scholarly journals Existence and non-existence of solutions to the Ginzburg-Landau equations in a semi-infinite superconducting film

2004 ◽  
Vol 63 (1) ◽  
pp. 1-12
Author(s):  
Y. Almog
Keyword(s):  
Existence Of Solutions ◽  
Superconducting Film ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

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.

RIGOROUS RESULTS FOR THE GINZBURG-LANDAU EQUATIONS ASSOCIATED TO A SUPERCONDUCTING FILM IN THE WEAK κ LIMIT

1996 ◽  
Vol 08 (01) ◽  
pp. 43-83 ◽  
Author(s):  
CATHERINE BOLLEY ◽  
BERNARD HELFFER
Keyword(s):  
Preceding Paper ◽  
Numerical Results ◽  
Principal Result ◽  
Superconducting Film ◽  
Rigorous Proof ◽  
Rigorous Results ◽  
Ginzburg Landau ◽  
Approximate Models ◽  
Ginzburg Landau Equations

In continuation with our preceding paper [10] concerning the superconducting film, we present in this article rigorous results concerning the superheating in the weak κ limit. The principal result is an important step toward the rigorous proof of a formula due to P. De Gennes [26] . This paper is complementary to our paper [11] where numerical results are presented and approximate models are discussed. Most of the results have been announced in [12] and [13].

Virial theorem and Abrikosov’s solution of the Ginzburg-Landau equations

1991 ◽  
Vol 44 (14) ◽  
pp. 7704-7707 ◽  
Author(s):  
U. Klein ◽  
B. Pöttinger
Keyword(s):  
Virial Theorem ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

Geometric effect on the vortex configuration and motion in mesoscopic superconducting cylinders

2015 ◽  
Vol 29 (03) ◽  
pp. 1550009 ◽  
Author(s):  
Shan-Shan Wang ◽  
Guo-Qiao Zha
Keyword(s):  
Phase Transitions ◽  
Vortex Dynamics ◽  
Axial Symmetry ◽  
Time Dependent ◽  
Vortex Matter ◽  
Ginzburg Landau ◽  
Geometric Effect ◽  
Multiply Connected ◽  
Vortex States ◽  
Ginzburg Landau Equations

Based on the time-dependent Ginzburg–Landau equations, we study numerically the vortex configuration and motion in mesoscopic superconducting cylinders. We find that the effects of the geometric symmetry of the system and the noncircular multiply-connected boundaries can significantly influence the steady vortex states and the vortex matter moving. For the square cylindrical loops, the vortices can enter the superconducting region in multiples of 2 and the vortex configuration exhibits the axial symmetry along the square diagonal. Moreover, the vortex dynamics behavior exhibits more complications due to the existed centered hole, which can lead to the vortex entering from different edges and exiting into the hole at the phase transitions.

scholarly journals ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

1980 ◽  
Vol 72 (3) ◽  
pp. 277-292 ◽  
Author(s):  
Clifford Henry Taubes
Keyword(s):  
Ginzburg Landau ◽  
First Order ◽  
Vortex Solutions ◽  
Ginzburg Landau Equations

In–Out Intermittency with Nested Subspaces in a System of Globally Coupled, Complex Ginzburg–Landau Equations

2021 ◽  
Vol 31 (01) ◽  
pp. 2130001
Author(s):  
Gerhard Dangelmayr ◽  
Iuliana Oprea
Keyword(s):  
Normal Form ◽  
Traveling Waves ◽  
Complex Dynamics ◽  
Invariant Subspaces ◽  
Chaotic Attractors ◽  
Governing Equations ◽  
Ginzburg Landau ◽  
Higher Dimensional ◽  
Ginzburg Landau Equations ◽  
Anisotropic Systems

Chaos and intermittency are studied for the system of globally coupled, complex Ginzburg–Landau equations governing the dynamics of extended, two-dimensional anisotropic systems near an oscillatory (Hopf) instability of a basic state with two pairs of counterpropagating, oblique traveling waves. Parameters are chosen such that the underlying normal form, which governs the dynamics of the spatially constant modes, has two symmetry-conjugated chaotic attractors. Two main states residing in nested invariant subspaces are identified, a state referred to as Spatial Intermittency ([Formula: see text]) and a state referred to as Spatial Persistence ([Formula: see text]). The [Formula: see text]-state consists of laminar phases where the dynamics is close to a normal form attractor, without spatial variation, and switching phases with spatiotemporal bursts during which the system switches from one normal form attractor to the conjugated normal form attractor. The [Formula: see text]-state also consists of two symmetry-conjugated states, with complex spatiotemporal dynamics, that reside in higher dimensional invariant subspaces whose intersection forms the 8D space of the spatially constant modes. We characterize the repeated appearance of these states as (generalized) in–out intermittency. The statistics of the lengths of the laminar phases is studied using an appropriate Poincaré map. Since the Ginzburg–Landau system studied in this paper can be derived from the governing equations for electroconvection in nematic liquid crystals, the occurrence of in–out intermittency may be of interest in understanding spatiotemporally complex dynamics in nematic electroconvection.

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