Global Jacobian and Γ-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices

In the theory of 2D Ginzburg-Landau vortices, the Jacobian plays a crucial role for the detection of topological singularities. We introduce a related distributional quantity, called the global Jacobian that can detect both interior and boundary vortices for a 2D map u. We point out several features of the global Jacobian, in particular, we prove an important stability property. This property allows us to study boundary vortices in a 2D Ginzburg-Landau model arising in thin ferromagnetic films, where a weak anchoring boundary energy penalising the normal component of u at the boundary competes with the usual bulk potential energy. We prove an asymptotic expansion by Γ-convergence at the second order for this mixed boundary/interior energy in a regime where boundary vortices are preferred. More precisely, at the first order of the limiting expansion, the energy is quantised and determined by the number of boundary vortices detected by the global Jacobian, while the second order term in the limiting energy expansion accounts for the interaction between the boundary vortices.     

2+1维Ginzburg-Landau方程的精确波解

分析研究了一个具有三次增益效应和五次耗散项的2+1维Ginzburg-Landau方程.利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解.     

On the Cauchy Problem of the Ginzburg-Landau Equations for Atomic Fermi Gases Near the BCS-BEC Crossover

In this paper we investigate time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the Fermion-Boson model. We obtain the global the equations in various spatial dimensions. existence and uniqueness of solution to     

超导材料NbS2上临界磁场的理论分析

根据两带Ginzburg-Landau 理论计算了层状超导材料NbS₂的上临界磁场, 以及上临界磁场各向异性参数随温度的变化情况, 并将NbS₂与MgB₂, NbSe₂上临界磁场的各向异性进行比较. 所得计算结果与已有实验数据符合得很好, 充分说明了NbS₂的超导电性具有两能隙特征. NbS₂上临界磁场各向异性参数在5.0 K附近逐渐变小, 这与MgB₂和NbSe₂有相似之处. 但NbS₂的上临界磁场各向异性参数大约为7.3, 明显大于MgB₂和NbSe₂. 计算结果还表明, NbS₂较大能隙所对应能带的有效质量比约为54, 另一能带的有效质量基本为各向同性.     

光纤放大器中的自相似抛物脉冲

本文研究在含有增益色散、增益饱和、三阶色散、自频移、自陡峭等效应的光纤放大器中自相似抛物脉冲的产生和传输。结果表明,在渐近约束条件下,自相似脉冲的中心区域可用倒置的抛物脉冲来描绘,并且它的有效脉宽和功率都是线性增长的,而峰值振幅和频谱宽度保持常量。数值模拟结果与理论预期符合的非常好,这表明:在光纤放大器中,在适当的条件下初始输入脉冲可自相似地演化为抛物脉冲。     

Dynamics of Stochastic Ginzburg-Landau Equations Driven by Colored Noise on Thin Domains

This work is concerned with the asymptotic behaviors of solutions to a class of non-autonomous stochastic Ginzburg-Landau equations driven by colored noise and deterministic non-autonomous terms defined on thin domains. The existence and uniqueness of tempered pullback random attractors are proved for the stochastic Ginzburg-Landau systems defined on $(n+1)$-dimensional narrow domain. Furthermore, the upper semicontinuity of these attractors is established, when a family of $(n+1)$-dimensional thin domains collapses onto an $n$-dimensional domain.