Cross-Newell equations for hexagons and triangles
patt-sol
2009-10-31 v1 Pattern Formation and Solitons
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.
Keywords
Cite
@article{arxiv.patt-sol/9910004,
title = {Cross-Newell equations for hexagons and triangles},
author = {Rebecca B. Hoyle},
journal= {arXiv preprint arXiv:patt-sol/9910004},
year = {2009}
}
Comments
24 pages, 1 figure