Nucleation of superconductivity in decreasing fields. II

1994 ◽  
Vol 5 (4) ◽  
pp. 469-494 ◽  
Author(s):  
S. J. Chapman
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Nonlinear Stability ◽  
Bifurcation Point ◽  
Superconducting State ◽  
Landau Theory ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Stability Analyses

The bifurcation from a normally conducting to a superconducting state as an external magnetic field is lowered is examined using the Ginzburg–Landau theory. Linear and weakly nonlinear stability analyses are performed near the bifurcation point, and the implications of the results for each of three examples is considered.

Nucleation of superconductivity in decreasing fields. I

1994 ◽  
Vol 5 (4) ◽  
pp. 449-468 ◽  
Author(s):  
S. J. Chapman
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
External Magnetic Field ◽  
Superconducting State ◽  
Landau Theory ◽  
Ginzburg Landau ◽  
Systematic Perturbation

The bifurcation from a normally conducting to a superconducting state as an external magnetic field is lowered is examined using the Ginzburg-Landau theory. The results for three specific examples are reviewed, extended and unified in the framework of a systematic perturbation theory introduced in [1].

Dynamics of vortex–antivortex creation and annihilation in current-driven mesoscopic superconducting squares

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550247
Author(s):  
Xiao-Meng Liang ◽  
Guo-Qiao Zha
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Landau Theory ◽  
Symmetric Case ◽  
Time Dependent ◽  
Dynamical Process ◽  
Applied Bias ◽  
Ginzburg Landau ◽  
Dc Drive ◽  
Vortex Velocity

In this paper, based on the time-dependent Ginzburg–Landau theory, we study the dynamics of vortex–antivortex (V–Av) pairs in a mesoscopic superconducting square with a small hole under applied bias currents. For the sample with a centered hole, a V–Av pair can nucleate at the hole edges and moves in opposite directions perpendicular to applied constant DC drive. The influence of the external magnetic field on the (anti)vortex velocity and the lifetime of V–Av pairs is mainly investigated. Different modes in the dynamical process of the V–Av collision and annihilation are identified. Moreover, in the case when the hole is displaced from the center of the square, the V–Av dynamics behaves quite differently from the symmetric case due to the shift of the V–Av creation point.

Vortices of mesoscopic rings in an external magnetic field: Phenomenological Ginzburg-Landau theory

2009 ◽  
Vol 79 (18) ◽  
Author(s):  
Liang-Ma Shi ◽  
Ling-Feng Zhang ◽  
Hao Meng ◽  
Hong-Wei Zhao ◽  
Guo-Qiao Zha ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Landau Theory ◽  
Ginzburg Landau

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.

Hydromagnetic Stability of a Thin Viscoelastic Magnetic Fluid on Coating Flow Using Landau Equation

2016 ◽  
Vol 32 (5) ◽  
pp. 643-651 ◽  
Author(s):  
C.-K. Chen ◽  
M.-C. Lin
Keyword(s):  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Viscoelastic Parameter ◽  
Weakly Nonlinear ◽  
Linear Mode ◽  
Coating Flow ◽  
The One

AbstractThis paper investigates the weakly nonlinear stability of a thin axisymmetric viscoelastic fluid with hydromagnetic effects on coating flow. The governing equation is resolved using long-wave perturbation method as part of an initial value problem for spatial periodic surface waves with the Walter's liquid B type fluid. The most unstable linear mode of a film flow is determined by Ginzburg-Landau equation (GLE). The coefficients of the GLE are calculated numerically from the solution of the corresponding stability problem on coating flow. The effect of a viscoelastic fluid under an applied magnetic field on the nonlinear stability mechanism is studied in terms of the rotation number, Ro, viscoelastic parameter, k, and the Hartmann constant, m. Modeling results indicate that the Ro, k and m parameters strongly affect the film flow. Enhancing the magnetic effects is found to stabilize the film flow when the viscoelastic parameter destabilizes the one in a thin viscoelastic fluid.

Linear and Weakly Nonlinear Stability Analyses of Cooperative Car-Following Models

2014 ◽  
Vol 15 (5) ◽  
pp. 2001-2013 ◽  
Author(s):  
Julien Monteil ◽  
Romain Billot ◽  
Jacques Sau ◽  
Nour-Eddin El Faouzi
Keyword(s):  
Nonlinear Stability ◽  
Weakly Nonlinear ◽  
Car Following ◽  
Stability Analyses

Ginzburg–Landau Theory for Two-Band Isotropic s-Wave Superconductors

2003 ◽  
Vol 17 (16) ◽  
pp. 3001-3020 ◽  
Author(s):  
I. N. Askerzade
Keyword(s):  
Magnetic Field ◽  
Critical Field ◽  
Landau Theory ◽  
Upper Critical Field ◽  
Single Band ◽  
S Wave ◽  
Ginzburg Landau ◽  
Surface Magnetic Field ◽  
Specific Heat Jump ◽  
Gl Theory

Temperature dependence of the upper critical field Hc2(T), lower critical field Hc1(T) and thermodynamic magnetic field Hcm(T) are studied in the vicinity of Tc using a two-band Ginzburg–Landau (GL) theory. The results are shown to be in a good agreement with experimental data for the superconducting magnesium diboride (MgB2) and non-magnetic borocarbides LuNi 2 B 2 C ( YNi 2 B 2 C ). In addition, two-band GL theory was applied for the calculation of specific heat jump, which is smaller than in single-band GL theory. Peculiarities of Little–Parks effect in two-band GL theory are studied also. It is shown that the quantization of the magnetic flux and the relation between surface magnetic field Hc3(T) and upper critical field Hc2(T) are the same as in single band GL theory.

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