Side-Band Instabilities and Defects of Quasi-Patterns
with Blas Echebarria
Physica D 158 (2001) 45
Quasipatterns have been found in dissipative systems
ranging from Faraday waves in vertically vibrated fluid
layers to nonlinear
optics. We describe the dynamics of
octagonal, decagonal and dodecagonal quasipatterns by means
of coupled Ginzburg-Landau equations and study their
stability to sideband perturbations analytically using long-wave
equations as well as by direct numerical simulation. Of particular interest
is the influence of the phason modes, which are associated
with the quasiperiodicity, on the stability of the patterns.
In the dodecagonal case, in contrast to the octagonal and the decagonal case,
the phase modes and the phason modes
decouple and there are parameter regimes in which the
quasipattern first becomes unstable with respect to phason
modes rather than phase modes. We also discuss the different
types of defects that can arise in each kind of quasipattern
as well as their dynamics and interactions. Particularly
interesting is the decagonal quasipattern, which allows two
different types of defects. Their mutual interaction can be
extremely weak even at small distances.
Movies:
Phason degree of freedom 1(1.7MB)
Phason degree of freedom 2(1.7MB)
Long-wave instability and formation of defects(800kB)
Defect in quasi-pattern(800kB)
Last modified: February 9, 2003
Hermann Riecke (h-riecke at northwestern.edu)
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