Explicit multi-symplectic method for the Zakharov—Kuznetsov equation

We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.     

Structure-Preserving Algorithms for the Lorenz System

Based on a splitting method and a composition method, we construct some structure-preserving algorithms with first-order, second-order and fourth-order accuracy for a Lorenz system. By using the Liouville＇s formula, it is proven that the structure-preserving algorithms exactly preserve the volume of infinitesimal cube for the Lorenz system. Numerical experimental results illustrate that for the conservative Lorenz system, the qualitative behaviour of the trajectories described by the classical explicit fourth-order Runge-Kutta （RK4） method and the fifth-order Runge-Kutta-Fehlberg （RKF45） method is wrong, while the qualitative behaviour derived from the structure-preserving algorithms with different orders of accuracy is correct. Moreover, for the small dissipative Lorenz system, the norm errors of the structure-preserving algorithms in phase space axe less than those of the Runge-Kutta methods.     

Construction of the Green's function for the pseudoharmonical oscillator

In the present paper we have constructed the Green's function for the pseudoharmonical potential, which is considered as an intermediate potential between the harmonic and anharmonic potentials. We have used a hybrid method, by combining the Laplace transformation method and the Green's function technique. The Green's function is used for obtaining the density matrix for a quantum-statistical system, in coordinate representation. Even if this is not a new result, the method can be applied to a class of exactly solvable potentials.     

适用于非对称系统的Wassermann-Wolf方程组

根据Wassermann-Wolf方程的思路推导了适用于非对称光学系统中的非球面设计计算公式,通过编制CODE V宏语言程序,实现了通用非球面设计的自动化。     

On the partial wave method for self energy calculations for non-hydrogenic electrons

Abstract

A method for computing the self-energy correction for highly-ionized and high-Z many electron atoms is proposed and developed. The method is based on a partical wave analysis, and is immediately applicable to general potentials and many-electron wavefunctions.

In this work we discuss the general approach, develop a formalism amenable to practical anal- ysis, provide the angular momentum reduction for arbitrary one-electron orbitals, and describe the computation of the twdimensional integrals and their kernels required for the partial wave analysis. Analytical results allowing for a practical renormalization scheme are discussed.

This work is exploratory and developmental, and the present document provides a status report of our eforts. To date we have obtained numerical evidence that the method successfully handles the renormalization, and we report on significant progress in numerical methods for evaluating and approximating the two-dimensional integrals which occur in the method. We believe that this method can ultimately achieve an accuracy which is competitive with that of modern Brown's method calculations.

The methods discussed within this work for approximating the two-dimensional radial matrix eIements including the full retarded couIomb interaction can be applied to other relativistic atomic physics calculations as a practical way to obtain improvements over the coulomb and Breit approximations.     

An algorithm for solving the optical problem for stratified anisotropic media

An algorithm for solving the Maxwell equations for propagation of light through anisotropic stratified media is considered. The algorithm uses the Berreman matrices of order 4 × 4. In contrast to the numerical methods suggested by Berreman, the new method is exact. The Sylvester theorem for calculating functions of a matrix and the Laguerre method for determining eigenvalues provide the basis for an algorithm with an efficiency comparable to that of the algorithms based on analytic solutions, which exist only in the case of uniaxial media. The method suggested in this paper allows for the analysis of complex optical systems where the effects of biaxiality, magnetic anisotropy, and optical activity play an important role.     

机器人视觉的“手-眼”关系快速标定算法

论述了机器人视觉传感器的内外参数标定的基本原理。设计了一种快速标定机器人"手 眼关系"的标定方法。该方法不需要外加辅助的坐标测量仪器,可一次性标定出视觉传感器的内外参数及机器人的"手 眼关系"。实验证明,该方法具有算法简便快捷和标定精度较高的特点。     

Error estimates for the fast multipole method

Error estimates for algorithms based on truncations for evaluating electrostatic interactions in molecular dynamics applications are very important for several reasons. For example, the estimates are necessary to establish the validity of the simulations and can be used to estimate various simulation parameters. Very precise estimates have been found for the Ewald method and the related particle mesh Ewald method. However, for the very popular fast multipole method such a precise estimate is not available. In this paper, we illustrate the rather complicated error behavior of the fast multipole method and we use statistical methods to derive an estimate for the root mean square error on the forces. Furthermore, the expected maximum error on the force acting on a single particle is studied. The estimates are tested against errors obtained from simulations and are found to be very precise.     

On the method for calculating the reflection function

We consider the problem of calculating the reflection function for the case of radio-wave propagation in a stratified inhomogeneous absorbing ionosphere. A stable method for calculating the reflection function is proposed. Examples of calculations by the proposed method are shown for symmetric and parabolic ionospheric layers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 9, pp. 766–772, September 2007.     

Integration method for the Dirac equation

An integration method for the Dirac equation is proposed. The method, based on diagonalization, reduces the problem to one of integration of independent second-order differential equations.     

