@MASTERSTHESIS\{IMM2005-06347,
    author       = "T. S. Alstr{\o}m",
    title        = "Type {II} superconductivity - studied by the Ginzburg-Landau equation",
    year         = "2005",
    school       = "",
    address      = "",
    type         = "",
    note         = "A journal paper based on this work has been published: http://www.imm.dtu.dk/pubdb/p.php?5949",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/6347-full.html",
    abstract     = "In this Master Thesis type I and {II} superconductors will be studied numerically. The numerical simulations are made using both the stationary and time–dependent Ginzburg–Landau equations. It turns out that it is hard to make simulations having more than one vortex using the stationary equations. This is due to the difficulty of providing an initial guess which is close enough to the solution. For this reason the time–dependent equations are used to create multi-vortex systems.

During the simulations made with the stationary equations, it becomes clear that the assumptions made to derive the London Penetration depth and Ginzburg–Landau coherence length are valid. It will be shown that the numerical simulations act as predicted.

In the time–dependent simulations, vortex dynamics are investigated. It will be seen how the vortices enter the superconductor, and how they approach the steady state solution. It also becomes clear that hysteresis exists in a superconductor. The equations are also solved for defect geometries, and in turns out that these defect has a large impact, on how the vortices enters the superconductor. Finally it will be suggested that based on the numerical solutions, the time–dependent equations converge towards solutions of the stationary Ginzburg–Landau equations."
}