Time dependent Ginzburg-Landau equations of superconductivity

In this paper, we study all the stationary solutions of the form u(r)einθ to the complex-valued Ginzburg–Landau equation on the complex plane: here (r, θ) are the polar coordinates, and n is any real number. In particular, we show that there exists a unique solution which approaches to a nonzero constant as r → ∞.

Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation

On an evolutionary system of ginzburg-landau equations with fixed total magnetic flux

It is proved that a two dimensional evolutionary Ginzburg-Landau superconductivity model is an approximation of a corresponding thin plate three dimensional superconductivity model when the thickness of the plate uniformly approaches zero. Some related topics such as existence of weak solutions to the three dimensional variable thickness model and the convergence when the variable thickness tends to zero are discussed. A numerical experiment using the now model is reported.

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Justification of a two dimensional evolutionary Ginzburg-Landau superconductivity model

We consider the Ginzburg–Landau model of superconductivity in two dimensions in the large $\kappa$ limit. For applied magnetic fields weaker than the onset field $H_{C_3}$ but greater than $H_{C_2}$ it is well known that the superconductivity order parameter decays exponentially fast away from the boundary. It has been conjectured by X. B. Pan that this surface superconductivity solution converges pointwise to a constant along the boundary. For applied fields that are in some sense between $H_{C_2}$ and $H_{C_3}$, we prove that the solution indeed converges to a constant but in a much weaker sense.

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The Distribution of Surface Superconductivity Along the Boundary: On a Conjecture of X. B. Pan

We consider the minimizers of the Gibbs free energy which couples a complex Ginzburg–Landau order parameter with a magnetic potential. It is established that the set on which the complex order parameter equals zero consists only of isolated points. Some estimates concerning the set on which the absolute value of the order parameter is small are also given. Numerical simulations are presented for the problem without a magnetic potential.

Tang Qi

Papers

Zeros of a complex Ginzburg–Landau order parameter with applications to superconductivity