560 research outputs found
Exact Phase Solutions of Nonlinear Oscillators on Two-dimensional Lattice
We present various exact solutions of a discrete complex Ginzburg-Landau
(CGL) equation on a plane lattice, which describe target patterns and spiral
patterns and derive their stability criteria. We also obtain similar solutions
to a system of van der Pol's oscillators.Comment: Latex 11 pages, 17 eps file
Model of coarsening and vortex formation in vibrated granular rods
Neicu and Kudrolli observed experimentally spontaneous formation of the
long-range orientational order and large-scale vortices in a system of vibrated
macroscopic rods. We propose a phenomenological theory of this phenomenon,
based on a coupled system of equations for local rods density and tilt. The
density evolution is described by modified Cahn-Hilliard equation, while the
tilt is described by the Ginzburg-Landau type equation. Our analysis shows
that, in accordance to the Cahn-Hilliard dynamics, the islands of the ordered
phase appear spontaneously and grow due to coarsening. The generic vortex
solutions of the Ginzburg-Landau equation for the tilt correspond to the
vortical motion of the rods around the cores which are located near the centers
of the islands.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let
Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''
We consider interaction of vortices in the vector complex Ginzburg--Landau
equation (CVGLE). In the limit of small field coupling, it is found
analytically that the interaction between well-separated defects in two
different fields is long-range, in contrast to interaction between defects in
the same field which falls off exponentially. In a certain region of parameters
of CVGLE, we find stable rotating bound states of two defects -- a ``vortex
molecule".Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let
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