振荡介质中平面波的反射

在复金慈堡-朗道方程描述的振荡介质中研究了平面波的反射.从理论上给出了产生反射的条件,导出了反射波和入射波这两个区域的分界线与两种介质分界线的夹角.发现两类反射,一类为回折射产生的反射,对于这类反射,理论上给出了反射角;另一类为纯反射,它与折射无关.理论分析与数值模拟结果均表明：只有当入射角大于临界入射角才会发生反射,而且反射角等于临界入射角;对于纯反射,反射角随波频率增大而增大. 关键词： 复金慈堡-朗道方程 平面波 反射     

单畴外延铁电薄膜的相结构与稳定性

本文采用动态金茨堡-朗道（DGL）方程研究了薄膜厚度与错配应变对 取向单畴外延PbTiO3（PTO）铁电薄膜相结构与稳定性的影响。结合平面内松弛应变（等效应变）、表面效应与退极化场等机电耦合边界条件,通过数值求解DGL方程获得外延单畴铁电薄膜错配应变-厚度相图和错配应变-温度相图。数值分析结果显示,由于生成的界面位错松弛了薄膜内错配应变,在理论高应变区相图与传统分析结果有较大差别,文中发现在更广的理论错配拉应变区出现稳定的四方相（c相）结构和单斜相（r相）结构。结果也显示,随着薄膜厚度的减小,表面效应与退极化效应会把顺电相扩展到更低温度区域,从而压缩稳定的铁电相存在的温度区域。     

Nonlinear density wave and energy consumption investigation of traffic flow on a curved road

A new car-following model is proposed based on the full velocity difference model(FVDM) taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau(TDGL) equation and the modified Korteweg-de Vries(mKdV) equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.     

磁场作用下超导圆环的涡旋演化

利用Ginzburg-Landau理论模拟在外磁场作用下超导圆环的涡旋演化,讨论了外磁场、材料参数以及圆环内外径对涡旋进入超导圆环体以及涡旋达到稳定分布的影响.研究结果表明:外磁场越大,材料参数κ越大,圆环环身越宽,则超导圆环体内容纳的涡旋就越多.当磁场较小时,涡旋只由内边界进入超导体,当磁场足够大时,涡旋则先由外边界,然后再从内边界进入超导体.     

Finite dimensional global and exponential attractors for a class of coupled time-dependent Ginzburg-Landau equations

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.     

Solitary Wave Solutions of Discrete Complex Ginzburg-Landau Equation by Modified Adomian Decomposition Method

In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method （mADM）, which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.     

Giant Vortex States in a Long Superconducting Cylinder with a Hole in Center

We have theoretically studied the nucleation of superconductivity in doubly connected superconductors in the form of long superconducting cylinders. The giant vortex states are investigated with the nonlinear Ginzburg-Landau theory. The solutions of Ginzburg-Landau equations are solved numerically with relaxation method. The quantum size effect is clearly shown through the calculation of free energy.     

Ginzburg-Landau方程的非齐次初边值问题

研究具非线性边界条件的一类广义Ginzburg-Landau方程解的整体存在性．推导了Ginzburg-Landau方程的非齐次初边值问题光滑解的几个积分恒等式,由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计;通过逼近技巧、先验估计和取极限方法证明了Ginzburg-Landau方程的非齐次初边值问题整体弱解的存在性．     

Approximation to Nonlinear Schrodinger Equation of the Complex Generalized Ginzburg-Landau Equation

In this paper, we prove that in the inviscid limit the solution of the generalized derivative Ginzburg-Landau equations converges to the solution of derivative nonlinear Schrödinger equation, we also give the convergence rates for the difference of the solution.