Solution of the poisson equation: Comparison of the Galerkin and control-volume methods

The two-dimensional Poisson equation is solved by the finite element method which uses rectangular elements and the bilinear shape function. Two kinds of weighting functions are employed, which correspond to the Galerkin method and the control-volume method. The results for three test problems, for which exact analytical solutions are available, show that the control-volume method leads to errors that are about one-half of the errors given by the Galerkin method. Incidentally, the five-point finite difference method is found to give errors which are nearly equal to those for the Galerkin method.     

On the superiority of the mixed element free Galerkin method for solving the steady incompressible flow problems

The element free Galerkin (EFG) method is a promising method for solving flow problems, but it meets the difficulty of volumetric locking for solving the incompressible flow problems. In this paper, a mixed EFG method is proposed for solving the steady incompressible flow problems, which avoids the volumetric locking and inherits the meshfree properties. The method employs two sets of nodes, one for the velocity approximation and the other for the pressure approximation. Specially, the ratio between the velocity node number and the pressure node number is taken as the only indicator for the locking behavior of the mixed EFG method. And inf–sup tests are carried out to investigate the relationship between the ratio and locking behavior. By two numerical examples, the accuracy, rate of convergence and efficiency of the mixed EFG method are also carefully studied. The results show that the accuracy, convergence and efficiency of the mixed EFG method are superior to that of the time-related fractional step methods.     

Characterization of flaws using the zeroes of the real and imaginary parts of the ultrasonic scattering amplitude

A new method for determining the size of flaws, such as cracks and voids, in structural materials is reported. The method is based on the observation that, for a wide class of flaws, the zeroes in the real and imaginary parts of the scattering amplitude occur at characteristic frequencies which depend on the flaw size. The method of reconstruction using the zeroes is simpler than the inverse Born approximation because the flaw sizes are extracted directly from the characteristic frequencies. The new method employs the same data input as the inverse Born algorithm and has certain common limitations. Following a theoretical treatment, experimental results are presented for a number of different types of flaws.     

Numerical solution of the EFIE by the meshfree collocation method

This paper contains guidelines for numerical solution of the EFIE meshfree. Degrees of freedom including mathematical statement, the meshfree method, shape functions and their parameters are considered and proper choices are selected by logical deduction, experience or previous reports. The method is based on decomposing the differential and integral parts of the EFIE, which is an integro-differential equation. These two independent parts could be processed in parallel. The differential and the integral parts are expanded over interpolants and approximant meshless shape functions, respectively. The final arrangement is applied to various scattering problems. Even though we applied the method mostly to linear and rectangular structures, the approach is applicable to all Electromagnetic integral equations of arbitrary geometries. For simple geometries with equidistance node arrangements and considering only the central node for support of the approximants, suggestions are made for bypassing numerical integration. In this case, although the differential part is still meshless, the integral part cannot be regarded as a meshless method in a strict sense and it may be considered a high-order collocation method. The results are compared with the low-order method of moments, previous reports and the FEKO software.     

Revisiting the method of cumulants for the analysis of dynamic light-scattering data

The method of cumulants is a standard technique used to analyze dynamic light-scattering data measured for polydisperse samples. These data, from an intensity-intensity autocorrelation function of the scattered light, can be described in terms of a distribution of decay rates. The method of cumulants provides information about the cumulants and the moments of this distribution. However, the method does not permit independent determination of the long-time baseline of the intensity correlation function and can lead to inconsistent results when different numbers of data points are included in the fit. The method is reformulated in terms of the moments about the mean to permit more robust and satisfactory fits. The different versions of the method are compared by analysis of the data for polydisperse-vesicle samples.     

Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles

The pseudospectral time-domain (PSTD) method is a powerful approach for computing the single-scattering properties of arbitrarily shaped particles with small-to-moderate-sized parameters. In the PSTD method, the spatial derivative approximation based on the spectral method is more accurate than its counterpart based on the finite-difference technique. Additionally, the PSTD method can substantially diminish accumulated errors that increase with the spatial scale and temporal duration of simulation. We report on the application of the PSTD method to the scattering of light by nonspherical ice particles. The applicability of the PSTD method is validated against the Lorenz-Mie theory and the T-matrix method. The phase functions computed from the PSTD method and the Lorenz-Mie theory agree well for size parameters as large as 80. Furthermore, the PSTD code is also applied to the scattering of light by nonspherical ice crystals, namely, hollow hexagonal columns and aggregates, which are frequently observed in cirrus clouds. The phase functions computed from the PSTD method are compared with the counterparts computed from the finite-difference time-domain (FDTD) method for a size parameter of 20 and an incident wavelength of 3.7 microm. The comparisons show good agreement between the two methods.     

