Global bifurcation structure of a one-dimensional Ginzburg–Landau model

2005 ◽  
Vol 46 (9) ◽  
pp. 095111 ◽  
Author(s):  
Satoshi Kosugi ◽  
Yoshihisa Morita ◽  
Shoji Yotsutani
Keyword(s):  
Global Bifurcation ◽  
Bifurcation Structure ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional

scholarly journals On the global bifurcation diagram for the one-dimensional Ginzburg–Landau model of superconductivity

2000 ◽  
Vol 11 (3) ◽  
pp. 271-291 ◽  
Author(s):  
E. N. DANCER ◽  
S. P. HASTINGS
Keyword(s):  
Boundary Value Problem ◽  
Normal State ◽  
Linear Equations ◽  
Global Bifurcation ◽  
Local Bifurcation ◽  
Lagrange Equations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
The One

Some new global results are given about solutions to the boundary value problem for the Euler–Lagrange equations for the Ginzburg–Landau model of a one-dimensional superconductor. The main advance is a proof that in some parameter range there is a branch of asymmetric solutions connecting the branch of symmetric solutions to the normal state. Also, simplified proofs are presented for some local bifurcation results of Bolley and Helffer. These proofs require no detailed asymptotics for solution of the linear equations. Finally, an error in Odeh's work on this problem is discussed.

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

scholarly journals LORENTZ SPACE ESTIMATES FOR THE COULOMBIAN RENORMALIZED ENERGY

2012 ◽  
Vol 14 (04) ◽  
pp. 1250027 ◽  
Author(s):  
SYLVIA SERFATY ◽  
IAN TICE
Keyword(s):  
Lorentz Space ◽  
Vortex Lattice ◽  
Construction Method ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Optimal Estimates ◽  
Renormalized Energy ◽  
Funct Anal ◽  
Math Phys

In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier–Serfaty [From the Ginzburg–Landau model to vortex lattice problems, to appear in Comm. Math. Phys. (2012); One-dimensional log gases and the renormalized energy, in preparation]. To derive the estimates, we use a technique that we introduced in [Lorentz space estimates for the Ginzburg–Landau energy, J. Funct. Anal. 254(3) (2008) 773–825], which couples the "ball construction method" to estimates in the Lorentz space L2,∞.

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