The Meissner effect and the Ginzburg–Landau equations in the presence of an applied magnetic field

1997 ◽  
Vol 38 (6) ◽  
pp. 3046-3054 ◽  
Author(s):  
Masayoshi Tsutsumi ◽  
Hironori Kasai ◽  
Takeshi Ōishi
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Meissner Effect ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

scholarly journals Random distribution of topological defects in mesoscopic superconducting samples

Respuestas ◽  
2020 ◽  
Vol 25 (1) ◽  
pp. 178-183
Author(s):  
Oscar Silva-Mosquera ◽  
Omar Yamid Vargas-Ramirez ◽  
José José Barba-Ortega
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Random Distribution ◽  
Topological Defects ◽  
Ginzburg Landau ◽  
Field Function ◽  
Strong Anchor ◽  
Different Temperatures ◽  
Ginzburg Landau Equations ◽  
Superconducting Sample

In the present work we analyze the effect of topological defects at different temperatures in a mesoscopic superconducting sample in the presence of an applied magnetic field H. The time-dependent Ginzburg-Landau equations are solved with the method of link variables. We study the magnetization curves M(H), number of vortices N(H) and Gibbs G(H) free energy of the sample as a applied magnetic field function. We found that the random distribution of the anchor centers for the temperatures used does not cause strong anchor centers for the vortices, so the configuration of fluxoids in the material is symmetrical due to the well-known Beam-Livingston energy barrier.

scholarly journals Weakly Nonlinear Magnetic Convection in a Nonuniformly Rotating Electrically Conductive Medium Under the Action of Modulation of External Fields

2020 ◽  
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Landau Equation ◽  
Temperature Modulation ◽  
External Fields ◽  
Ginzburg Landau ◽  
Electrically Conductive ◽  
Weakly Nonlinear ◽  
Conductive Fluid ◽  
Ginzburg Landau Equations

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

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.

scholarly journals Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity

2005 ◽  
Vol 2005 (8) ◽  
pp. 863-887
Author(s):  
Fouzi Zaouch
Keyword(s):  
Magnetic Field ◽  
Existence And Uniqueness ◽  
Uniform Boundedness ◽  
Strong Solutions ◽  
Time Dependent ◽  
Dynamical Process ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Uniformly Bounded ◽  
Weak And Strong Solutions

The time-dependent Ginzburg-Landau equations of superconductivity with a time-dependent magnetic fieldHare discussed. We prove existence and uniqueness of weak and strong solutions withH1-initial data. The result is obtained under the “φ=−ω(∇⋅A)” gauge withω>0. These solutions generate a dynamical process and are uniformly bounded in time.

THE TOPOLOGICAL STRUCTURE OF SINGLE VORTEX IN THE FF STATE

2011 ◽  
Vol 25 (26) ◽  
pp. 2041-2051
Author(s):  
XINLE SHANG ◽  
PENGMING ZHANG ◽  
WEI ZUO
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Topological Structure ◽  
Single Vortex ◽  
Ginzburg Landau ◽  
The Core ◽  
The Magnetic Field

In this paper, we study the coexistence of the vortex and the FF state by using the generalized Ginzburg–Landau (GL) functional with the applied magnetic field, and obtain the numeric solutions. Furthermore, we investigate the topological structure of the vortex and find that the property of vortices relies heavily on the modulation q along z-axis. There is no topological vortex when q < qp, and the value [Formula: see text] is more favorable for the topological vortex. Moreover the magnetic field at the core of the vortex is obtained for the topological vortex.

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