Dynamic scaling and quasiordered states in the two-dimensional Swift-Hohenberg equation

K. R. Elder, Jorge Viñals, Martin Grant

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

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 quasiordered 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 1/4 in the intermediate-time regime.

Original languageEnglish (US)
Pages (from-to)7618-7629
Number of pages12
JournalPhysical Review A
Volume46
Issue number12
DOIs
StatePublished - Jan 1 1992

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