Temperature-dependent vortex matter in a superconducting mesoscopic circular sector

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Vortices in a mesoscopic superconducting circular sector

In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the magnetization, and the number of vortices. This algorithm is applied to a circular sector. We evaluate the superconduting-normal magnetic field transition, the magnetization, and the superconducting density. Our results point out that, as we reduce the superconducting area, the nucleation field increases. Nevertheless, as the angular width of the circular sector goes to small values the asymptotic behavior is independent of the sample area. We also show that the value of the first nucleation field is approximately the same independently of the form of the circular sector. Furthermore, we study the nucleation of giant and multivortex states for the different shapes of the present geometry.

Superconducting boundary conditions for mesoscopic circular samples

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

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.