Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

Details Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

2008-03-03

arxiv.org/abs/0803.0346v1

Nonlinear Sciences

Pattern Formation and Solitons

22 pages, 18 figures (38 total plots and pictures). For associated .mov files, see http://www.esam.northwestern.edu/~riecke/

Scientific paper

Motivated by the rich variety of complex patterns observed on the surface of fluid layers that are vibrated at multiple frequencies, we investigate the effect of such resonant forcing on systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. We use an extension of the complex Ginzburg-Landau equation that systematically captures weak forcing functions with a spectrum consisting of frequencies close to the 1:1-, the 1:2-, and the 1:3-resonance. By slowly modulating the amplitude of the 1:2-forcing component we render the bifurcation to subharmonic patterns supercritical despite the quadratic interaction introduced by the 1:3-forcing. Our weakly nonlinear analysis shows that quite generally the forcing function can be tuned such that resonant triad interactions with weakly damped modes stabilize subharmonic patterns comprised of four or five Fourier modes, which are similar to quasi-patterns with 4-fold and 5-fold rotational symmetry, respectively. Using direct simulations of the extended complex Ginzburg-Landau equation we confirm our weakly nonlinear analysis. In simulations domains of different complex patterns compete with each other on a slow time scale. As expected from energy arguments, with increasing strength of the triad interaction the more complex patterns eventually win out against the simpler patterns. We characterize these ordering dynamics using the spectral entropy of the patterns. For system parameters reported for experiments on the oscillatory Belousov-Zhabotinsky reaction we explicitly show that the forcing parameters can be tuned such that 4-mode patterns are the preferred patterns.

Affiliated with

Also associated with

No associations

Rating

Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-405602