Layer solutions for a one-dimensional nonlocal model of Ginzburg–Landau type

2017 ◽  
Vol 12 (6) ◽  
pp. 68-90 ◽  
Author(s):  
K.-S. Chen ◽  
C.B. Muratov ◽  
X. Yan
Keyword(s):  
Nonlocal Model ◽  
Ginzburg Landau ◽  
One Dimensional

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.

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.

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

Amplitude wave in one-dimensional complex Ginzburg—Landau equation

2011 ◽  
Vol 20 (11) ◽  
pp. 110503 ◽  
Author(s):  
Ling-Ling Xie ◽  
Jia-Zhen Gao ◽  
Wei-Miao Xie ◽  
Ji-Hua Gao
Keyword(s):  
Landau Equation ◽  
Amplitude Wave ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation

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 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
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