We study discrete vortices in coupled discrete nonlinear Schrödinger equations. We focus on the vortex cross configuration that has been experimentally observed in pho-torefractive crystals. Stability of the single-component vortex cross in the anti-continuum limit of small coupling between lattice nodes is proved. In the vector case, we consider two coupled configurations of vortex crosses, na...

The semi-Lagrangian Vortex method (VM) and the Lattice Boltzmann (LBM) are used to investigate flows simulations in incompressible regime. In this study, a proven version of each is compared on different three dimensional benchmarks terms numerical accuracy, convergence, diffusion dissipation. first comparisons made convected vortex study compare dissipation LBM VM. Then Taylor–Green investigat...

For a model with isotropic nearest neighbor exchange combined with easy-plane exchange or single-ion anisotropies, the static effects of a magnetic vacancy site on a nearby magnetic vortex are analyzed on square, hexagonal and triangular lattices. Numerical energy minimization and linear stability analysis using the vortex instability mode are employed. When the vortex is centered on a vacancy,...

The distinguished work by A.A. Abrikosov awarded of the Nobel Prize in Physics for 2003 not only has determined the orientation of all investigations of the mixed state of type II superconductors during forty years but also has provoked a mass delusion. Most scientists consider the Abrikosov state first of all as a vortex lattice. But Abrikosov has found a periodic lattice structure with crysta...

We study the vortex state in a magnetic field parallel to the c axis in the framework of the extended Ginzburg Landau equation. We find the vortex acquires a fourfold modulation proportional to cos(4φ) where φ is the angle r makes with the a-axis. This term gives rise to an attractive interaction between two vortices when they are aligned parallel to (1, 1, 0) or (1,−1, 0). We predict the first...

We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the abelian-projected lattice has at most Z2, rather than U(1), global symmetry. We also find a severe breakdown of the monopole dominance approximation, as well as positiv...

BACKGROUND Systolic blood flow has been simulated in the abdominal aorta and the superior mesenteric artery. The simulations were carried out using two different computational hemodynamic methods: the finite element method to solve the Navier Stokes equations and the lattice Boltzmann method. RESULTS We have validated the lattice Boltzmann method for systolic flows by comparing the velocity a...

We present a framework for studying vortex lattice patterns and their structural transitions, using the Parrinello–Rahman (PR) method for molecular-dynamics (MD) simulations. Assuming an interaction between vortices derived from a Ginzburg–Landau field-theoretic context, we extract the ground-state of a “vortex gas” using the PR-MD technique and find it to be a triangular pattern. Other pattern...

We show that a Bose-Einstein condensate with a vortex lattice in a rotating anisotropic harmonic potential exhibits a very low frequency scissors mode. The appearance of this mode is due to the SO 2 symmetry breaking introduced by the vortex lattice. The corresponding Goldstone mode in an isotropic trap becomes, in an anisotropic trap, a scissors mode, whose frequency is finite and tends to zer...

We examine the manner in which a linear potential results from fluctuations due to vortices linked with the Wilson loop. Our discussion is based on exact relations and inequalities between the Wilson loop and the vortex and electric flux order parameters. We show that, contrary to the customary naive picture, only vortex fluctuations of thickness of the order of the spatial linear size of the l...