Phys. Rev. E 75 (2007) 055203(R). doi:10.1103/PhysRevE.75.055203

Quasipatterns in parametrically forced systems

A.M.Rucklidge(1) and M. Silber(2).

(1) Department of Applied Mathematics,
University of Leeds, Leeds, LS2 9JT, UK

(2) Department of Engineering Sciences and Applied Mathematics,
Northwestern University, Evanston, IL 60208, USA

Abstract. We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency 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, 12-fold and 14-fold quasipatterns. The second mechanism, which requires more delicate tuning, can be used to select particular angles between wavevectors in the quasipattern.