各向异性超导体的Ginzburg-Landau理论

本文内容主要有二个方面：1）由各各同性均匀系的BCS理论扩展到各向异性非均匀系，并给出各种异性非均匀系的完整的GL方程式，定出了各个宏微观参量间的关系式。2）结合层状结构氧化物超导体的导电层在导电层相间的特征等，用有效调制势模型和电子有效质量近似，交各向同性均匀系的BCS理论较具体的扩展到各向异性非均匀系并进行深化研究，扩展理论所给出的临界温度和能隙方程公式，主要的热力学性质和电磁性质公式等应用到YBaCuO超导体上，理论结果与实验结果均相符，并也给出各向异性非均匀系的完整的GL方程式，与上面1所给出的形式相同，也定出了各个宏微观参量间的关系，应用到YBaCuO超导体的一些主要性质上也与实验结果相符。     

各向异性超导体的Ginzburg-Landau理论

本文内容主要有二个方面 :1 )由各向同性均匀系的BCS理论扩展到各向异性非均匀系 ,并给出各向异性非均匀系的完整的GL方程式 ,定出了各个宏微观参量间的关系式。2 )结合层状结构氧化物超导体的导电层与非导电层相间的特征等 ,用有效调制势模型和电子有效质量近似 ,将各向同性均匀系的BCS理论较具体地扩展到各向异性非均匀系并进行深化研究。扩展理论所给出的临界温度和能隙方程公式 ,主要的热力学性质和电磁性质公式等应用到YBaCuO超导体上 ,理论结果与实验结果均相符 ,并也给出各向异性非均匀系的完整的GL方程式 ,与上面 1所给出的形式相同 ,也定出了各个宏微观参量间的关系 ,应用到YBaCuO超导体的一些主要性质上也与实验结果相符。     

随机Ginzburg-Landau方程的数值模拟

对随机Ginzburg-Landau方程进行数值研究,构造一个非线性差分格式和一个线性化差分格式.通过对确定性和随机Ginzburg-Landau方程的计算,表明所构造的格式具有较高的精度和较快的计算效率.对随机Ginzburg-Landau方程就噪声振幅的不同取值进行了数值模拟,并对由此引发的各种行为进行了描述.     

Time Dependent Ginzburg-Landau方程的Weierstrass椭圆函数解

将文[22]中提出的求解非线性演化方程的Weierstrass椭圆函数解的一个新方法应用于Time Dependent Ginzburg-Landau方程,获得了该方程的一些新的双周期解,并在退化情形下得到了一些新的精确孤波解.     

Transition to Antispirals in the Complex Ginzburg-Landau Equation

We report a continuous transition from outwardly rotating spiral waves to antispirals in the complex GinzburgLandau equation. Numerical simulations demonstrate that the normal spiral to antispiral transition is fulfilled through a rest spiral wave with zero propagation speed. The propagation direction of spiral waves and the power law behaviour close to the transition boundary are examined.     

Phase Space Compression in One-Dimensional Complex Ginzburg-Landau Equation

The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.     

激光系统的Ginzburg-Landau方程及其相位扩散方程

讨论了激光系统Ginzburg-Landau方程的主要动力学行为,它描述激光系统的自发时空对称性破缺。当方程有非均匀静态解时,它存在合作频率锁定效应;而当方程有时空振荡解时,各横模仍有一个共同的光学载频。此模型还表明,混沌解可以发生在低抽运条件下。在较小失谐时,该方程的约化相位扩散方程能较精确地再现原方程的全程动力学行为。这说明在激光横向图形分布的自发形成中,电场的相位分布导引其动力学行为。 关键词：     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

层状铁基超导体的Ginzburg-Landau方程（英文）

基于铁基超导体的多带能隙特征,采用两带模型,假设带内电子配对为各项同性,带间电子配对序参量为coskxcosky形式.利用Gro′kov理论,推导了层状铁基超导体的二维Ginzburg-Landau方程,并给出了自由能密度和垂直于二维载流子运动平面的上临界场表达式.计算表明,上临界场在转变温度附近随温度变化的曲线呈对数形,该特征与最近的一些实验结果相符合,并且与三维体系的上临界场有显著不同,这一特点是由系统的准二维特征所决定.     

环域反馈下复Ginzburg-Landau系统的螺旋波动力学行为

针对自激振荡系统的复金兹伯格-朗道(Complex Ginzbury-Landau, 简称CGL)方程, 研究圆形环域与方形环域两种反馈控制下的螺旋波动力学。结果表明: 圆形环域反馈控制下, 螺旋波波头通常经过一段过渡漂移后进入圆形吸引子, 圆形吸引子的半径以及反馈刚启动时波头的漂移方向随环域参数呈周期性变化, 过渡漂移阶段波头轨道的平缓程度与复反馈信号模的时间函数中钟形部分的陡度有关, 且反馈增益的正负与大小也会影响受控螺旋波的动力学行为。方形环域反馈控制下的螺旋波波头的吸引子更为丰富, 主要包括方形吸引子、小的极限环吸引子、菱形吸引子以及点吸引子, 点吸引子通常位于方形环域的两条对角线上, 且波头运动随环域控制参数呈现规律性变换。     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

复变系数Ginzburg-Landau方程的啁啾组合孤波解

基于描述非均匀光纤系统的复系数Ginzburg-Landau方程,通过拟解法得到了该方程的精确啁啾组合孤波解,并分析了该解的特性.通过大量的数值模拟,发现在有限的初始扰动下这些组合孤波解是在非均匀光纤系统中稳定的.最后,为了进一步研究组合孤波解的稳定性,我们还探讨了组合孤波的相互作用.     

