相关论文: Numerical Study of Quantized Vortex Interaction in…
We consider the relative dynamics -- the dynamics modulo rotational symmetry in this particular context -- of $N$ vortices in confined Bose--Einstein Condensates (BEC) using a finite-dimensional vortex approximation to the two-dimensional…
We present the results of simulation of the chaotic dynamics of quantized vortices in the bulk of superfluid He II. Evolution of vortex lines is calculated on the base of the Biot-Savart law. The dissipative effects appeared from the…
Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant-Friedrichs-Lewy…
The classic Lorenz equations were originally derived from the two-dimensional Rayleigh-B\'enard convection system considering an idealised case with the lowest order of harmonics. Although the low-order Lorenz equations have traditionally…
Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the…
This work establishes the well-posedness and a priori error analysis for the mixed FEEC-type finite element approximation of the three-dimensional vector Laplace boundary value problem subject to the Dirichlet boundary condition. The…
We study the Ginzburg-Landau equations in order to describe a two-dimensional superconductor in a bounded domain. Using the properties of a particular integrability point ($\kappa = 1/ \sqrt2$) of these nonlinear equations which allows…
In this paper, the two-component Ginzburg-Landau (TCGL) model, which is an important research object in mathematics and physics of two scalar fields with $U(1)\times U(1)$ symmetry, is studied in detail by the shooting method and the fixed…
Using two innovations, smooth, but distinctly different, scaling laws for the numerical reconnection of pairs of initially orthogonal and anti-parallel quantum vortices are obtained using the three-dimensional Gross-Pitaevskii equations,…
The dynamic phase diagram of vortex lattices driven in disorder is calculated in two and three dimensions. A modified Lindemann criterion for the fluctuations of the distance of neighboring vortices is used, which unifies previous analytic…
We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by…
We consider the problem of dynamical stability for the $n$-vortex of the Ginzburg-Landau model. Vortices are one of the main examples of topological solitons, and their dynamic stability is the basic assumption of the asymptotic ``particle…
For each given $n\geq 2$, we construct a family of entire solutions $u_\varepsilon (z,t)$, $\varepsilon>0$, with helical symmetry to the 3-dimensional complex-valued Ginzburg-Landau equation \begin{equation*}\nonumber \Delta u+(1-|u|^2)u=0,…
The motion of a vortex-(anti)vortex pair is studied numerically in the framework of a dynamical Ginzburg-Landau model, relevant to the description of a superconductor or of an idealized bosonic plasma. It is shown that up to a fine…
We complete our study of the three dimensional Ginzburg--Landau functional with magnetic field, in the asymptotic regime of a small inverse Ginzburg--Landau parameter $\varepsilon$, and near the first critical field $H_{c_1}$ for which the…
We calculate the renormalized quartic vertex function of the Ginzburg-Landau model for a superconducting film in a magnetic field by summing an infinite subset of diagrams, the so-called parquet graphs. Using this non-perturbative solution,…
We study the properties of the Ginzburg-Laundau model in the self-dual point for a two-dimensional finite system . By a numerical calculation we analyze the solutions of the Euler-Lagrange equations for a cylindrically symmetric ansatz. We…
The interaction of trailing and leading vortex structures in low Reynolds number forced (varicose) jet with coflow is studied using Direct Numerical Simulation (DNS), where we report the dynamics of these vortices for a range of varying…
We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which contains initially many vortices at arbitrary locations. We present first the analytical solution of the dynamics in a homogeneous medium…
We derive an effective action for the vortex position degree-of-freedom in a superfluid by integrating out condensate phase and density fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected,…