Design of parametrically forced patterns and quasipatterns

摘要: The Faraday wave experiment is a classic example of system driven by parametric forcing, and it produces wide range complex patterns, including superlattice patterns quasipatterns. Nonlinear three-wave interactions between weakly damped modes play key role in determining which are favoured. We use this idea to design single multi-frequency forcing functions that produce examples quasipatterns new model PDE with forcing. make quantitative comparisons the predicted solutions PDE. Unexpectedly, agreement good only for parameter values very close onset. reason validity limited theory requires strong damping all apart from pattern-forming modes. This conflict requirement weak if coupling influence pattern selection effectively. distinguish two different ways can be used stabilise quasipatterns, present 12-, 14- 20-fold approximate identify computational domains provide most accurate approximations 12-fold systematically investigate Fourier spectra approximations.