Solution Existence for the Complex One-Dimensional Ginzburg-Landau Equations of Superconductivity

2019 ◽  
Author(s):  
El Azzouzi Fatima ◽  
El Khomssi Mohammed
Keyword(s):  
Solution Existence ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equations

scholarly journals Simplified models of superconducting-normal-superconducting junctions and their numerical approximations

1999 ◽  
Vol 10 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Q. DU ◽  
J. REMSKI
Keyword(s):  
Thin Layer ◽  
Order Of Convergence ◽  
Numerical Results ◽  
Numerical Approximations ◽  
Simplified Models ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Superconducting Material ◽  
Superconducting Junction ◽  
Ginzburg Landau Equations

When a thin layer of normal (non-superconducting) material is placed between layers of superconducting material, a superconducting-normal-superconducting junction is formed. This paper considers a model for the junction based on the Ginzburg–Landau equations as the thickness of the normal layer tends to zero. The model is first derived formally by averaging the unknown variables in the normal layer. Rigorous convergence is then established, as well as an estimate for the order of convergence. Numerical results are shown for one-dimensional junctions.

One-Dimensional Solutions of the Ginzburg-Landau Equations for Thin Superconducting Films

1966 ◽  
Vol 145 (1) ◽  
pp. 231-236 ◽  
Author(s):  
V. D. Arp ◽  
R. S. Collier ◽  
R. A. Kamper ◽  
H. Meissner
Keyword(s):  
Superconducting Films ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equations ◽  
Thin Superconducting Films

scholarly journals ON THE SYMMETRY AND UNIQUENESS OF SOLUTIONS OF THE GINZBURG–LANDAU EQUATIONS FOR SMALL DOMAINS

2001 ◽  
Vol 03 (01) ◽  
pp. 1-14 ◽  
Author(s):  
A. AFTALION ◽  
E. N. DANCER
Keyword(s):  
Order Parameter ◽  
A Priori Estimates ◽  
A Priori ◽  
Small Radius ◽  
Uniqueness Of Solutions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Priori Estimates ◽  
Ginzburg Landau Equations ◽  
Dimensional Domain

In this paper, we study the Ginzburg–Landau equations for a two dimensional domain which has small size. We prove that if the domain is small, then the solution has no zero, that is no vortex. More precisely, we show that the order parameter Ψ is almost constant. Additionnally, we obtain that if the domain is a disc of small radius, then any non normal solution is symmetric and unique. Then, in the case of a slab, that is a one dimensional domain, we use the same method to derive that solutions are symmetric. The proofs use a priori estimates and the Poincaré inequality.

scholarly journals ANOMALOUS SYNCHRONIZATION OF SPATIALLY EXTENDED CHAOTIC SYSTEMS IN THE PRESENCE OF ASYMMETRIC COUPLING

2005 ◽  
Vol 05 (02) ◽  
pp. L251-L258
Author(s):  
S. BOCCALETTI ◽  
C. MENDOZA ◽  
J. BRAGARD
Keyword(s):  
Chaotic Systems ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Turbulence Regime ◽  
Asymmetric Coupling ◽  
Spatially Extended ◽  
Ginzburg Landau Equations ◽  
Phase Singularities ◽  
Coupling Strengths ◽  
Spatially Extended Systems

This paper describes the effects of an asymmetric coupling in the synchronization of two spatially extended systems. Namely, we report the consequences induced by the presence of asymmetries in the coupling configuration of a pair of one-dimensional fields obeying Complex Ginzburg–Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of enhancing synchronization and play a crucial role in setting the threshold for the appearance of the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion. We discuss the process of synchronization in the presence of asymmetries by using some analytic expansions valid for a regime of soft spatial temporal chaos (i.e. phase turbulence regime). The influence of phase singularities that break the validity of the analysis is also discussed.

Asymptotic analysis of the bifurcation diagram for symmetric one-dimensional solutions of the Ginzburg–Landau equations

1999 ◽  
Vol 10 (5) ◽  
pp. 477-495 ◽  
Author(s):  
A. AFTALION ◽  
S. J. CHAPMAN
Keyword(s):  
Asymptotic Analysis ◽  
Bifurcation Diagram ◽  
Triple Point ◽  
Normal Solution ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Landau Parameter ◽  
Formal Asymptotics ◽  
Ginzburg Landau Equations ◽  
The One

The bifurcation of symmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg–Landau equations by the methods of formal asymptotics. The behaviour of the bifurcating branch depends upon the parameters d, the size of the superconducting slab, and κ, the Ginzburg–Landau parameter. It was found numerically by Aftalion & Troy [1] that there are three distinct regions of the (κ, d) plane, labelled S1, S2 and S3, in which there are at most one, two and three symmetric solutions of the Ginzburg–Landau system, respectively. The curve in the (κ, d) plane across which the bifurcation switches from being subcritical to supercritical is identified, which is the boundary between S2 and S1∪S3, and the bifurcation diagram is analysed in its vicinity. The triple point, corresponding to the point at which S1, S2 and S3 meet, is determined, and the bifurcation diagram and the boundaries of S1, S2 and S3 are analysed in its vicinity. The results provide formal evidence for the resolution of some of the conjectures of Aftalion & Troy [1].

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