时域耦合模理论引入“理论力学”教学中的可行性的探究

被广泛地用于力学、光学、电学等相关学科中的时域耦合模理论,在前沿科学研究中扮演着越来越重要的角色.在教学和科研相结合的本科教学理念下,将时域耦合模理论引入“理论力学”中已刻不容缓.本文结合拉格朗日方程和久期微扰理论,将振子耦合的二阶微分方程退化为一阶微分方程,即时域耦合模理论的主方程.该探究为本科生顺利接受时域耦合模理论提供了一种方案,并且在本科生素质培养方面有一定的意义.     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

偏振表象和偏振表象变换理论以及应用

借用量子力学中的表象与表象变换概念,本文系统地提出了偏振光学中的偏振表象和偏振表象变换理论,可以加深对琼斯空间的琼斯矢量、琼斯矩阵描述偏振光和偏振光变换的理解,更加深刻认识其中的物理机理.本文还利用偏振表象和表象变换理论解读了光纤通信中的光纤偏振模色散和偏振相关损耗对传输的偏振光的作用和影响.     

Fokker-Planck方程与Vlasov方程在模耦合理论研究中的比较

模耦合理论比较成功地解释了微波不稳定性的发生,其理论基础是Vlasov方程.Fokker-Planck方程包含了束团的辐射阻尼效应和量子激发效应,是比较完备地描述粒子运动状态的束团分布方程.比较了Fokker-Planck方程和Vlasov方程在来源、意义和解法方面的关联和不同,同时介绍了一种多项式展开束团耦合模式来求解Fokker-Planck方程的方法,并在静态分布中包含了势阱畸变的效应.     

利用表象变换精确求解最一般双耦合谐振子的能量本征值

将变换后的哈密顿量进一步变换到占有数表象,使哈密顿量对角化,精确求解出最一般双耦合谐振子,即哈密顿量中含非对角项(-λx1x2 vp1p2)的玻色谐振子的能量本征值．讨论了由耦合所引起的能级分裂。     

耦合广义非线性薛定谔方程的相互作用表象龙格库塔算法及其误差分析

本文通过表象变换, 将耦合广义非线性薛定谔方程 (C-GNLSE) 变换成相互作用表象中的向量方程, 再利用向量形式的4阶龙格-库塔迭代格式, 建立了一种在频域内求解C-GNLSE的同步更新迭代算法. 通过将该向量形式的相互作用表象中的4阶龙格-库塔 (V-JH-RK4IP) 算法应用于高双折射光子晶体光纤中超连续谱产生的数值模拟, 验证了算法的有效性, 通过与现有其他典型算法的比较, 表明以V-JH-RK4IP算法求解C-GNLSE具有最高的计算精度和计算效率. 关键词： 耦合广义非线性薛定谔方程(C-GNLSE) 相互作用表象 4阶龙格-库塔算法 超连续谱产生     

Hylleraas-Breit变换在类氦离子Schrdinger方程中的应用

给出了Hylleraas Breit变换 (HBT)的具体形式 ,并用之将类氦离子不动核问题的六维Schr dinger方程化为三维的形式。给出了求解类氦离子任一能量定态问题的三维能量方程或方程组以及对应的变分形式     

神经网络在结构响应预测中的应用研究

本文讨论动态神经网络结构及其算法，然后利用所设计的动态神经网络对杜芬(Duffing)方程和一实际结构在不同输入条件下的响应进行预测。仿真结果表明，利用动态神经网络对结构响应有较好的预测效果。     

A Hopf-like equation and perturbation theory for differential delay equations

We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion.     

运用线性量子变换理论和定态微扰论求解线型多原子分子振动的一般方法

采用键长伸缩和垂直键轴位移为内坐标,多维耦合谐振子、势函数中超过二次幂的项分别为零级近似和微扰的线型多原子分子振动模型,运用广义线性量子变换理论和定态微扰论对线型多原子分子振动进行了普遍求解,将线型多原子分子简谐振动能量本征值和态的求解转化成正定和半正定矩阵的对角化问题,微扰矩阵元、能量和波函数各级修正的计算转换到多维无耦合谐振子的本征表象中进行.并以CO2分子为例进行了具体求解.     

Asymptotical solutions of coupled nonlinear Schrodinger equations with perturbations

In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.     

Exact solutions to two coupled nonlinear physical equations

In this paper, a two-step ansatz is proposed, which leads to some new solutions to two coupled nonlinear physical equations.     

Analysis and engineering of coupled cavity waveguides based on coupled-mode theory

The analytical expression for the transmission spectra of coupled cavity waveguides （CCWs） in photonic crystals （PCs） is derived based on the coupled-mode theory （CMT）. Parameters in the analytical expression can be extracted by simple numerical simulations. We reveal that it is the phase shift between the two adjacent PC defects that uniquely determines the flatness of the impurity bands of CCWs. In addition, it is found that the phase shift also greatly affects the bandwidth of CCWs. Thus, the engineering of the impurity bands of CCWs can be realized through the adjustment of the phase shift. Based on the theoretical results, an interesting phenomenon in which a CCW acts as a single PC defect and its impurity band possesses a Lorentz lineshape is predicted. Very good agreement between the analytical results and the numerical simulations based on transfer matrix method has been achieved.     

内开槽螺纹回旋行波管线性理论研究

基于耦合波理论，运用阻抗微扰法得到了内开槽螺纹波导的色散方程及耦合条件，并从相对论电子运动方程入手得到了自洽非线性方程组，通过一阶线性近似导出了注-波互作用线性关系及色散方程.运用数值计算及3维粒子模拟软件冷腔分析对该波导冷腔色散特性及注-波互作用色散特性进行了研究. 关键词： 内开槽螺纹波导 阻抗微扰 线性理论 自洽非线性方程组     

Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations

The formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations. The system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers, but no highers-mers. We derive thermodynamic perturbation theory, using the system interacting with only the repulsive potential as a reference system. Two distinct integral equations for the pair correlation are derived. The first one treats both parts of the interaction approximately; the other one employs the repulsive reference system used in perturbation theory. We show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature. In the first case this applies to a pressure consistent with the compressibility relation, in the second to the excess Helmholtz free energy over the reference system.Supported by the NSF under Grant No. CHE-82-11236 and by the U.S. Air Force under Grant No. AFOSR 82-0016A.     

Critical exponents and large-order behavior of perturbation theory

The principles of the recent calculations of critical exponents from three- and two-dimensional field theory are reviewed. They rely on the Callan-Symanzik equations, diagram calculations, and on the characterization of the asymptotic behavior of perturbation series at large order. We then present new results concerning the normalization of the large-order behavior.On leave of absence from INFN, Frascati.