Phys. Rev. E 75 (2007) 055203(R).
Quasipatterns in parametrically forced systems
(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
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.
pdf version of this paper (0.4MB)
animated gif movie of the
transition from 12-fold to 14-fold quasipatterns (19MB)