Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation
Abstract
The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of infinite aspect ratio. The stationary solutions are shown to be strongly influenced by the strength of noise. Stationary states for small and large noise strengths appear to be quasi-ordered and disordered respectively. The dynamics of ordering from an initially inhomogeneous state is very slow in the former case and fast in the latter. Both numerical and analytic calculations indicate that the slow dynamics can be characterized by a simple scaling relationship, with a characteristic dynamic exponent of in the intermediate time regime.
Keywords
Cite
@article{arxiv.cond-mat/9205015,
title = {Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation},
author = {K. R. Elder and Jorge Viñals and Martin Grant},
journal= {arXiv preprint arXiv:cond-mat/9205015},
year = {2009}
}