驾驶斑图（pattern）的新方法—空间微扰法

提出了一种控制斑图的新方法－空间微扰法,以一个光学系统为例,用这一微扰法成功地稳定,选择和跟踪了不稳定的卷形,方形和六角形斑图。这一具有普适性的新方法极易被应用到实际空间延展非线性系统中。     

含非线性微扰项的二阶动力学系统的一阶近似守恒量的一种新求法

从一阶近似守恒量的性质出发,把受微扰系统视为未受微扰系统与微扰项的迭加,提出一种分三步求得一阶近似守恒量的新方法:先选择合适的方法求得未受微扰系统的守恒量I0,再考虑微扰项对守恒量I0的影响,最后利用一阶近似守恒量的性质求得一阶近似守恒量.用该方法研究了一实际的受非线性微扰作用的两自由度动力学系统,得到4个稳定的一阶近似守恒量.用坐标变换法和微扰法得到系统一阶近似解的表达式,并讨论4种特殊情况下的一阶近似解.     

微扰实验法测试螺旋线行波管耦合阻抗及模拟仿真

 应用有限元仿真软件HFSS,建立了准确的3维螺旋线行波管耦合阻抗仿真模型。应用该模型,对微扰实验法在微扰杆内电场所做出的4个假设和近似,进行了定量的分析和讨论：电场在轴向是均匀的,忽略掉轴向高次空间谐波的存在;电场在角向是均匀的,忽略掉角向高次空间谐波的存在;忽略掉电场中TE波部分,认为电场角向分量为零;假设微扰前后的电场是相等的。同时,对微扰杆的尺寸和介电常数与耦合阻抗的依赖关系进行了模拟分析。结果表明：当微扰法所引入的假设和近似逐步消失后,微扰法的结果最后收敛于定义法。     

QCD中等时方程的赝标介子解

本文讨论在背景场量子色动力学框架中的等时方程赝标介子解. 方程的积分核由微扰和非微扰贡献两部分组成．微拔部分是通常的单胶子交换图的贡献；非微扰部分的贡献来自于最低阶的夸克和胶子凝聚效应. 当输入合理的夸克质量参数和耦合常数时，可以得到与实验相符合的赝标介子谱．     

气体放电系统中多臂螺旋波的数值分析

采用Purwins的三变量模型, 在二维空间对气体放电系统中多臂螺旋波的形成和转化进行了数值研究. 通过分析方程参数对系统空间的影响, 确定了系统获得稳定螺旋波的参数空间; 得到了斑图由简单静态六边形到螺旋波的演化过程, 分析了螺旋波的形成机制和时空特性; 进一步获得六种不同臂数的多臂螺旋波斑图(例如: 双臂、三臂、四臂、五臂、六臂和七臂螺旋波). 结果表明: 螺旋波斑图出现在图灵-霍普夫(Turing-Hopf)空间, 是Turing模和Hopf模相互竞争、相互作用的结果; 不同臂数的螺旋波波头均在持续地旋转运动, 其运动速度随螺旋波臂数的增加而增大; 随着螺旋波臂数的增加, 其波头的运动形式愈加复杂; 由于受微扰及边界条件的影响, 多臂螺旋波可以向臂数少一的螺旋波发生转变, 数值模拟结果与实验结果符合较好. 关键词： 螺旋波 数值模拟 气体放电     

基于图像分形相关位移测量新方法的研究

本文从分形理论出发提出了图像分形相关位移测量的新方法。较之20世纪80年代发展起来的以像素的灰度相关为基础的数字散斑相关法，分形相关法更充分地利用了散斑图的相关性特征，有关更深入的发展潜力。为了验证理论与方法的可靠性，进行了验证性实验并和数字散斑相关法的测试结果进行了比较。测试结果显示，测试精度至少可达0.06个像素。最后讨论了这一方法的发展前景。     

钾原子基态的定量证明

用原子实模型简化钾原子的哈密顿,把原子实极化和轨道贯穿视为微扰,用微扰法计算了钾原子的能量,定量证明了钾原子的基态是4s态．     

量子力学中的微扰论

简要介绍了量子力学中三种定态微扰方法：一是通常的Ｒａｙｌｅｉｇｈ－Ｓｃｈｒｏｄｉｎｇｅｒ（Ｒ－Ｓ）微扰，但其缺点是高阶微扰项的表达式很繁，且无一般的通项公式，这里介介绍了一个能量和波函数的递推公式，便于计算机编程计算，二是由Ｂｒｉｌｌｏｕｉｎ－Ｗｉｇｎｅｒ（Ｂ－Ｗ）微扰论演变出发迭代微扰法，对于有限维不变子空间或在有限维空间截断近似下计算，收敛是很快的，收敛范围大于Ｒ－２法，最便于上机计算，三是近     

用傅里叶变换法测试平面衍射光栅的分辨特性

本文提出了测试平面衍射光栅的分辨特性的新方法,用干涉法测量光栅衍射的波阵面的相位,得出衍射波阵面的三维波面图,并用所取得的相位数据作傅里叶变换求得其在谱面上的光谱衍射斑——光谱线像的强度分布,并可据此确定半宽度值和分辨极限.文中叙述了这一新方法的优点、基本原理和实验方法,并给出应用这方法测量一批光栅所得结果中的两个例子,结果表明,与通常所用直接扫描光谱线法所测结果相符合.     

