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Cross-Newell equations for hexagons and triangles

Cross-Newell equations for hexagons and triangles
Cross-Newell equations for hexagons and triangles
The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in flux-divergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case is also discussed; in contrast with the gradient case, the equations are not flux divergent. In all cases, the phase stability boundaries and modes of instability for general distorted hexagons and triangles can be recovered from the Cross-Newell equations
1539-3755
2506-2512
Hoyle, Rebecca B.
e980d6a8-b750-491b-be13-84d695f8b8a1
Hoyle, Rebecca B.
e980d6a8-b750-491b-be13-84d695f8b8a1

Hoyle, Rebecca B. (2000) Cross-Newell equations for hexagons and triangles. Physical Review E, 61 (3), 2506-2512. (doi:10.1103/PhysRevE.61.2506).

Record type: Article

Abstract

The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in flux-divergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case is also discussed; in contrast with the gradient case, the equations are not flux divergent. In all cases, the phase stability boundaries and modes of instability for general distorted hexagons and triangles can be recovered from the Cross-Newell equations

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PhysRevE.61.2506 - Version of Record
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Published date: 1 March 2000
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 380245
URI: http://eprints.soton.ac.uk/id/eprint/380245
ISSN: 1539-3755
PURE UUID: 06eb8e8f-1c26-4b54-a171-5b759475615c
ORCID for Rebecca B. Hoyle: ORCID iD orcid.org/0000-0002-1645-1071

Catalogue record

Date deposited: 10 Aug 2015 13:56
Last modified: 20 Jul 2019 00:46

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