ON THE HESSIAN OF THE ENERGY FORM IN THE GINZBURG–LANDAU MODEL OF SUPERCONDUCTIVITY

2004 ◽  
Vol 16 (04) ◽  
pp. 421-450 ◽  
Author(s):  
MYRIAM COMTE ◽  
MYRTO SAUVAGEOT
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Radial Solutions ◽  
Ginzburg Landau ◽  
Landau Model ◽  
The Stability

The purpose of this work is to study the stability of radial solutions of degree d for the Ginzburg–Landau model of superconductivity with an applied magnetic field in a disk of radius [Formula: see text]. We consider the branch of solutions introduced in [24] as a branch with the radius of the ball as parameter. We prove that for small radii the branch is stable while it is unstable for large radii, see [6]. We then study in detail the Hessian of the energy at the symmetric vortex at the stability transition. Finally under a couple of extra assumptions, we construct a branch of solutions bifurcating from the radial one at this point, and describe it.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

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 Effect of Background Magnetic Field on Type-II Superconductor under Oscillating Magnetic Field Simulated Using Ginzburg-Landau Model

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Hasnain Mehdi Jafri ◽  
Congpeng Zhao ◽  
Houbing Huang ◽  
Xingqiao Ma
Keyword(s):  
Magnetic Field ◽  
Carrier Concentration ◽  
Static Magnetic Field ◽  
Thermal Quenching ◽  
Phase Changes ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Background Magnetic Field ◽  
Oscillating Magnetic Field ◽  
Energy Components

Cubic superconducting sample was simulated using time-dependent Ginzburg-Landau model under oscillating magnetic field with and without additional background static magnetic field. Vortex dynamics including entrance and exit from the sample was simulated. Magnetization and carrier concentration densities of the sample were studied as a function of external magnetic field variations. Anomalies in carrier concentration density were observed at certain values of the magnetic field which were correlated with the entrance and exit processes of vortices. Area swept by superconductor magnetization with magnetic field was observed to have a hysteresis-like behavior where area representing energy dissipated per cycle. This energy accumulation was suggested to cause instability in superconductor over the number of cycles and may result in thermal quenching. Temporal distribution of energy components showed consistency with the pattern observed for carrier concentration and magnetization under oscillating magnetic field. Rapid phase changes with magnetic oscillations resulted in oscillations in energy components, and irregular peaks and ripples in superconducting energy represent the situation of exit and entry of vortices. While the rise in interaction energy with cycles is referred to vortex relaxation time in a cycle, this energy is expected to accumulate and take other forms (e.g., heat) and is predicted to cause thermal quenching. In the presence of background static magnetic field, this energy dissipation was calculated to increase significantly while superconductor is subjected to oscillating magnetic field.

Superconductors With Structured Surfaces: Fields and Currents

1987 ◽  
Vol 101 ◽  
Author(s):  
Z.C. Wu ◽  
Daniel A. Jelski ◽  
Thomas F. George
Keyword(s):  
Magnetic Field ◽  
The Other ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Structured Surfaces ◽  
Field Parallel ◽  
First Case ◽  
The Magnetic Field ◽  
Effect Of Structure ◽  
Effect Of Surface

ABSTRACTThis paper discusses the behavior of currents and fields along a structured superconductor. First the effect of surface structure on supercurrents is investigated. Then the effect of structure on the critical nucleation field is discussed in two cases, one with the magnetic field parallel to the ripples and the other with the field parallel to the grating wavenumber. In the first case, it is found that the critical field is reduced as a function of grating height, whereas in the latter case it is increased. Finally, the relevance of this work for laser-induced chemistry above a superconducting surface is discussed. The Ginzburg-Landau model is used throughout.

ON THE CONTINUITY OF THE RESPONSE MAP AND AN ALTERNATIVE SHOOTING METHOD FOR THE HALF-SPACE GINZBURG–LANDAU MODEL

2006 ◽  
Vol 16 (09) ◽  
pp. 1527-1558
Author(s):  
CATHERINE BOLLEY ◽  
BERNARD HELFFER
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Shooting Method ◽  
The Other ◽  
Complete Analysis ◽  
Qualitative Properties ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Ginzburg Landau Equations ◽  
Physical Literature

As a consequence of a rather complete analysis of the qualitative properties of the solutions of the Ginzburg–Landau equations, we prove, in this paper, both the continuity of a fundamental map σ, called response map in the physical literature on superconductors, and the convergence of an efficient algorithm for the computation of the graph of σ. The response map σ gives the intensity h of the external magnetic field for which the Ginzburg–Landau equations (in a half-space) have a solution such that the parameter order has a prescribed value at the boundary of the sample. Our study involves a shooting method on either one or the other unknown of the system; our algorithm has been introduced in Bolley–Helffer for small values of the Ginzburg–Landau parameter κ and extended in Bolley to any value of κ. Our preceding mathematical studies were not sufficient to prove the convergence, but a recent result (in Ref. 3) on the monotonicity of the solutions with respect to h, combined with a more extensive use of the properties of the solutions of the Ginzburg–Landau system, allow us to complete the proof and to get, as a by-product, the continuity of σ.

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