Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superlattice Patterns in the Complex Ginzburg-Landau Equation with
  Multi-Resonant Forcing   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.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio