The Ginzburg–Landau equations for superconducting films and the Meissner effect

1990 ◽  
Vol 31 (5) ◽  
pp. 1284-1289 ◽  
Author(s):  
Yisong Yang
Keyword(s):  
Meissner Effect ◽  
Superconducting Films ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

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

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.

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.

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