Theoretical Model for Faraday Waves with Multiple-Frequency Forcing
arXiv:cond-mat/9704060 · doi:10.1103/PhysRevLett.79.1261
Abstract
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a fluid driven by a linear combination of two frequencies. The model exhibits steady-state solutions with two-, four-, six-, and twelve-fold symmetric patterns, similar to the periodic and quasiperiodic patterns observed in recent experiments.
4 pages, 2 figures. Final published version. Also available at http://www.cmp.caltech.edu/~lifshitz/patterns.html
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