310 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
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
Nucleation of Spontaneous Vortices in Trapped Fermi Gases Undergoing a BCS-BEC Crossover
We study the spontaneous formation of vortices during the superfluid
condensation in a trapped fermionic gas subjected to a rapid thermal quench via
evaporative cooling. Our work is based on the numerical solution of the time
dependent crossover Ginzburg-Landau equation coupled to the heat diffusion
equation. We quantify the evolution of condensate density and vortex length as
a function of a crossover phase parameter from BCS to BEC. The more interesting
phenomena occur somewhat nearer to the BEC regime and should be experimentally
observable; during the propagation of the cold front, the increase in
condensate density leads to the formation of supercurrents towards the center
of the condensate as well as possible condensate volume oscillations.Comment: 5 pages, 3 figure
Structure formation in electromagnetically driven granular media
We report structure formation in submonolayers of magnetic microparticles
subjected to periodic electrostatic and magnetic excitations. Depending on the
excitation parameters, we observe the formation of a rich variety of
structures: clusters, rings, chains, and networks. The growth dynamics and
shapes of the structures are strongly dependent on the amplitude and frequency
of the external magnetic field. We find that for pure ac magnetic driving at
low densities of particles, the low-frequency magnetic excitation favors
clusters while high frequency excitation favors chains and net-like structures.
An abrupt phase transition from chains to a network phase was observed for a
high density of particles.Comment: 4 pages, 5 figure
Nucleation-induced transition to collective motion in active systems
While the existence of polar ordered states in active systems is well
established, the dynamics of the self-assembly processes are still elusive. We
study a lattice gas model of self-propelled elongated particles interacting
through excluded volume and alignment interactions, which shows a phase
transition from an isotropic to a polar ordered state. By analyzing the
ordering process we find that the transition is driven by the formation of a
critical nucleation cluster and a subsequent coarsening process. Moreover, the
time to establish a polar ordered state shows a power-law divergence
Spiral Motion in a Noisy Complex Ginzburg-Landau Equation
The response of spiral waves to external perturbations in a stable regime of
the two-dimensional complex Ginzburg-Landau equation (CGLE) is investigated. It
is shown that the spiral core has a finite mobility and performs Brownian
motion when driven by white noise. Combined with simulation results, this
suggests that defect-free and quasi-frozen states in the noiseless CGLE are
unstable against free vortex excitation at any non-zero noise strength.Comment: RevTex, 4 pages, 3 figures, submitted to Phys. Rev. Let
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