Additive Temporal Coloured Noise Induced Eckhaus Instability in Complex Ginzburg-Landau Equation System

The effect of additive coloured noises, which are correlated in time, on one-dimensional travelling waves in the complex Ginzburg-Landau equation is studied by numerical simulations. We found that a small coloured noise with temporal correlation could considerably influence the stability of one-dimensional wave trains. There exists an optimal temporal correlation of noise where travelling waves are the most vulnerable. To elucidate the phenomena, we statistically calculated the convective velocities Vg of the wave packets, and found that the coloured noise with an appropriate temporal correlation can decrease Vg, making the system convectively more unstable.     

Soliton Solutions of Discrete Complex Ginzburg-Landau Equation via Extended Hyperbolic Function Approach

In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple,we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.     

Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model

The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.     

基于复Ginzburg-Landau方程的双核光纤中调制不稳定性的仿真研究

在双核光纤光学系统中,应用复Ginzburg-Landau方程,研究了连续波的不稳定性问题.双核光纤光学系统是由一个非线性离散主核和一个线性附核构成的.研究发现,在线性微扰下存在调制不稳定性.系统仿真结果表明：如果充分考虑调制不稳定性,则该系统将产生规则或者不规则的脉冲序列.反之,如果不考虑调制不稳定性它将产生一连串具有连续增长振幅的离散峰.这表明在反常群速度色散情况下,一串归零脉冲的峰值或者单一归零脉冲峰值仍然是增强的.在光纤中产生归零序列脉冲源,这一研究结果对全光纤通信有一定的价值,对光纤光学及物理学 关键词： 光孤子 复Ginzburg-Landau方程 双核光纤 调制不稳定性     

Chern-Simons Gauge Theory and Ginzburg-Landau Type Theories: (Ⅰ) Abelian Cases

We show that after the spontaneous symmetry breaking has taken place the Abelian Higgs models with or without the Chern-Simons term would satisfy the same field equation with the massive Chern-Simons gauge theory and have the same anyon solutions. So we regard the massive Chern-Simons gauge theory as an effective gauge theory of the Abelian Higgs models.     

Interactions between optical bullets with different velocities in the three-dimensional cubic-quintic complex Ginzburg-Landau equation

By using the three-dimensional complex Ginzburg--Landau equation with cubic--quintic nonlinearity, this paper numerically investigates the interactions between optical bullets with different velocities in a dissipative system. The results reveal an abundance of interesting behaviours relating to the velocities of bullets: merging of the optical bullets into a single one at small velocities; periodic collisions at large velocities and disappearance of two bullets after several collisions in an intermediate region of velocity. Finally, it also reports that an extra bullet derives from the collision of optical bullets when optical bullets are at small velocities but with high energies.     

耦合Ginzburg-Landau方程的啁啾类亮灰孤子对传输特性研究

从数值模拟角度出发,将复变系数的耦合Ginzburg-Landau方程作为非均匀光纤放大器的理论模型,对啁啾类亮灰孤子对和亮亮孤子对两组孤波在该理论模型中的传输特性进行详细地研究.结果表明,在考虑了非线性增益(损耗)和增益带宽限制放大效应的情况下,啁啾类亮孤子和灰孤子在合适的色散区可以不受非均匀条件的影响而稳定传输.为了进一步讨论孤子对的稳定性,又讨论了加入振幅微扰和噪声微扰对传输的稳定性.     

Phase Turbulence in the Complex Ginzburg-Landau Equation via Kuramoto–Sivashinsky Phase Dynamics

We study the Complex Ginzburg-Landau initial value problem for a complex field uC, with ,R. We consider the Benjamin–Feir linear instability region We show that for all and for all initial data u₀ sufficiently close to 1 (up to a global phase factor eⁱ₀,₀R) in the appropriate space, there exists a unique (spatially) periodic solution of space period L₀. These solutions are small even perturbations of the traveling wave solution, and s, have bounded norms in various L^p and Sobolev spaces. We prove that apart from corrections whenever the initial data satisfy this condition, and that in the linear instability range the dynamics is essentially determined by the motion of the phase alone, and so exhibits phase turbulence. Indeed, we prove that the phase satisfies the Kuramoto–Sivashinsky equation for times while the amplitude 1+² s is essentially constant.Supported in part by the Fonds National Suisse.