基于共振参数微扰法的SEPIC变换器的混沌控制

本文以SEPIC变换器中前置电感电流为控制对象, 采用共振参数微扰法对电流模式控制SEPIC 变换器中的混沌现象进行控制. 该方法通过对电路参数的微小扰动实现了对SEPIC变换器中混沌现象的控制, 并通过时域波形、功率谱及分岔图等对结果进行了分析. 最后实验结果表明, 以前置电感电流为控制对象, 利用共振参数微扰法可以实现SEPIC变换器的混沌控制. 关键词： SEPIC变换器 混沌 混沌控制 共振参数微扰     

用直线稳定方法控制耦合哈密顿系统的混沌运动

讨论了不稳定不动点邻域的不稳定轨道的稳定问题．通过对系统施加外部的控制信号，将直线稳定方法推广到控制高维保守系统一耦合标准映象的混沌运动．通过对外加控制信号的调整，使系统不稳定不动点邻域的不稳定轨道沿着连接任意时刻轨道点和该不动点的直线趋向不动点，从而使难于控制的高维保守系统的不稳定轨道趋于稳定．这种方法不需要事先掌握系统动力行为，而且具有较强的抗干扰能力。     

Control of chaos via an unstable delayed feedback controller

Delayed feedback control of chaos is well known as an effective method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, it had been shown that the method works only for a certain class of periodic orbits characterized by a finite torsion. Modification based on an unstable delayed feedback controller is proposed in order to overcome this topological limitation. An efficiency of the modified scheme is demonstrated for an unstable fixed point of a simple dynamic model as well as for an unstable periodic orbit of the Lorenz system.     

Eigenvector method for unstable resonator simulations

Eigenvector method is a numerical method for laser resonator with which all the eigenmodes and eigenvalues can be solved at the same time. This method is extended for unstable resonators combined with the Collins formula and the ABCD ray matrix in this paper. The mode behavior in a resonator with arbitrary irregular structures can be studied exactly and conveniently. An asymmetrical practical unstable resonator and a non-confocal practical unstable resonator are numerically simulated under varying structure parameters, and some new characteristics are found.     

二维不稳定流形的计算

提出了动力系统中稳定流形和不稳定流形的一种实用的快速算法,可以求得稳定流形和不稳定流形的直观图像,从而从几何角度研究动力系统的动态行为和稳定性区域的边界特征.算法由两步构成:①在不稳定流形上求得一些分布均匀的点,以精确反映流形的每个细节;②借助三角形剖分或二维单纯形剖分利用①的算法将这些点画出直观流形图像.     

Factorization method in the model of unstable particles with a smeared mass

The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the decay rate and cross section can be represented in the universal factorized form for an arbitrary set of particles. An exact factorization is caused by the specific structure of unstable particles propagators. We performed the phenomenological analysis of the factorization effect. The text was submitted by the authors in English.     

非稳腔傍轴波动方程高斯球面波修正方法的数值研究

在分析用差分方法求解虚共焦非稳腔三维傍轴波动方程,及用数值积分方法与快速付氏变换(FFT)方法求解三维菲涅耳积分方程优缺点的基础上,从激光束在虚共焦非稳腔中以修正高斯球面波形式传输的特征出发,经坐标变换把发散(或会聚)的光束拉直成平行光束,然后用FFT方法求解了在新坐标系中修正函数满足的傍轴波动方程.把相同条件下得到的结果与国内外文献给出的结果进行了比较;计算COIL实验非稳腔给出的近远场结果图象合理正确.     

Controlling chaos by a modified straight-line stabilization method

By adjusting external control signal, rather than some available parameters of the system, we modify the straight-line stabilization method for stabilizing an unstable periodic orbit in a neighborhood of an unstable fixed point formulated by Ling Yang et al., and derive a more simple analytical expression of the external control signal adjustment. Our technique solves the problem that the unstable fixed point is independent of the system parameters, for which the original straight-line stabilization method is not suitable. The method is valid for controlling dissipative chaos, Hamiltonian chaos and hyperchaos, and may be most useful for the systems in which it may be difficult to find an accessible system parameter in some cases. The method is robust under the presence of weak external noise. Received 10 January 2001     

Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback

In this paper we discuss the control of complex spatio-temporal dynamics in a spatially extended nonlinear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A presented method is connected with stabilization of unstable homogeneous equilibrium state and the unstable spatio-temporal periodical states analogous to unstable periodic orbits of chaotic dynamics of the systems with few degrees of freedom. We show that this method is effective and allows to achieve desired regular dynamics chosen from a number of possible in the considered system.     

In-plane antisymmetric response of cables through bifurcation under symmetric sinusoidally time-varying load

Analysis and results for in-plane non-linear antisymmetric responses of a cable, supported at the same level, through bifurcation under in-plane symmetric sinusoidally time-varying load are presented. The non-linear equation of the in-plane motion of the cable is solved by a Galerkin method and the harmonic balance method. From the computed results the frequency range, where the antisymmetric response occurs, varies with the sag-to-span ratio of the cable and is broad in the particular sag-to-span ratios. The second unstable region is important compared with the principal unstable region. Strong coupling between symmetric and antisymmetric modes is observed in the unstable regions for the particular sag-to-span ratios.     

硬边非稳腔平面波导激光器的光束特性

基于衍射理论和坐标变换,采用数值模拟的方法分析了硬边非稳腔平面波导激光器的光束特性,研究了存在非均匀抽运和增益饱和时,输出激光的光束质量.在端面抽运和边缘抽运时,比较了正支和负支非稳腔的输出光束特性.结果表明:利用优化的离轴硬边非稳腔可以得到近衍射极限的输出.在相同的抽运不均匀性情况下,对于边缘抽运和端面抽运,正支非稳腔的光束质量因子M2分别为3.9和2.3,而相同条件下负支非稳腔的M2因子为1.8和1.7.