用傅里叶分析法研究艾里光束远场传播特性

为了从理论上深入分析新型无衍射光束艾里光束在有限能量条件下的远场传播特性,首先,从决定光波在自由空间传播的一维旁轴波动方程入手,采用傅里叶分析法,结合艾里函数的特殊性质,并利用经过指数衰减的有限能量初始条件,完整给出了有限能量条件下用于精确描述一维艾里光束在自由空间传播特性的波动方程解析解.然后,利用所得到解析解分别对一维和二维艾里光束在自由空间的传播特性进行了研究,重点分析了不同参量条件对艾里光束进行无衍射传播和横向自加速的影响.研究表明:当任意横向尺度为100μm,衰减系数为0.03、0.05、0.07、0.1、0.2时,二维艾里光束无衍射传播距离分别为1 014、624、455、338、193mm;当横向尺度保持不变时,衰减系数越小,艾里光束保持无衍射传播的距离越大;当衰减系数保持不变时,横向尺度越小,艾里光束横向自加速越大.所采用的研究方法也可用于研究艾里光束在介质中的传播特性.     

On the oscillons in the signum-Gordon model

New periodic solutions of signum-Gordon equation are presented. We first find solutions φ₀(x, t) defined for (x, t) ∈ ? × [0, T ] and satisfying the condition φ₀(x, 0) = φ₀(x, T ) = 0. Then these solutions are extended to the whole spacetime by using (2.4).     

Symmetry Groups and Exact Solutions of New （4＋1）-Dimensional Fokas Equation

In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.     

Photoinduced optical activity of C<Subscript>70</Subscript> fullerene in organic solvents

We have experimentally studied for the first time the effect of photoinduced rotation of the plane of polarization for pulsed laser radiation in solutions of C₇₀ fullerene in organic solvents and their mixtures. We have shown that the effect is observed for elliptical polarization of the laser radiation and is absent for linear polarization. We present the results of a study of the nonlinear optical characteristics of the C₇₀ solutions. We discuss the physical mechanisms by which nonlinear gyrotropy is induced in solutions. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 93–99, January–February, 2009.     

多维漫透射光谱提高复杂混合溶液分析能力

多维漫透射光谱技术利用传统的近红外透射测量方式,增加一维扫描装置,获得透射方向上的径向光谱,并利用多点漫透射光谱对复杂混合溶液进行成分分析。实验设计了基于氙灯光源、精密电控平移台和光谱仪的检测装置,选用Intralipid-20%,India Ink和C₆H₁₂O₆共配制225种成分含量不同的混合溶液,分别测量距其透射中心点0～5 mm(间隔0.25 mm)范围内的20点漫透射光谱信号,以偏最小二乘回归算法对单点和多点漫透射光谱信号进行建模分析。实验得到India Ink含量和Intralipid-20%含量随漫透射光位置点的增加建模及预测的精度提高,C₆H₁₂O₆含量随漫透射光位置点的增加建模及预测精度没有明显变化。结果表明,增加不同位置信息的漫透射光谱信号,能够提高复杂混合溶液中强吸收物质和强散射物质的信噪比,对于弱吸收弱散射物质有望在提升系统精度的前提下提高其预测能力。     

精确跟瞄控制技术研究

针对目标跟瞄多功能的需求,将最小方差估计和跟踪控制的思想结合,设计了一种跟瞄控制器,实现了目标位置预测与伺服控制的融合,优化了系统结构。采用基于当前统计模型的改进卡尔曼滤波算法,预测出目标运动状态参数;采用自适应滑模的解算控制方法,实现伺服系统的位置控制。通过仿真实验,系统状态稳定,抗干扰能力加强,通过对数据分析,跟瞄精度明显提高。     

Approximate Solutions of Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method

By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.     

An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.     

经典单色短峰水波理论的三阶完备解

针对经典的有限水深三阶单色短峰波,考虑环境均匀流效应,赋予一新的解析解,从而与原经典解析解构成完备的解析解.这就在第二阶解、第三阶解结构上显示出多种相互作用机制.     

Approximate solution for the Klein Gordon-Schrdinger equation by the homotopy analysis method

The Homotopy analysis method is applied to obtain the approximate solution of the Klein--Gordon--Schr?dinger equation. The Homotopy analysis solutions of the Klein--Gordon--Schr?dinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.