Phase instabilities in hexagonal patterns

Details Phase instabilities in hexagonal patterns Phase instabilities in hexagonal patterns

1998-05-26

arxiv.org/abs/patt-sol/9805007v1

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1209/epl/i1998-00315-2

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.

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