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Steady squares and hexagons on a subcritical ramp

Steady squares and hexagons on a subcritical ramp
Steady squares and hexagons on a subcritical ramp
Steady squares and hexagons on a subcritical ramp are studied, both analytically and numerically, within the framework of the lowest-order amplitude equations. On the subcritical ramp, the external stress or control parameter varies continuously in space from subcritical to supercritical values. At the subcritical end of the ramp, pattern formation is suppressed, and patterns fade away into the conduction solution. It is shown that three-dimensional patterns may change shape on a subcritical ramp. A square pattern becomes a pattern of rolls as it fades, with the roll axes aligned in the direction orthogonal to that in which the control parameter varies. Hexagons in systems with horizontal midplane symmetry become a pattern of rectangles before reaching the conduction solution. There is a suggestion that hexagons in systems which lack this symmetry might fade away through a roll pattern. Numerical simulations are used to illustrate these phenomena.

1539-3755
310-315
Hoyle, R. B.
e980d6a8-b750-491b-be13-84d695f8b8a1
Hoyle, R. B.
e980d6a8-b750-491b-be13-84d695f8b8a1

Hoyle, R. B. (1995) Steady squares and hexagons on a subcritical ramp. Physical Review E, 51 (1), 310-315. (doi:10.1103/PhysRevE.51.310).

Record type: Article

Abstract

Steady squares and hexagons on a subcritical ramp are studied, both analytically and numerically, within the framework of the lowest-order amplitude equations. On the subcritical ramp, the external stress or control parameter varies continuously in space from subcritical to supercritical values. At the subcritical end of the ramp, pattern formation is suppressed, and patterns fade away into the conduction solution. It is shown that three-dimensional patterns may change shape on a subcritical ramp. A square pattern becomes a pattern of rolls as it fades, with the roll axes aligned in the direction orthogonal to that in which the control parameter varies. Hexagons in systems with horizontal midplane symmetry become a pattern of rectangles before reaching the conduction solution. There is a suggestion that hexagons in systems which lack this symmetry might fade away through a roll pattern. Numerical simulations are used to illustrate these phenomena.

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Published date: 1995
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 380303
URI: https://eprints.soton.ac.uk/id/eprint/380303
ISSN: 1539-3755
PURE UUID: 09ec1623-ffb5-479c-90b9-00cff52fa65a
ORCID for R. B. Hoyle: ORCID iD orcid.org/0000-0002-1645-1071

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Date deposited: 12 Aug 2015 09:18
Last modified: 06 Jun 2018 12:33

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Author: R. B. Hoyle ORCID iD

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