2,676 research outputs found
Temporal Modulation of Traveling Waves in the Flow Between Rotating Cylinders With Broken Azimuthal Symmetry
The effect of temporal modulation on traveling waves in the flows in two
distinct systems of rotating cylinders, both with broken azimuthal symmetry,
has been investigated. It is shown that by modulating the control parameter at
twice the critical frequency one can excite phase-locked standing waves and
standing-wave-like states which are not allowed when the system is rotationally
symmetric. We also show how previous theoretical results can be extended to
handle patterns such as these, that are periodic in two spatial direction.Comment: 17 pages in LaTeX, 22 figures available as postscript files from
http://www.esam.nwu.edu/riecke/lit/lit.htm
Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere
We consider a small SO(2)-equivariant perturbation of a reaction-diffusion
system on the sphere, which is equivariant with respect to the group SO(3) of
all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a
rotating wave on the sphere that persists to a normally hyperbolic
SO(2)-invariant manifold . We investigate the effects of this
forced symmetry breaking by studying the perturbed dynamics induced on
by the above reaction-diffusion system. We prove that depending
on the frequency vectors of the rotating waves that form the relative
equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating
waves or SO(2)-orbits of modulated rotating waves (if some transversality
conditions hold). The orbital stability of these solutions is established as
well. Our main tools are the orbit space reduction, Poincare map and implicit
function theorem
Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field
Chirality is one of the most fundamental properties of many physical,
chemical and biological systems. However, the mechanisms underlying the onset
and control of chiral symmetry are largely understudied. We investigate
possibility of chirality control in a chemical excitable system (the BZ
reaction) by application of a chiral (rotating) electric field using the
Oregonator model. We find that unlike previous findings, we can achieve the
chirality control not only in the field rotation direction, but also opposite
to it, depending on the field rotation frequency. To unravel the mechanism, we
further develop a comprehensive theory of frequency synchronization based on
the response function approach. We find that this problem can be described by
the Adler equation and show phase-locking phenomena, known as the Arnold
tongue. Our theoretical predictions are in good quantitative agreement with the
numerical simulations and provide a solid basis for chirality control in
excitable media.Comment: 21 pages with 9 figures; update references; to appear in J. Chem.
Phy
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