927 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
Hole Solutions in the 1d Complex Ginzburg-Landau Equation
The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family
of traveling localized source solutions. These so called 'Nozaki-Bekki holes'
are (dynamically) stable in some parameter range, but always structually
unstable: A perturbation of the equation in general leads to a (positive or
negative) monotonic acceleration or an oscillation of the holes. This confirms
that the cubic CGLE has an inner symmetry. As a consequence small perturbations
change some of the qualitative dynamics of the cubic CGLE and enhance or
suppress spatio-temporal intermittency in some parameter range. An analytic
stability analysis of holes in the cubic CGLE and a semianalytical treatment of
the acceleration instability in the perturbed equation is performed by using
matching and perturbation methods. Furthermore we treat the asymptotic
hole-shock interaction. The results, which can be obtained fully analytically
in the nonlinear Schroedinger limit, are also used for the quantitative
description of modulated solutions made up of periodic arrangements of
traveling holes and shocks.Comment: 20 pages (RevTex) , 7 figures (postscript
Flagella bending affects macroscopic properties of bacterial suspensions
To survive in harsh conditions, motile bacteria swim in complex environment
and respond to the surrounding flow. Here we develop a PDE model describing how
the flagella bending affects macroscopic properties of bacterial suspensions.
First, we show how the flagella bending contributes to the decrease of the
effective viscosity observed in dilute suspension. Our results do not impose
tumbling (random re-orientation) as it was done previously to explain the
viscosity reduction. Second, we demonstrate a possibility of bacterium escape
from the wall entrapment due to the self-induced buckling of flagella. Our
results shed light on the role of flexible bacterial flagella in interactions
of bacteria with shear flow and walls or obstacles
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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