过阻尼分数阶Langevin方程及其随机共振

通过对广义Langevin方程阻尼核函数的适当选取,在过阻尼的情形下, 推导出分数阶Langevin方程.给合反常扩散理论和分数阶导数的记忆性, 讨论了分数阶Langevin方程的物理意义,进而得出分数阶Langevin方程产生随机共振的内在机理.数值模拟表明,在一定的阶数范围内,分数阶Langevin方程可以产生随机共振, 并且分数阶下的信噪比增益好于整数阶情形.     

基于非线性薛定谔方程的一种孤子特性的分析

光孤子通信是解决光信息在光纤中长距离传输时衰减和色散问题的一种较为有效的方法.本文在现有带有群速度色散、非线性项、三阶非线性系数以及增益/损耗项的非线性薛定谔方程孤子解的基础上,给出了灵活性的孤子解.采用具有复振幅的行波解作为试探解,将试探解代入原方程,在实部和虚部分离的基础上,引入三个变量函数,最后表征出孤子解波函数的平方,并应用Matlab选择不同的变量函数进行数值模拟,得到图示结果.结果表明孤子解对于参变量变化是敏感的.选择适当的参量,得到合适的孤子,这一结论对光纤中孤子通信具有重要意义.     

阻尼耦合振动的Lagrange函数和Hamilton函数

本文研究两种阻尼耦合振动的分析力学化.首先,利用坐标变换将方程变换成自伴随形式;其次,根据Engels方法计算得到Lagrange函数;最后,由逆变换导出原始方程的Lagrange函数,以及Hamilton函数.     

无阻尼单摆运动微分方程的反正切分式变换精确解

无阻尼单摆运动微分方程是一种具有物理背景的非线性常微分方程,研究其精确解和解法是非线性科学中的一个重要内容.在F展开法的基础上,应用反正切分式变换正弦函数方法,并引入Riccati辅助方程,得到了4种无阻尼单摆方程精确解的结果.达到了丰富此类方程求解技巧和精确解的目的.总结得出此类方程应用反正切分式变换方法具有一定普适性的结论.     

受激拉曼散射对非线性介质波导的时空不稳定性影响

基于非线性包络方程我们研究了平面非线性介质波导中的时空不稳定性,得到了有拉曼散射效应情形下不稳定性调制的增益谱的表达式.结果表明在正常和反常两种群速度色散情形下,拉曼散射效应都会导致出现新的不稳定性区域,并且使原有的每一个谱分量的增益上升从而使谱的范围扩大.并通过分析反常色散情况下四种不同函数分布的非线性色散介质系数对不稳定性增益谱的影响,得到呈双曲函数分布的非线性色散介质最为理想.     

多波长宽带拉曼放大器的优化设计

简化多波长宽带拉曼放大器功率耦合方程,利用多步平均功率法进行数值计算得到密集波分复用系统信号的合成拉曼增益.对传统的模拟退火优化算法进行改进,并应用于宽带拉曼放大器增益谱的优化设计.提出新的目标函数,综合考虑增益带宽、开关增益、增益平坦度等特征参数.基于该简化模型和优化方法研究多泵浦光源的个数、输入功率和波长分布对信号拉曼增益的影响,揭示拉曼放大器增益带宽、开关增益、增益平坦度、泵浦数目等主要参数之间的内在联系.仿真结果显示,信号平坦增益带宽△λ随着泵浦数的增多显著加宽,随开关增益的提高和平坦度的增加明显变窄.     

基于竖直平面圆弧轨道的阻尼因数测量

利用圆柱体在自制圆弧轨道上的弱阻尼运动测量阻尼因数.通过Tracker视频分析软件对阻尼运动视频进行分析,得到运动曲线,并利用Origin软件对运动曲线进行拟合,根据拟合曲线方程得到阻尼因数的测量值.本实验可对阻尼因数的测量提供参考.     

HIRFL–CSRm纵向随机冷却——Palmer冷却研究

对拟在HIRFL-CSRm上建造的纵向Palmer冷却进行了数值优化计算,得出了最佳带宽、最佳增益及最短冷却时间,并运用Fokker-Planck方程进行了模拟,得到了动量散度分布函数在冷却过程中随时间的变化,从而为纵向冷却系统的具体设计和优化提供了重要的理论依据.     

增益平坦拉曼放大器优化算法研究

在分析受激拉曼散射耦合方程的基础上，介绍了一种反向设计多波长抽运光纤拉曼放大器的方法，并使用一种改进遗传算法和新型打靶法，讨论了体现特定的高增益和宽带平坦的适应度函数，对抽运波长和功率进行了优化，得到高增益，宽带平坦的增益谱，其开关增益可达15dB，增益带宽达80nm，增益波动小于1dB，这种放大器结构比现有的宽带光纤放大器在增益平坦上有一定的进步。     

夸克的半经典输运方程

对夸克的量子输运方程取半径典近似时保留到Wigner函数的一次微商项;在色空间和自旋空间展开这个半经典输运方程,得到了色单态自旋标量和色单态自旋矢量的输运方程:并把得到的结果和阿贝尔等离子体进行比较讨论了QGP的非阿见尔性质.     

