Related papers: Vortex Velocity Pair Correlations
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry.…
The motion of a pair of counter-rotating point vortices placed in a uniform flow around a circular cylinder forms a rich nonlinear system that is often used to model vortex shedding. The phase portrait of the Hamiltonian governing the…
The vortex-vortex and vortex-antivortex correlation functions are determined for the two-dimensional O(2) model undergoing phase ordering. We find reasonably good agreement with simulation results for the vortex-vortex correlation function…
Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled…
Vortex motion in type II superconductors is studied starting from a variant of the time dependent Ginzburg-Landau equations, in which the order parameter relaxation time is taken to be complex. Using a method due to Gor'kov and Kopnin, we…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having the Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to…
Neutron $^3P_2$ superfluids consisting of neutron pairs with the total angular momentum $J=2$ with spin-triplet and $P$-wave are believed to be realized in neutron star cores. Within the Ginzburg-Landau theory it was previously found that a…
The dynamics of a large point vortex system whose initial configuration consists in uniformly distributed independent positions is investigated. Time correlations of local observables of the vortex configuration are shown to be compatible…
A micromagnetic numerical study of the precessional motion of the vortex and antivortex states in soft ferromagnetic circular nanodots is presented using Landau-Lifshitz-Gilbert dynamics. For sufficiently small dot thickness and diameter,…
The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a…
The nature of vortex flows in the nonequilibrium region arising in the vicinity of phase-slip lines at the S-N boundary are investigated experimentally. It is shown that vortices continue to move when charge imbalance appears in a film that…
We study the Lagrangian dynamics of systems of N point vortices and passive particles in a two-dimensional, doubly periodic domain. The probability distribution function of vortex velocity, p_N, has a slow-velocity Gaussian component and a…
We study the structure of vortex solutions in a Ginzburg-Landau system for two complex valued order parameters. We consider the Dirichlet problem in the disk in R^2 with symmetric, degree-one boundary condition, as well as the associated…
Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially…
We consider the mixed Ginzburg-Landau flow that is supplemented with convective derivatives of the unknown function. We show that the associated vortex motion law is the mixed flow of the renormalized energy with new nonlinear forcing…
In this note, a brief introduction to the physical and mathematical background of the two-component Ginzburg-Landau theory is given. From this theory we derive a boundary value problem whose solution can be obtained in part by solving a…
It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff--Routh point vortex system. In this paper,…