Ripples and dots generated by lattice gases

TL;DR

This paper demonstrates that surface pattern formation such as ripples and dots can be modeled using simple nonequilibrium lattice gases, enabling large-scale simulations and insights into surface growth universality classes.

Contribution

It introduces a mapping of surface pattern formation to lattice gases, allowing efficient simulation and analysis of surface growth phenomena and universality classes.

Findings

KPZ universality class remains stable under certain conditions

Strong smoothing diffusion causes logarithmic growth in 2D

Model effectively describes anisotropic surface diffusion

Abstract

We show that the emergence of different surface patterns (ripples, dots) can be well understood by a suitable mapping onto the simplest nonequilibrium lattice gases and cellular automata.Using this efficient approach difficult, unanswered questions of surface growth and its scaling can be studied. The mapping onto binary variables facilitates effective simulations and enables one to consider very large system sizes.We have confirmed that the fundamental Kardar-Parisi-Zhang (KPZ) universality class is stable against a competing roughening diffusion,while a strong smoothing diffusion leads to logarithmic growth, a mean-field type behavior in two dimensions.The model can also describe anisotropic surface diffusion processes effectively. By analyzing the time-dependent structure factor we give numerical estimates for the wavelength coarsening behavior.