Broken symmetries and pattern formation in two-frequency forced Faraday waves

Details Broken symmetries and pattern formation in two-frequency forced Faraday waves Broken symmetries and pattern formation in two-frequency forced Faraday waves

2002-03-05

arxiv.org/abs/nlin/0203004v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 6 figures

Scientific paper

10.1103/PhysRevLett.89.084501

We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the effects of time translation, time reversal and Hamiltonian structure for three illustrative examples: hexagons, two-mode superlattices, and two-mode rhomboids. By means of explicit parameter symmetries, we show how the size of various three-wave resonant interactions depends on the frequency ratio m:n and on the relative temporal phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.

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