An application of a transcorrelated procedure to the calculation of the energy of the hydrogen molecule

The ground-state energy of the hydrogen molecule is calculated using both the standard variational method and a new transcorrelated method. The value obtained with the new method compares favourably with that obtained by the standard method. If the method used in this paper can be extended to more complicated systems, it is expected that it will enable more accurate energies to be calculated for these systems than is possible using the standard variational method.     

On the nature of the generalized WKB method

The nature and the conditions of applicability of the generalized WKB method (the Petrashen-Miller-Good method) are investigated. It is shown that the generalized WKB method is a new approximate method for quantum mechanics, differing essentially from the WKB method.In conclusion I wish to express my sincere appreciation to Academicians V. A. Fok and M. I. Petrashen for their interest in this work and their valuable advice in the process of its completion.     

Equivalence of the method of the kinetic equation and the fluctuating-frequency method in the theory of the broadening of spectral lines

A new expression for the Stark profiles of spectral lines in plasma has been obtained by the method of the kinetic equation taking into account the dynamics of the plasma microfield. The result represents a dynamic line profile in the form of simple functionals of a static profile. The relation of the new solution with the known fluctuating-frequency method has been analyzed. It has been shown that this method is a discrete analog of the method of the kinetic equation and passes to the latter method in the limit of the continuous fluctuations. Simple formulas (4), (5), and (21) for dynamic line profiles provide ultrafast calculations of the profiles of spectral lines taking into account the dynamics of the plasma microfield.     

Application of the imaginary time step method to the solution of the static Hartree-Fock problem

A method of solution of the static Hartree-Fock problem is proposed. The method, based upon the extension of the method of solution of the time-dependent Hartree-Fock problem to imaginary time, promises to be more efficient, and applicable to more complex systems than previously proposed numerical methods.     

高精度测量孔径光阑面积方法概述

一些辐射学和光度学的测量是以高精度测量精密光阑面积为基础的, 因此高精度测量孔径光阑的面积有着至关重要的意义. 目前高精度测量孔径光阑面积主要有以下两类方法: 接触法与非接触法, 几何法与有效面积法.本文首先对各种方法进行简单介绍, 并对非接触法、 几何法和有效面积法进行重点阐述.最后通过对比不同方法的测量精度、 实现难易程度以及测量设备成本情况, 得出结论: 几何法和有效面积法是非常有前景的.然而要进一步提高孔径光阑面积的测量精度, 稳定的激光光源、精准的移动平台是必不可少的. 关键词： 高精度测量 测量方法 光阑面积     

On the question of the error in the partial capacitance method

An analytical method is proposed for calculating the capacitance of a planar capacitor constructed in the form of a two-layer structure. The method is used to calculate the capacitance of a planar capacitor containing a ferroelectric film. A number of calculations were performed to check the accuracy of the partial capacitance method. The calculations made it possible to determine the limits of accuracy of the partial capacitance method for a permissible calculational error of ±3%. Zh. Tekh. Fiz. 69, 8–13 (April 1999)     

The reduction of the sorting bias in the eigenvalues of the diffusion tensor.

One of the most intrinsic quantities when measuring the diffusion properties of a system is the set of principal diffusivities, which represents diffusion along the fibre axes. System noise is a well-known cause of systematic sorting bias when closely spaced diffusivities are ordered according to their magnitude and leads to their inaccurate estimation. This paper describes a new method for the ordering of the principal diffusivities in which local fibre directional coherence was used as a basis for sorting. The method was applied and tested in computer simulations and experimental data acquired in an isotropic water phantom and healthy human brain. Our results demonstrate that this method leads to significant reduction in the sorting bias in comparison to other techniques and thus a more accurate estimation of the eigenvalues. The method is advantageous over other proposed alternatives to the conventional magnitude sorting method because it is not reliant on a large region-of-interest averaging scheme.     

On the simplification of the technique for calculating the envelope of trajectories of particles in accelerators

In order to simplify the technique of calculating the envelope of trajectories of particles in accelerators the author proposes to use the matrix method to find the square modulus of the Floquet function of the equation of betatron oscillations. This method allows us to obtain this real quantity directly without the necessity, in actual cases, of calculating with complex quantities. The application of this method to the cases of the racetrack, strong focusing accelerator and regenerative deflector is considered.     

An angular singularity-free method for the dynamics of the rovibrational motion of diatomic molecules

An angular singularity-free method for the dynamics of the rovibrational motion of diatomic molecules has been proposed. The present method is based on a formulation that the orientation of a diatomic molecule is expressed by the Cartesian coordinates of the unit vector parallel to the molecular axis. In this light, the present method can be considered as a modification of a method proposed for the rigid rotational motion to the rovibrational motion. Illustrations of the present method have been performed for the classical dynamics of the rovibrational motion of a diatomic molecule, and for the semiclassical dynamics of the collision between an atom and a diatomic molecule, including comparisons with other conventional methods. It is concluded that the present method is free from angular singularity, and that the present method is superior to other conventional methods in view of computational efficiency.     

Alternative approaches to the construction of the Poincare-invariant spin operators of the Dirac particles

At present a number of methods of constructing the Poincare-invariant spin operators for relativistic particles with half-integer spin in the one-particle theory are well known. The method of odd operator constructing, the Lorentz method of bilinear covariant form transformation, and the method with the Foldy–Wouthuysen representation belong to them. New approaches to the construction of spin operators are developed in the present work, namely, a method of separating space-like component directly from the spin matrices of bilinear covariant forms, including the method of multiplication of the covariant Hamiltonian of the Dirac equation by these matrices. By this means we succeeded in constructing the Poincare-invariant spin operators by simpler and mathematically faultless methods. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 10–15, November, 2008.     

