Asymptotics of minimizers for the one-dimensional Ginzburg–Landau model of superconductivity

2001 ◽  
Vol 45 (3) ◽  
pp. 295-308 ◽  
Author(s):  
Wanghui Yu
Keyword(s):  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
The One

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 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.

Another look at recent results concerning bifurcation in one-dimensional models of superconductivity

2000 ◽  
Vol 11 (1) ◽  
pp. 121-128 ◽  
Author(s):  
S. P. HASTINGS
Keyword(s):  
Preceding Paper ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Dimensional Models ◽  
The One

In the preceding paper of this issue of EJAM, Bolley & Helffer [5] add to their extensive set of results on bifurcation in the one-dimensional Ginzburg–Landau model of superconductivity. One of their new results concerns the direction of bifurcation of symmetric solutions. We give another approach to this problem.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation

1992 ◽  
Vol 57 (3-4) ◽  
pp. 241-248 ◽  
Author(s):  
B.I. Shraiman ◽  
A. Pumir ◽  
W. van Saarloos ◽  
P.C. Hohenberg ◽  
H. Chaté ◽  
...  
Keyword(s):  
Landau Equation ◽  
Spatiotemporal Chaos ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

scholarly journals Studies of phase turbulence in the one-dimensional complex Ginzburg-Landau equation

1997 ◽  
Vol 55 (5) ◽  
pp. 5073-5081 ◽  
Author(s):  
Alessandro Torcini ◽  
Helge Frauenkron ◽  
Peter Grassberger
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

2007 ◽  
Vol 62 (7-8) ◽  
pp. 368-372
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Landau Equation ◽  
Model Parameters ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Paraxial Ray Approximation ◽  
New Family ◽  
Ginzburg Landau Equation ◽  
The Stability ◽  
The One ◽  
Paraxial Ray

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

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