Quasipatterns in parametrically forced systems

Abstract

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single and multi-frequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-frequency forcing, does not select a specific quasipattern: we find, for two different forcing strengths, a 12-fold quasipattern and the first known example of a spontaneously formed 14-fold quasipattern. The second mechanism, which requires more delicate tuning, can be used to select particular angles between wavevectors in the quasipattern.

4 pages, 3 figures, submitted to Phys. Rev. E. Full resolution version (including a movie) available on http://www.maths.leeds.ac.uk/~alastair/papers/RS_qp_pre_abs.html

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Cited by in corpus (4)

• On the existence of quasipattern solutions of the Swift-Hohenberg equation
• Existence of quasipatterns solutions of the Swift-Hohenberg equation
• Statistical mechanics characterization of spatio-compositional inhomogeneity
• Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing