Numerical simulations of the quantized vortices on a thin superconducting hollow sphere

In this paper, we investigate the vortex nucleation on a thin superconducting hollow sphere. The problem is studied using a simplified system of Ginzburg-Landau equations. We present numerical algorithms which preserve the discrete gauge invariance for both time dependent and time independent simulations. The spatial discretization is based on a spherical centroidal Voronoi tessellation which offers a very effective high resolution mesh on the sphere for the order parameter as well as other physically interesting variables such as the super-current and the induced magnetic field. Various vortex configurations and energy diagrams are computed. Dynamic responses of the vortices to the applied current are also simulated. (C) 2004 Elsevier Inc. All rights reserved.