强阻尼广义sine-Gordon方程特征问题的变分迭代法

研究了在数学、力学中广泛出现的一类非线性强阻尼广义sine-Gordon扰动微分方程问题. 首先, 引入行波变换, 求出退化方程的精确解. 再构造一个泛函, 创建了一个变分迭代算法, 最后, 求出原非线性强阻尼广义sine-Gordon扰动微分方程问题的近似行波解析解. 用变分迭代法可得到的各次近似解, 具有便于求解、精度高等特点. 求得的近似解析解弥补了单纯用数值方法的模拟解的不足.     

Cooperative effects in a quartz medium with quantum dots

Features of the generation of super radiance short pulses in a dielectric medium with quantum dots allowing for the nonlinear dissipative effects of the local field are considered. It is shown that the problem can be reduced to an equation of a nonlinear pendulum with an additional term for the harmonic loss/gain.     

Occurrence of stable periodic modes in a pendulum with cubic damping

Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the harmonic balancing method; the resulting nonlinear response curves are studied further for resonance and stability of symmetric oscillations with relatively low damping. The stability analysis is carried out by transforming the system of equations to the linear Mathieu equation.     

微型自由电子激光电子运动特性分析

作者曾首次提出以铁电单晶表面势代替摇摆器磁场的自由电子激光新机制.本文从单电子的洛仑兹方程出发,对电子的单摆方程,共振行为进行了研究,获得了第j个表面势共振态的增益公式.单摆方程和文献[1]中从能量方程得到的一致,本文的研究充实了文献[1]的论据。     

Crystalline undulator radiation and sub-harmonic bifurcation of system

Looking for new light sources, especially short wavelength laser light sources has attracted widespread attention. This paper analytically describes the radiation of a crystalline undulator field by the sine-squared potential. In the classical mechanics and the dipole approximation, the motion equation of a particle is reduced to a generalized pendulum equation with a damping term and a forcing term. The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and the numerical method, and the stability of the system is discussed. The results show that, in principle, the stability of the system relates to its parameters, and only by adjusting these parameters appropriately can the occurrence of bifurcation be avoided or suppressed.     

One-body electron dynamics in a free electron laser

The free electron laser is analyzed by solving the one-body classical Lorentz force equation in the presence of periodic magnetic field and a plane electromagnetic wave. Phase space paths for electrons are related to those of a simple pendulum and describe laser gain, saturation, and coherent electron beam modulation.     

周期弯晶作为束流控制元件的动力学稳定性

在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和受迫项的广义摆方程。利用Melnikov方法讨论了沟道运动次谐分叉及其稳定性, 导出了周期弯晶的临界条件和退道长度。结果表明, 要试图获得高的引出效率, 除了要求弯晶长度必须小于退道长度外, 还必须保证沟道粒子的运动是稳定的。对临界条件的分析表明, 系统的稳定性与它的参数有关, 只须适当调节系统参数, 就可以保证周期弯晶作为引出元件的稳定性。In the classical mechanics frame and with a dipole approximation the particle motion equation in the periodic bent crystal is reduced to the general pendulum equation with a damping term and the forced term by using the sine squared potential． This paper discusses the problem of the sub harmonic bifurcation of the periodic orbit and the stabilities of the channeling motion by using Melnikov method, so as to derive the critical condition and the dechanneling length of the periodic bent crystal. The results show that channeling motion must be stable in addition that the crystal length is smaller than the dechanneling length in order to ensure higher extracted efficiency. The analysis of the critical condition shows that the system stabilities are related to its parameters. Just by properly regulating the parameters of the system, the dynamic stabilities by the use of periodic bent crystal as beam control cell can be ensured.     

秋千参数自激振动的数学模型与数值模拟

将秋千视为变长度单摆,基于归一化高斯函数构造了摆球相对摆杆的速度表达式.在此基础上建立了秋千的非线性动力学微分方程,并据此数学模型对秋千运动进行了数值模拟,得到了秋千的运动规律和功能转化的机制.     

Inverse iteration for damped natural vibration

Inverse iteration is extended to internally and/or externally damped natural vibration. Each iteration involves one matrix multiplication and one linear equation solution of order n. The symmetric band form of the original undamped eigenvalue problem is preserved. If the undamped mode is taken as the first approximation, the inverse iteration will converse to the corresponding damped mode in about four iterations. However, the one step method is divergent for heavy damping. Therefore, it is advisible to subdivide the damping into successive steps if inverse iteration does not converge in say five iterations. The method is successful for both discrete systems and distributed systems. The implementation is very simple by means of complex arithmetic which is readily available in many FORTRAN compilers.