Uniqueness Theorem of the Regularizable Redial Ginzburg-Landau Type Minimizers

The author proves the uniqueness of the regularizable radial minimizers of a Ginzburg-Landau type functional in the case n - 1 < p < n,and the location of the zeros of the regularizable radial minimizers of this functional is discussed.     

Asymptotic behavior of 2D generalized stochastic Ginzburg-Landau equation with additive noise

The 2D generalized stochastic Ginzburg-Landau equation with additive noise is considered. The compactness of the random dynamical system is established with a priori estimate method, showing that the random dynamical system possesses a random attractor in H^1 0.     

Accurate Monte Carlo tests of the stochastic Ginzburg-Landau model with multiplicative colored noise

A accurate and fast Monte Carlo algorithm is proposed for solving the Ginzburg-Landau equation with multiplicative colored noise. The stable cases of solution for choosing time steps and trajectory numbers are discussed.     

非均匀外加磁场中二型超导体的能量估计

本文研究当κ很大时置于非均匀外加磁场中超导体的能量,其中外加磁场远离第一与第二临界磁场．我们得到了任意外加磁场中极小能量的渐进性态,从而解决了Sandier和Serfatv提出的猜想:极小能量与变磁场的权的形式成比例．     

含有杂质的Ginzburg-Landau泛函的径向极小元

研究了含有杂质的超导体的Ginzburg—Landau模型，给出了Ginzburg—Landau泛函的径向极小元的零点分布，并证明了径向极小元的惟一性。     

Frequency-dependent fluctuational conductivity above in anisotropic superconductors: effects of a short wavelength cutoff

We discuss the excess conductivity at nonzero frequencies in a superconductor above T_c within the Gaussian approximation. We focus the attention on the temperature range not too close to T_c: within a time-dependent Ginzburg-Landau formulation, we phenomenologically introduce a short wavelength cutoff (of the order of the inverse coherence length) in the fluctuational spectrum to suppress high momentum modes. We treat the general cases of thin wires, anisotropic thin films and anisotropic bulk samples. We obtain in all cases explicit expressions for the finite frequency fluctuational conductivity. The dc case directly follows. Close to T_c the cutoff has no effect, and the known results for Gaussian fluctuations are recovered. Above T_c, and already for ε = ln(T/T _c) > 10^-2, we find strong suppression of the paraconductivity as compared to the Gaussian prediction, in particular in the real part of the paraconductivity. At high ε the cutoff effects are dominant. We discuss our results in comparison with data on high-T_c superconductors. Received 19 March 2002 Published online 25 June 2002     

Vector potential gauge for superconducting regular polygons

An approach to the Ginzburg-Landau problem of superconducting polygons is developed, based on the exact fulfillment of superconducting boundary conditions along the boundary of the sample. To this end an analytical gauge transformation for the vector potential A is found which gives A _n = 0 for the normal component along the boundary line of an arbitrary regular polygon. The use of the new gauge reduces the Ginzburg-Landau problem of superconducting polygons in external magnetic fields to an eigenvalue problem in a basis set of functions obeying Neumann boundary conditions. The advantages of this approach, especially for low magnetic fields, are illustrated and novel vortex patterns are obtained which can be probed experimentally. Received 28 February 2002 and Received in final form 12 April 2002 Published online 6 June 2002     

二维广义Ginzburg-Landau方程在Banach空间的指数吸引子

本文应用能量积分和解析半群的有关估计,研究广义二维Ginzburg-Landau方程 在Banach空间LP(Ω)的子空间X-α的指数吸引子.     

Rotating superconductors: Ginzburg-Landau equations

Superconductors put into rotation develope a spontaneous internal magnetic field (the “London field”). In this paper Ginzburg Landau equations for order parameter, field, and current distributions for superconductors in rotation are derived. Two simple examples are discussed: the massive cylinder and the “Little and Parks geometry”: a thin film of superconducting material deposited on a cylinder of normal material. A dependence of T _c on rotational frequency is predicted. The magnitude of the effect is estimated and should be observable. Received 28 May 2001     

关于各向异性的Ginzburg-Landau 泛函极小元的上界估计

在H^1g(Ω)中讨论关于向各异性的Ginzburg-Landau泛函E（u,Ω）=1/2∫Ω[2∑i,j=1aij(x)uxi^-uxj 1/2ε^2b(x)(|u|^2-β^2(x))^2]dx的极小元uε的两个重要的上界估计，为研究uε在H^1g(Ω)中的收敛性及确定uε的奇点分布提供了重要的估计，利用拓扑度理论，通过一系列的变换及适当的比较函数，得到了能量估计，通过在有界光滑单连通区域Ω上的局部分析，得到了△↓uε的L ^∞模及D^2u的L^2模的上界，以及它们在边界上的模的上界，从而得到1/ε^2∫Ω(|u|^2-β^2(x))^2dx的上界估计，而另一个上界估计，则揭示了各向异性Ginzburg-Landau泛函极小元的基本性质。