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New stability results for patterns in a model of long-wavelength convection

Skeldon, AC and Silber, M (1998) New stability results for patterns in a model of long-wavelength convection Physica D-Nonlinear Phenomena, 122 (1-4). 117 - 133. ISSN 0167-2789

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Abstract

We consider the transition from a spatially uniform state to a steady, spatially- periodic pattern in a partial differential equation describing long-wavelength convec- tion [1]. This both extends existing work on the study of rolls, squares and hexagons and demonstrates how recent generic results for the stability of spatially-periodic patterns may be applied in practice. We find that squares, even if stable to roll perturbations, are often unstable when a wider class of perturbations is considered. We also find scenarios where transitions from hexagons to rectangles can occur. In some cases we find that, near onset, more exotic spatially-periodic planforms are preferred over the usual rolls, squares and hexagons.

Item Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Physica D Nonlinear Phenomena. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D Nonlinear Phenomena, 122(1-4), November 1998, DOI 10.1016/S0167-2789(98)00171-7.
Uncontrolled Keywords: pattern formation, symmetry, hexagons, convection, PLANFORMS, SELECTION
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 01 Feb 2012 14:39
Last Modified: 23 Sep 2013 18:57
URI: http://epubs.surrey.ac.uk/id/eprint/72365

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