Matrix elements of doubly degenerate vibrations and the Herzberg-Teller series

The non-zero terms in doubly degenerate vibrations in the Herzberg-Teller series are discussed and simplified formulae for the matrix elements for transitions between the degenerate l-components of such vibrational levels in upper and lower electronic states are given, with the emphasis on the change of vibrational frequency accompanying the transition. The results are applied to the analysis of degenerate components in the ν₆ and ν₁₆ vibrational transitions in the benzene system, and it is shown that in cases where the second order Herzberg-Teller terms are important, cancelation effects in the matrix elements can lead to the disappearance of certain transitions which are otherwise allowed.     

Local radial point interpolation method for the fully developed magnetohydrodynamic flow

In this paper, a local radial point interpolation method (LRPIM) is presented to obtain the numerical solutions of the coupled equations in velocity and magnetic field for the fully developed magnetohydrodynamic (MHD) flow through a straight duct of rectangular section with arbitrary wall conductivity and orientation of applied magnetic field. Local weak forms are developed using weighted residual method locally for the governing equations of fully developed MHD flow. The shape functions from LRPIM possess the delta function property. Therefore, essential boundary conditions can be applied as easily as that in the finite-element method. The implementation procedure of LRPIM method is node based, and it doesn’t need any “mesh” or “element”. Computations have been carried out for different Hartmann numbers, wall conductivities and orientations of applied magnetic field.     

A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

This paper presents a meshless method, which replaces the inhomogeneous biharmonic equation by two Poisson equations in terms of an intermediate function. The solution of the Poisson equation with the intermediate function as the right-hand term may be written as a sum of a particular solution and a homogeneous solution of a Laplace equation. The intermediate function is approximated by a series of radial basis functions. Then the particular solution is obtained via employing Kansa’s method, while the homogeneous solution is approximated by using the boundary radial point interpolation method by means of boundary integral equations. Besides, the proposed meshless method, in conjunction with the analog equation method, is further developed for solving generalized biharmonic-type problems. Some numerical tests illustrate the efficiency of the method proposed.     

Asymptotic solutions for Mathieu instability under random parametric excitation and nonlinear damping

A theoretical analysis is presented of the response of a lightly and nonlinearly damped mass-spring system in which the spring constant contains a small randomly fluctuating component. Damping is represented by a combination of linear and nonlinear power-law damping. System response to some initial disturbance at time zero is described by a sinusoidal wave whose amplitude and phase vary slowly and randomly with time. Leading order formulations for the equations of amplitude and phase are obtained through the application of methods of stochastic averaging of Stratonovich. The equations of amplitude and phase are given in two versions: Fokker-Planck equations for transient probability and Langevin equations for response in the time-domain. Solutions in closed-form of these equations are derived by methods of mathematical and theoretical physics involving higher transcendental functions. They are used to study the behavior of system response for ever increasing time applying asymptotic methods of analysis such as the method of steepest descent or saddle-point method. It is found that system behavior depends on the power density of the parametric excitation at twice the natural frequency and on the magnitude and form of the damping. Depending on these parameters different types of system behavior are found to be possible: response which decays exponentially to zero, response which leads to a stationary state of random behavior, and response which can either grow unboundedly or which approaches zero in a finite time.     

阻尼对水平滚筒内二元颗粒体系径向分离模式形成的影响

采用离散单元数学模型对一充装量为50%的水平薄滚筒内S形二元颗粒体系的分离模式进行了数值模拟试验,研究了不同碰撞阻尼参数下的分离过程,分析了阻尼对分离过程及分离模式的影响.模拟结果表明阻尼对滚筒内颗粒的分离过程及分离模式影响很大,在S形二元颗粒体系水平薄滚筒内,阻尼可控制渗透和离析的协同作用以及自由表面层的流动形式,最终影响分离模式的形成;当阻尼太大时分离模式只能形成月亮模式,阻尼太小时可形成不明显的花瓣模式,只有当阻尼在适当的范围内,自由表面流动层形成雪崩流型式时,分离模式才会呈现规则的花瓣模式,试验结 关键词： 滚筒 模式形成 径向分离 离散单元法     

基于径向增长因子的二维不变流形计算

在计算二维不变流形时,为均衡各方向的增长速度,便于构建动力系统的全局流形结构,引入径向控制因子对原始动力学系统进行归一化.以流的切向量的径向分量为标准,控制其在径向的增长速度.理论分析和实例计算的结果均表明,归一化后的动力学系统和原始系统的流同轨,即全局流形结构一致.最后,通过对Lorenz和Duffing系统的流形计...     

长脉冲二极管绝缘子真空表面闪络

 在长脉冲强流无箔二极管实验过程中观察到绝缘子沿面闪络现象。分析实验现象认为是屏蔽环与绝缘子距离过近造成了屏蔽环边缘高场强,从而产生场致发射电子。电子在强电磁场作用下撞击绝缘子表面引起了二次电子雪崩从而导致真空表面闪络。运用静电场模拟和粒子束模拟,改进屏蔽环结构。改进后的二极管工作电压500 kV,电流12 kA,在1 T引导磁场下稳定运行,没有再发生真空表面闪络。     

基于JMCT-JBURN的燃料棒径向功率分布计算北大核心CSCD

研究给出基于蒙特卡罗粒子输运软件JMCT耦合燃耗分析软件JBURN计算燃料棒径向功率分布的方法。介绍了计算模型的建立、输运及燃耗计算的相关设置以及裂变功率、俘获功率的统计方法。UO_(2)燃料棒径向功率分布的计算结果表明,采用JMCT-JBURN软件的结果与工程常用软件符合较好,最大偏差不超过3%,证明了计算方法和计算软件的适用性。该方法可用于工程设计。     

Size-consistent multireference configuration interaction method through the dressing of the norm of determinants

A new determinant-specific, effective change (‘dressing’) of the norm of the multireference configuration interaction (MRCI) wavefunction is proposed in order to achieve the size-consistency of the MRCI method. The new approach provides a unifying framework for analysis of size-consistent extensions of the MRCI method that are based on the coupled pair functional (CPF) strategy and lead to simplified computations of the analytical gradients. Using the new framework, a generalized multireference full coupled pair functional (MR-FCPF) method is introduced. The MR-FCPF method may be viewed as a functional counterpart of the recently proposed generalized (‘full’) coupled electron pair approximation (CEPA), referred to as the size-consistent self-consistent CI ((SC)²CI) method. A straightforward extension of the MR-FCPF method leads to a pseudo-functional form of the coupled cluster (CC) type formalisms. Therefore, the new approach may be used to introduce a simple alternative to existing CC-type gradient techniques. The new procedure is formally derived and compared with similar methods from the literature. Model systems calculations (H₂O, LiF, CH⁺ ₂) are further used to demonstrate the effect of various approximations and to elucidate the hierarchy of functional MR-CEPA schemes.     

Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations

The existence and uniqueness of positive radial solutions of the equations of the type [IML0001] in B_R, p>1 with Dirichlet condition are proved for λ large enough and f satisfying a condition[IML0002] is non-decreasing on [IML0003] It is also proved that all the positive solutions in C₁ ⁰(B^R) of the above equations are radially symmetric solutions for f satisfying [IML0004] and λ large enough.