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
2506-2512
Hoyle, Rebecca B.
e980d6a8-b750-491b-be13-84d695f8b8a1
1 March 2000
Hoyle, Rebecca B.
e980d6a8-b750-491b-be13-84d695f8b8a1
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
Text
PhysRevE.61.2506
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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
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Date deposited: 10 Aug 2015 13:56
Last modified: 15 Mar 2024 03:36
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