-called…

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This work develops a novel semi-implicit time discretization of the gradient flow, inspired by the classical minimizing movements scheme (known as the JKO scheme in the 2-Wasserstein case), and uses a primal dual gradient (PDHG) method to compute each element of the semi- Implicit scheme.

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