Phase instability and coarsening in two dimensions

TL;DR

This paper investigates pattern formation and coarsening in two-dimensional nonequilibrium systems, revealing how phase diffusion dynamics determine whether a system stabilizes or coarsens, with analytical examples based on nonlinear equations.

Contribution

It demonstrates that phase diffusion equations can predict coarsening behavior in two dimensions, extending understanding beyond one-dimensional cases.

Findings

Coarsening is linked to the mbda-dependence of the phase diffusion coefficient D_{11}(mbda).

The results depend on lattice symmetry and conservation laws.

Analytical examples are provided using prototypical nonlinear equations.

Abstract

Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one dynamics prevails over the other is a longstanding problem, particularly beyond one dimension. It is shown that the challenge can be defied in two dimensions, using the concept of phase diffusion equation. We find that coarsening is related to the \lambda-dependence of a suitable phase diffusion coefficient, D_{11}(\lambda), depending on lattice symmetry and conservation laws. These results are exemplified analytically on prototypical nonlinear equations.