Variational method for determining the extraterrestrial constant for a solar ultraviolet spectrometer/ozonometer

A theoretical rationale is presented for a variational method for determining the extraterrestrial constant of a solar ultraviolet spectrophotometer for measuring total column ozone in the atmosphere. We have established the connection between this method and the familiar Langley method for calibration of extraterrestrial constants of solar spectrophotometers. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 2, pp. 291–297, March–April, 2009.     

A One-Dimensional Method for Calculating the Exit Wavefunction

We develop the multi-slice method for calculating wavefunction of a crystal consisting of atomic columns. The new method reduces numerical calculation from two dimensions to one dimension and is much faster than that of the traditional multi-slice method. The calculated result by the one-dimensional method is in agreement with that of the traditional one.     

Properties of the difference method for searching for anisotropy of primary cosmic rays

Methodical properties and features of the original difference method for searching for the anisotropy in the knee region of the primary cosmic ray energy spectrum are analyzed. It is shown that the method in which properties of particle fluxes, rather than intensities, are studied is stable to randomexperimental errors andmakes it possible to separate anomalies associatedwith the laboratory coordinate system from anomalies in the celestial coordinates. The method uses multiple scattering of charged particles in galactic magnetic fields for studying the entire celestial sphere, including sky regions beyond the installation line of sight.     

Quasi-equilibrium closure hierarchies for the Boltzmann equation

In this paper, explicit method of constructing approximations (the triangle entropy method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a problem (such as, for example, rates of processes) as new independent variables.

The work of the method is demonstrated on the Boltzmann's-type kinetics. New macroscopic variables are introduced (moments of the Boltzmann collision integral, or scattering rates). They are treated as independent variables rather than as infinite moment series. This approach gives the complete account of rates of scattering processes. Transport equations for scattering rates are obtained (the second hydrodynamic chain), similar to the usual moment chain (the first hydrodynamic chain). Various examples of the closure of the first, of the second, and of the mixed hydrodynamic chains are considered for the hard sphere model. It is shown, in particular, that the complete account of scattering processes leads to a renormalization of transport coefficients.

The method gives the explicit solution for the closure problem, provides thermodynamic properties of reduced models, and can be applied to any kinetic equation with a thermodynamic Lyapunov function.     

ICP-MS对土壤样品中有效硼的测定

文章建立了一种用ICP-MS测定土壤中有效硼(B)的方法。与常规检测方法相比, 该方法无须过滤,避免了样品的沾污。并简便快捷, 具备良好的精密度和准确度。方法检出限为0.009 ng·g-1, 相对标准偏差为2.66%, 回收率为93.0%～102.0%。     

求Emden-Fowler方程积分的分析力学方法

研究求Emden-Fowler方程积分的分析力学方法,包括Hamilton-Poisson方法,Lagrange-Noether方法,Lie-Hojman方法以及Hamilton-Jacobi方法等.     

The utility of the Galerkin method for the acoustic transmission in an attenuating duct

A comprehensive solution technique that can be applied to shear flow analysis for acoustic transmission in both hard and soft walled ducts with boundary layer dependence in one or two spatial directions is presented. The method, the weighted residual method of Galerkin, is applied in this paper to the two-dimensional channel for the purpose of ascertaining its applicability to more complicated geometries and with certain limitations appears to be a reliable method for treating both the hard and soft walled configurations. Even though the original intent was to establish the validity of the method for more general cases, it is considered to be a good alternative to the Runge-Kutta method in common use and indeed is superior for certain applications.     

Matrix method for the determination of scaling factors for quantum-mechanical force fields

A computer-assisted method for the calculation of scaling factors for refining the quantum-mechanical force fields of polyatomic molecules by the Pulay technique is suggested. The method is an iteration procedure and does not involve the calculation of derivatives of the frequencies of vibrations with respect to the scaling factors. The correlation between the experimental and calculated frequencies upon scaling of the force field is discussed.     

Scaling algorithms for the calculation of solar radiative fluxes

We derived new scaling formulae based on the method of successive orders of scattering to calculate solar radiative flux. In this report, we demonstrate a multiple scaling method, in which we introduce scaling factors for each scattering order independently. The formula of radiative transfer by the method of successive orders of scattering cannot be solved rapidly except in the case of optically thin atmospheres. Then we further derived a double scaling method, which scales the ordinary radiative transfer equation by two scaling factors. We applied the double scaling method to two-stream and four-stream approximations of the discrete ordinates method. Comparing the results of the double scaling method with those of the delta-M method, we found that the double scaling method improved the accuracy of radiative fluxes at large solar zenith angles, especially in the optically thin region, and that in the region where multiple scattering dominates, its accuracy was comparable to that of the delta-M method. Once we determined the scaling factors appropriately, the double scaling method calculated radiative fluxes as rapidly as the delta-M method in the two-stream and four-stream approximations. This method, therefore, is useful for accurate computation of solar radiative fluxes in general circulation models.     

Similarity Reductions for the Khokhlov-Zabolotskaya Equation

In this paper, we first give the Lie point symmetries of the Khokhlov-Zabolotskaya equationby a simple direct method developed by LOU for some (2+1)-dimensional evolution equations,and then discuss all their similarity reductions from these symmetries, finally obtaintheir similarity analysis by using direct method introduced by Clarkson and Kruskal.