Noisy Kuramoto-Sivashinsky equation for an erosion model

TL;DR

This paper derives a stochastic continuum equation, specifically the Kuramoto-Sivashinsky equation, from a discrete ion sputtering model using a master equation approach, linking microscopic dynamics to macroscopic behavior.

Contribution

It introduces a novel derivation of the noisy Kuramoto-Sivashinsky equation from a discrete ion sputtering model via a systematic continuum limit process.

Findings

Derivation of the continuum equation from a discrete model.

Mapping of the master equation to a Langevin equation.

Identification of the stochastic noise term in the continuum limit.

Abstract

We derive the continuum equation for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how it can be truncated to a Fokker-Planck equation and mapped to a discrete Langevin equation. By taking the continuum limit, we arrive at the Kuramoto-Sivashinsky equation with a stochastic noise term.