Abstract
Based on a shooting alternative that allows one to numerically solve the one-dimensional system of Ginzburg–Landau in an unbounded domain, a numerical study of the stability of solutions of this system is performed here. This stability notion, from a physical point of view, means that each solution of the system is identified as stable when it minimizes the corresponding Ginzburg–Landau functional. As opposed to a previous paper, the present one is concerned with a more general study since the weak and large regimes of the Ginzburg–Landau parameter are considered and the initial data are no longer subject to the de Gennes condition. Certain conjectures regarding the superheating field are also investigated numerically.
Highlights
IntroductionThis framework requires the combination of a shooting approach (introduced rigorously in [17]) with a semi-implicit method (which is A−stable) for the numerical computation of solutions, as well as Hermite element approximations in the stage of the stability study
The Ginzburg-Landau theory allows one to describe the states of a superconducting material in an exterior magnetic field He
As opposed to [18], here we numerically study the stability of solutions of (1) - (2): in the weak and large−κ regimes, in the context where the pairs (f (0), h) are not subject to the de Gennes condition, and for f (0) ∈ (0, 1)
Summary
This framework requires the combination of a shooting approach (introduced rigorously in [17]) with a semi-implicit method (which is A−stable) for the numerical computation of solutions, as well as Hermite element approximations in the stage of the stability study The efficiency of this framework is distinguished by the fact that small values of the initial datum f0 = f (0) can be here considered, contrary with an approach using the method of matched asymptotic expansions as in [20], where the formal pair, from which the expansion of hsh(κ) is determined, cannot be an approximate solution of (1) - (3) for such an initial value.
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