We present a method for numerically building a vortex knot state in the superfluid wave function of a Bose-Einstein condensate. We integrate in time the governing Gross-Pitaevskii equation to determine evolution and shape preservation of the two (topologically) simplest vortex knots which can be wrapped over a torus. We find that the velocity of a vortex knot depends on the ratio of poloidal an...

The vortex method is applied to the calculation of a decaying homogeneous isotropic turbulence of Reλ = 25, 50 and the results are compared with a spectral method calculation. Vortex method calculations were accelerated by the use of a fast multipole method for periodic boundary conditions. The core spreading method and particle strength exchange were selected as the viscous diffusion scheme. T...

Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-Babuška-Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interior penalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution...

We propose a method for the stabilization of a stack of parallel vortex rings in a Bose–Einstein condensate. The method makes use of a ‘hollow’ laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilize up to nine vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of...

Here the hollow vortex Gaussian beam is described by the exact solution of the Maxwell equations. By means of the method of the vectorial angular spectrum, analytical expressions of the electromagnetic fields of a hollow vortex Gaussian beam propagating in free space are derived. By using the electromagnetic fields of a hollow vortex Gaussian beam beyond the paraxial approximation, one can calc...

A grid free method for approximating incompressible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used w...

This paper presents an approach to classify static foreground blobs in surveillance scenarios. Possible application is the detection of abandoned and removed objects. In order to classify the blobs, we developed two novel features based on the assumption that the neighborhood of a removed object is fairly continuous. In other words, there is a continuity, in the input frame, ranging from inside...