双包层光纤激光器的受激拉曼散射与热应力

 建立了高功率掺镱双包层光纤激光器的速率方程模型与热应力模型,对影响受激拉曼散射效应和热应力效应的关键参数（如纤芯半径、光纤长度、泵浦波长、泵浦方式）进行了数值模拟。结果表明:对于较小的纤芯半径,光纤内的斯托克斯光功率较大且增长迅速,因此增加纤芯半径能有效减弱受激拉曼散射效应;减小光纤长度能提高受激拉曼散射的阈值,而纤芯的热应力也增大,因此在不出现热应力引起光纤断裂的情况下,可以减小光纤长度以提高输出功率;采用976 nm波段泵浦源能提高输出功率,降低热应力的影响;两端均匀泵浦方式可以有效降低纤芯热应力,同时维持高功率输出。     

变系数广义KdV方程新的类孤波解和精确解

用普通KdV方程作变换，构造变系数广义KdV方程的解，获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词： KdV方程 变系数广义KdV方程 类孤波解 精确解     

相对论情况下赝自旋对称性势场中运动粒子的束缚态

在赝自旋对称性条件下,分别求解了在M rse型和Tan2(πηr)型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

两个玻色-爱因斯坦凝聚体间相互作用的数值研究

本文采用辛算法数值求解一维含时Gross-Pitaevskii(GP)方程.研究了存在陷俘势和撤掉陷俘势时两个凝聚体间的相互作用.发现当存在陷俘势时两个凝聚体间发生弹性碰撞;在零时刻撤掉陷俘势时两个凝聚体间发生干涉现象;当t=2时撤掉陷俘势两个凝聚体间发生了复杂现象.     

色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解

采用对称约简的分析方法，得出了变系数Ginzburg-Landau方程的抛物渐近自相似脉冲解析解的一般表达式.给出了二阶色散系数纵向双曲型变化和纵向指数型变化的色散渐减光纤中自相似脉冲的振幅、啁啾以及脉冲宽度的具体形式，并与数值解进行了对比，其结果符合得很好.从而证实了稀土元素掺杂的色散渐减光纤中，在增益色散因子的影响下，脉冲的演化具有抛物型自相似特性.     

单量子双能级系统和双态系统关联函数的研究

以具有简单三能级结构染料分子的单量子系统为研究对象,用带有边界条件的速率方程来反映低功率单色连续激光激励下单分子发射荧光的动力学过程.该方法可以通过时间分辨光子探测获得处理单分子动力学随机过程.研究给出了一种通过求解反映单量子系统动力学过程的物理量——延迟函数计算关联函数的方法,并给出了双能级系统和双态系统延迟函数和关联函数的具体表达式.研究表明,在实际测量中只要获得关联函数曲线,就可以通过数据拟合计算出分子跃迁的动力学参量.     

稳态问题混合边界积分方程的高精度求积法与分裂外推

提出了求积法解稳态问题的混合边界积分方程,它拥有高精度,低复杂度.通过并行地解粗网格上的离散方程,根据误差的多参数渐近展开,应用分裂外推算法得到高精度的近似解,同时获得后验误差估计.     

Analytical study of a flattened Gaussian beam through multi-apertured optical imaging systems of B = 0

By using the methods of the matrix decomposition and expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expressions for a flattened Gaussian beam (FGB) through multi-apertured optical imaging systems of B = 0 are derived and illustrated with numerical examples. Comparisons with the straightforward numerical integration of the Collins formula and with the previous work are made. It is shown that the main advantages of our methods and results are the more accuracy and great reduction of computer time.     

Generalized Riccati equation expansion method and its application to the Bogoyavlenskii's generalized breaking soliton equation

Based on the computerized symbolic system Maple and a Riccati equation, a Riccati equation expansion method is presented by a general ansatz. Compared with most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nonlinear differential equations. Making use of the method, we study the Bogoyavlenskii's generalized breaking soliton equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions.     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.