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