Analytical solutions of the Ginzburg–Landau equations for deformable superconductors in a weak magnetic field

2010 ◽  
Vol 97 (16) ◽  
pp. 162505 ◽  
Author(s):  
Huadong Yong ◽  
Fangzhong Liu ◽  
Youhe Zhou
Keyword(s):  
Magnetic Field ◽  
Analytical Solutions ◽  
Weak Magnetic Field ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

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.

scholarly journals Released power in a vortex-antivortex pairs annihilation process

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Cristian Aguirre-Tellez ◽  
Miryam Rincón-Joya ◽  
José José Barba-Ortega
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Diffusion Equation ◽  
Power Dissipation ◽  
Time Dependent ◽  
Thermal Dissipation ◽  
Annihilation Process ◽  
Ginzburg Landau ◽  
Dissipation Process ◽  
Ginzburg Landau Equations

In this paper, we studied the power dissipation process of a Shubnikov vortex-antivortex pair in a mesoscopic superconducting square sample with a concentric square defect in presence of an oscillatory external magnetic field. The time-dependent Ginzburg-Landau equations and the diffusion equation were numerically solved. The significant result is that the thermal dissipation is associated with a sizeable relaxation of the superconducting electrons, so that the power released in this kind of process might become calculated as a function of the time. Also, we analyzed the effect that the Ginbzurg-Landau κand deformation τparameters have on the magnetization, dissipate power and super-electrons density.

Proximity effect enhancement induced by a superconducting anti-dot

2014 ◽  
Vol 28 (31) ◽  
pp. 1450242
Author(s):  
Sindy J. Higuera ◽  
Miryam R. Joya ◽  
J. Barba-Ortega
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Proximity Effect ◽  
Magnetization Curve ◽  
Order Parameter ◽  
Proximity Effects ◽  
Time Dependent ◽  
Critical Fields ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

In this work, we study the proximity and pinning effects of a rectangular superconducting anti-dot on the magnetization curve of a mesoscopic sample. We solve the nonlinear time-dependent Ginzburg–Landau equations for a superconducting rectangle in the presence of a magnetic field applied perpendicular to its surface. The pinning effects are determined by the number of vortices into the anti-dot. We calculate the order parameter, vorticity, magnetization and critical fields as a function of the external magnetic field. We found that the size and nature of the anti-dot strongly affect the magnetization of the sample. The results are discussed in framework of pinning and proximity effects in mesoscopic systems.

scholarly journals Dimer structure as topological pinning center in a superconducting sample

2020 ◽  
Vol 19 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Cristian A Aguirre ◽  
MiryamR. Joya ◽  
J. Barba-Ortega
Keyword(s):  
Magnetic Field ◽  
Pulsed Laser ◽  
Vortex State ◽  
Vortex Matter ◽  
Ginzburg Landau ◽  
Pinning Centers ◽  
Dimer Structure ◽  
Ginzburg Landau Equations ◽  
Superconducting Sample ◽  
Pinning Center

Solving the Ginzburg-Landau equations, we analyzed the vortex matter in a superconducting square with a Dimer structure of circular pinning centers generated by a pulsed heat source in presence of an applied magnetic field. We numerically solved the Ginzburg-Landau equations in order to describe the effect of the temperature of the circular defects on the Abrikosov state of the sample. The pulsed laser produced a variation of the temperature in each defect. It is shown that an anomalous vortex-anti-vortex state (A-aV) appears spontaneously at higher magnetic fields. This could be due to the breaking of the symmetry of the sample by the inclusion of the thermal defects

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.

Sign in / Sign up

Export Citation Format

Share Document