Modeling and Computation of Random Thermal Fluctuations and Material Defects in the Ginzburg–Landau Model for Superconductivity

Abstract

It is well known that thermal fluctuations and material impurities affect the motion of vortices in superconductors. These effects are modeled by variants of a time-dependent Ginzburg-Landau model containing either additive or multiplicative noise. Numerical computations are presented that illustrate the effects that noise has on the dynamics of vortex nucleation and vortex motion. For an additive noise model with relatively low variances, it is found that the vortices form a quasi-steadystate lattice in which the vortex core sizes remain roughly fixed but their positions vibrate. Two multiplicative noise models are considered. For one model having relatively long-range order, the sizes of the vortex cores vary in time and from one vortex to another. Finally, for the additive noise case, we show that as the variance of the noise tends to zero, solutions of the stochastic time-dependent GinzburgLandau equations converge to solutions of the corresponding equations with no noise. c 2002 Elsevier Science (USA)

Vortices in a stochastic parabolic Ginzburg-Landau equation

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On the Method of Construction of the Dependence of the Heat Extension Coefficient on Temperature in Heat-resistant Alloys

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Milstein-type semi-implicit split-step numerical methods for nonlinear stochastic differential equations with locally Lipschitz drift terms

“…al. [1] and the references there. When the coefficients of a non-linear homogeneous SDE of the form ( )…”