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 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.

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.

The Ginzburg–Landau equations in a semi-infinite superconducting film in the large κ limit

1997 ◽  
Vol 8 (4) ◽  
pp. 347-367 ◽  
Author(s):  
CATHERINE BOLLEY ◽  
BERNARD HELFFER
Keyword(s):  
A Priori ◽  
Stable Solution ◽  
Superconducting Films ◽  
Superconducting Film ◽  
Existence Of A Solution ◽  
Ginzburg Landau ◽  
Variational Techniques ◽  
Ginzburg Landau Equations ◽  
Formal Solutions ◽  
Subsolutions And Supersolutions

Following our preceding papers [1, 2] concerning semi-infinite superconducting films, we consider new a priori estimates on the exterior magnetic field h=A′(0), when (f, A) is a solution of the corresponding Ginzburg–Landau system. The main new results concern the limit as κ→∞, but we prove also the existence of a finite superheating field. We also discuss recent results [3] concerning the superheating field in the large κ limit, and show how to relate these formal solutions to suitable subsolutions and supersolutions giving the existence of a solution for h<1/√2 and κ large enough. We also analyse the same problem by variational techniques and get the existence of a locally stable solution for h<1/√2 and any κ>0.

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.

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