Phase instability and coarsening in two dimensions

Details Phase instability and coarsening in two dimensions Phase instability and coarsening in two dimensions

2009-04-14

arxiv.org/abs/0904.2204v2

Phys. Rev. E 80, 030106(R) (2009)

Physics

Condensed Matter

Statistical Mechanics

Five pages. Introduction and summary strongly revised. One page of supplementary material has been added

Scientific paper

10.1103/PhysRevE.80.030106

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.

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