Numerical Simulation of Vortex Dynamics in Type-II Superconductors

A Hierarchy of Models for Type-II Superconductors

“…A similar asymptotic analysis can be carried out in the presence of a varying equilibrium density of superconducting electrons as in (39)- (40). In this case the London equation becomes…”

“…We note though the mathematical reviews of the model in [17,31,41], the pioneering work on the vortex state by Abrikosov [1], and the numerical simulations of [23,29,30,40,42].…”

Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d + s)-wave superconductors

“…16 The main idea behind this technique is to guarantee that the discretization of the TDGL equations preserves gauge invariance. 10,11 Otherwise, one may obtain undesirable non-physical solutions. Another advantage is that, by incorporating this field into the conventional TDGL equation for the order parameter, we obtain an equation which resembles a diffusion equation, the discretization of which has a very well defined stability criterion.…”

Effect of an columnar defect on vortex configuration in a superconducting mesoscopic sample

“…We used Uψ method [4] for solve the TDGL equations in a discrete grid. Complex link variables U x and U y are introduced to preserve the gauge-invariant properties of the discretized equations.…”

“…Several phenomenological theories have been developed during the decades of research in superconductivity. The London theory, the Ginzburg -Landau theory and its time dependent extension, known as Time Dependent Ginzburg -Landau (TDGL) theory have been widely used during the years of research into superconductivity [3,4]. In previous work, we have studied the properties of mesoscopic superconducting samples surrounded by different metallic materials using TDGL equations [9][10][11].…”