Phase instabilities in hexagonal patterns

Abstract

The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and the contributions of the new spatial terms are analysed in this paper. From these coefficients the phase stability regions in a hexagonal pattern are determined. In the case of Benard-Marangoni instability our results agree qualitatively with numerical simulations performed recently.

6 pages, 6 figures, to appear in Europhys. Lett

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• Instabilities of Hexagonal Patterns with Broken Chiral Symmetry
• Instabilities and Spatio-temporal Chaos of Long-wave Hexagon Patterns in Rotating Marangoni Convection
• Induced defect nucleation and side-band instabilities in hexagons with rotation and mean flow