Noisy Kuramoto-Sivashinsky equation for an erosion model

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.

latex (w/ multicol.sty), 4 pages; to appear in Physical Review E (Oct 1996)

References in corpus (3)

• Dynamic Scaling of Ion-Sputtered Surfaces
• Stochastic Model for Surface Erosion Via Ion-Sputtering: Dynamical Evolution from Ripple Morphology to Rough Morphology
• Renormalization Group Analysis of a Noisy Kuramoto-Sivashinsky Equation

Cited by in corpus (12)

• Anomalous scaling in a non local growth model in the Kardar-Parisi-Zhang universality class
• Numerical analysis of the quantum dots on off-normal incidence ion sputtered surfaces
• Sampling conditioned hypoelliptic diffusions
• Height Fluctuations and Intermittency of $V_2{O}_5$ Films by Atomic Force Microscopy
• Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
• Discrete model for laser driven etching and microstructuring of metallic surfaces
• Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media
• Transition between chaotic and stochastic universality classes of kinetic roughening
• Kinetic Monte Carlo simulations of self organized nanostructures on Ta Surface Fabricated by Low Energy Ion Sputtering
• Multiscale Analysis for SPDEs with Quadratic Nonlinearities
• Scaling properties of generalized two-dimensional Kuramoto-Sivashinsky equations
• On the Stochastic Kuramoto-Sivashinsky Equation