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arXiv · patt-sol/9910004

Cross-Newell equations for hexagons and triangles

Rebecca B. Hoyle
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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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BibTeXRIS

Rebecca B. Hoyle. 1999-10-16. Cross-Newell equations for hexagons and triangles. https://doi.org/10.1103/physreve.61.2506

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