Application of the RBF meshless method to the solution of the radiative transport equation

In this paper, we introduce a radial basis function collocation method for computing solutions to the time-dependent radiative transfer equation. For these computations, we use finite differences to discretize the time coordinate, a discrete ordinate method to discretize the directional variable, and an expansion in radial basis functions to approximate the spatial dependence of the solution. The main advantages of the RBF method are that it does not require any mesh or grid, achieves spectral accuracy in multi-dimensions for arbitrary node layouts, and it is extremely simple to implement.     

利用垂直邻边入射法测量三棱镜的折射率简

提出垂直邻边入射法测量折射率。从理论上分析了该方法的测量公式,通过实验测定了不同波长的光对于样品的折射率。与最小偏向角法相比,垂直邻边入射法不需要确定临界位置,在实际研究中更容易施行。     

软件控制实现高速摄影机的收片启动特性

对棱镜补偿式高速摄影机的收片启动特性进行了定量分析 ,根据分析给出了在工程中实现这一运动特性的步骤和方法 ,该方法的核心思想是从试验中得到控制运行所需要的参数 ,然后用软件控制实现摄影机的收片启动特性。实际的工程使用证明该方法简便且行之有效 ,方便了摄影机调试     

Estimation of the direction of auditory events in the median plane

An instrumental method based on parametrically described spectral cues is proposed to estimate the direction of auditory events in the median plane. In contrast to a previous method where the shapes of two spectra are compared, the current method is based on known psychoacoustic features of the auditory system. The algorithm is described and the results of verification experiments are reported.     

Applicability of the Friedberg-Lee-Zhao Method

Friedberg, Lee and Zhao (FLZ) proposed a method for effectively evaluating the eigenenergies and eigen wavefunctions of quantum systems. In this work, we study several special cases to investigate applicability of the method.Concretely, we calculate the ground-state eigenenergy of the Hellmann potential as well as the Cornell potential, and also evaluate the energies of the systems where linear term is added to the Coulomb as a perturbation. The results obtained in this method have a surprising agreement with the traditional method or the numerical results. Since the results in this method have obvious analyticity compared to that in other methods, and because of the simplicity for calculations this method can be applied to solving the Schrodinger equation and provides us a better understanding of the physical essence of the concerned systems. But meanwhile applications of the FLZ method are restricted at present, especially for certain potential forms, but due to its obvious advantages, it should be further developed.     

蒙特卡洛法计算空间辐射制冷器耦合因子的研究

为了研究蒙特卡洛法计算空间辐射制冷器耦合因子 ,文中通过计算平面 W型空间辐射制冷器二级冷块耦合因子 ,介绍了计算流程 ,并以积分分布概率为基础研究了相关核心算法。计算结果表明 ,采用以积分分布概率为基础的核心算法 ,蒙特卡洛法替代传统耦合因子计算方法 ,具有计算结果精度高的优点 ,达到了实用要求     

数控传声器阵列反卷积法对飞机噪音的应用与实验研究

本文主要讨论传声器阵列反卷积法对于飞机发动机噪音测量的实际应用及反卷积法对于飞机过顶测噪的数值模拟。传统"波束成型法"的成像是点源与点分布函数卷积的结果,只有在满足瑞利限制的前提下可以分辨多个相距较近的声源。本文介绍了一种简称反卷积法的传声器阵列新方法,它是将原有的Beamforming结果作为已知条件,从中提取有用的声源信息,去除掉旁瓣的干扰,使得处理出来的声源幅值与位置更加准确。观察运动声源会产生多普勒效应,特别是在频域中处理声信号时会使发声源产生频率偏移,因此在反卷积法使用前引入平均多普勒频移因子,它使得运用反卷积法在频域中预测飞机进场噪音成为可能。     

Applications of the direct Trefftz boundary element method to the free-vibration problem of a membrane

In this paper, the direct Trefftz method is applied to solve the free-vibration problem of a membrane. In the direct Trefftz method, there exists no spurious eigenvalue. However, an ill-posed nature of numerical instability encountered in the direct Trefftz method requires some treatments. The Tikhonov's regularization method and generalized singular-value decomposition method are used to deal with such an ill-posed problem. Numerical results show the validity of the current approach.     

Evaluation of the errors in the measurements of silencer characteristics

This paper is concerned with an evaluation of the errors committed when measuring the transmission loss and the flow noise of silencers; these errors are mainly due to both source and end reflection. It is shown that in measuring the transmission loss, the direct method is more likely to give small errors than the substitution method. Yet whenever the substitution method is used special attention must be paid to the reflection coefficient toward the source. Moreover, it appears necessary to use rather long ducts in order to avoid the effects of axial resonances.     

Determination of the parameters of condensed media by the dual-wavelength differential absorption method

A method of dual-wavelength differential absorption with the use of diode lasers is proposed. The method makes it possible to detect changes in parameters of media that cause broad absorption lines of selected molecular components of these media either to shift or to deform. The potentialities of the method proposed are demonstrated in experiments on remote contactless measurement of the temperature of aqueous solutions and measurement of the deviations of the composition of a mixture of dyes from the equilibrium state. These investigations show ways of increasing the sensitivity of the method proposed in solving particular experimental tasks.