Non-conventional vortex configurations in a mesoscopic flat disk

The influence of superficial defects on the vortex configurations of a thin superconducting disk is investigated within the time dependent Ginzburg-Landau formalism. The free energy, magnetization, vorticity, and the Cooper pair density are calculated for both metastable and stable vortex configurations and different number of defects on its surface in the presence of an external magnetic field applied perpendicular to the disk area. We show that the competition between the confinement geometry and the geometric position of the defects leads to non-conventional vortex configurations which are not compatible with the symmetry of the sample geometry.

Critical currents and melting temperature of a two-dimensional vortex lattice with periodic pinning

The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two-dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength. © 2012 Springer Science+Business Media New York.

Surface effects on moving vortices in superconducting stripes

Size and surface dynamical effects are investigated in thin superconducting stripes with variable width. We perform numerical simulations of the vortex dynamics, with the inclusion of the surface confining potential and a random distribution of pinning centers. To fully characterize the vortex flow, we calculate the differential resistance, the transverse diffusion coefficient, the structure factor and the intensity of the Bragg peaks, as functions of the transport force. We found that surface effects induce a premature ordering of the flux line lattice, and the system displays plastic and smectic behavior only in a very narrow range of forces. (c) 2007 Elsevier B.V. All rights reserved.

Fourth-order method for solving the Navier-Stokes equations in a constricting channel

A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.

Anisotropy in the transport properties of type II superconducting films with periodic pinning

Using numerical simulations, we analyze the anisotropy effects in the critical currents and dynamical properties of vortices in a thin superconducting film submitted to hexagonal and Kagomé periodical pinning arrays. The calculations are performed at zero temperature, for transport currents parallel and perpendicular to the main axis of the lattice, and parallel to the diagonal axis of the rhombic unit cell. We show that the critical currents and dynamic properties are anisotropic for both pinning arrays and all directions of the transport current. The anisotropic effects are more significant just above the critical current and disappear with higher values of current and both pinning arrays. The dynamical phases for each case and a wide range of transport forces are analyzed. © 2012 Springer Science+Business Media, LLC.

Triangular arrangement of defects in a mesoscopic superconductor

By solving the time dependent Ginzburg-Landau equations, we investigated the influence of an internal triangular arrangement of point-like defects on the vortex configurations in a thin mesoscopic sample. The effect of the number of internal defects and their nature on the entrance position of the vortex is studied for a very thin circular sample. We found that the interplay between the vortex-vortex repulsion, the vortex-defect interaction and the interaction with the sample border leads to non-commensurate vortex configurations. © 2012 Elsevier B.V. All rights reserved.

The effects of pinning on critical currents of superconducting films

Using molecular dynamics simulations, we analyze the effects of artificial periodic arrays of pinning sites on the critical current of superconducting thin films as a function of vortex density. We analyze two types of periodic pinning array: hexagonal and Kagomé. For the Kagome pinning network we make calculations using two directions of transport current: along and perpendicular to the main axis of the lattice. Our results show that the hexagonal pinning array presents higher critical currents than the Kagomé and random pinning configuration for all vortex densities. In addition, the Kagomé networks show anisotropy in their transport properties. © 2012 Springer Science+Business Media, LLC.

Role of interstitial pinning in the dynamical phases of vortices in superconducting films

We analyze the vortex dynamics in superconducting thin films with a periodic array of pinning centers. In particular, we study the effect of anisotropy for a Kagomé pinning network when longitudinal and transverse transport currents are applied. By solving the equations of motion for the vortex array numerically at zero temperature, we find different phases for the vortex dynamics, depending on the pinning and driving force. An unusual sequence of peaks for driving force along and perpendicular to the main lattice axes is observed for the differential resistance, reflecting the anisotropy of the transport properties and the complex behavior of the vortex system. This behavior may be understood in terms of interstitial pinning vacancies, which create channels of vortices with different pinning strengths. © 2012 Springer Science+Business Media, LLC.

FLOW AROUND A SQUARE CYLINDER POSITIONED NEAR A SMOOTH FLAT PLATE

Vortex shedding phenomenon produced by a square cylinder placed close to a smooth flat plate is experimentally studied by means of flow visualization techniques and hot-film anemometry. Qualitative and quantitative information about the flow field has been obtained for Reynolds numbers up to 1,000. Vortex shedding images in several Reynolds number have been captured and the non dimensional vortex shedding frequency has been obtained as a function of the Reynolds number.