压力表检定中数据判读及测试问题的解决

分析讨论了压力表检定中数据的设定、读取及判定,给出了压力表示值误差是否超出允许误差的快速判定方法,对压力表检定过程中耐压测试和压力表指针偏转平稳性测试中的问题进行了讨论。     

Choice of a Method of Solving the Problem of Identifying the Distribution Laws of the Random Errors of Measuring Instruments

A choice is made of a method for solving the problem of identifying the distribution laws of the random errors of measuring instruments in terms of the results of an analysis of the characteristics of three methods of utilizing experimental data to determine an analytical model for a distribution law. The defects of the chosen method are considered and particular problems are formulated for eliminating them.     

Mathematical model of the exact fraction method for the order of interference

An improved method of interpreting the exact fraction method for the order of interference used in multiwavelength interferometry is examined. Optimal algorithms for choosing possible values of the integral orders of interference and a new, more exact method of calculating the result of two wavelength interference measurements are presented. The metrological problems of multiwavelength interferometry are shown to be closely related to the formalism of convergents of continued fractions in number theory.     

Investigation of the bubbling method of determining the density of petroleum products

The fundamental principles of the bubbling method of determining the density of liquid media are considered. The relation between the density of the liquid and the frequency at which bubbles appear in the measuring tubes is obtained. An experimental check of this method is carried out and the limits of the bubble mode for measurements on petroleum products are established.     

Measurement of the thermal characteristics of materials without the action of heat

The theoretical principles of a qualitatively new method for the express measurement of the thermal characteristics of materials (the thermal conductivity and the thermal diffusivity) are presented. The operating principle and the basic technical data of an instrument for realizing the proposed method are described. __________ Translated from Izmeritel’naya Tekhnika, No. 9, pp. 44–47, September, 2007.     

Mixed Approximation Scheme of the Finite-Element Method for the Solution of Two-Dimensional Problems of the Elasticity Theory

For the solution of two-dimensional boundary-value problems of the elasticity theory, a triangular finite element, ensuring stability and convergence of mixed approximation, is proposed. The system of resolving equations of the mixed method is derived with account of strict satisfaction of static boundary conditions at the surface. To solve matrix equations of the mixed method, various algorithms of the conjugate-gradient method with the pre-conditional matrix have been considered. Numerical data on convergence and accuracy of the solution for a number of test problems of the elasticity theory and fracture mechanics are given. The results obtained by the conventional and mixed finite-element method approaches are compared.     

一种新的六端口测量系统自校准方法

提出了一种新的六端口自校准方法.本方法从六端口相对功率理论出发,导出了六端口系统常数的自校准方程,给出了求解系统常数初值的方法,并利用梯度法对方程组求解,仿真结果表明用一个匹配负载、四个失配负载就可以解出系统常数.     

On the accuracy of the Haar wavelet discretization method

Current study contains adaption of Haar wavelet discretization method (HWDM) for FG beams and its accuracy estimates. The convergence analysis is performed for differential equations covering a wide class of composite and nanostructures. Corresponding error bound has been derived. It has been shown that the order of convergence of the HWDM can be increased from two to four by applying Richardson extrapolation method. The theoretical estimates are validated by numerical samples considering FGM beam as a model problem. The results obtained by applying HWDM are compared with the results of finite difference method (FDM).     

附加物对材料低温比热测量精度的影响

介绍了真空绝热法测量材料低温比热的原理及方法。考虑到测量系统中样品架、加热器及温度计等附加物引入的热容因素，建立了比热测量误差的传递关系式，并给出了分析数据。对具体测量中有关精度的问题进行了探讨。     

Method of including the anisotropy of the optical properties of the surface and the nonunidimensionality of the system in determining the effective radiation

Based on the method of successive substitutions, an integral equation is derived in which multiple reflections are explicitly identified. This equation is used provide simple methods of estimating the local effective radiation of two-dimensional and three-dimensional systems of surfaces, with due regard for the anisotropy of their optical properties. A cylindrical cavity confined by the surface of a right circular cylinder with a side pyrometric hole is treated as an example. The results obtained by the suggested method are compared with the data of direct solution of an integral equation for the two-dimensional problem.     

Simple method for improving the sampling in profile measurements by use of the Ronchi test

We present a simple method for increasing the number of data points obtained during performance of profilometric measurements with the Ronchi test. The method is based on multiple ronchigram acquisitions that are superimposed after a few very simple data-processing operations. The measurement method, experimental setup, and data processing are described in detail from the ronchigram to the measured profile, and experimental results for a concave surface of an spherical ophthalmic lens are provided. The radius of curvature values measured for that surface are compared with the ones obtained with a high-precision radioscope, showing very good agreement and demonstrating the capability of the technique to measure topographic profiles of reflective samples.     

A comparison study of the LMAPS method and the LDQ method for time-dependent problems

This paper compares numerical solutions of spatial-temporal partial differential equations based on two RBF-based meshless methods: the local method of approximate particular solutions (LMAPS) and the local RBFs-based DQ method (LDQ). To avoid the ill-conditioned problems of the global version, the weighting coefficients at the supporting points are determined by solving low-order linear systems instead of large dense linear systems. The Runge–Kutta method is adopted for time stepping schemes. The numerical experiments have shown that the LMPAS method and the LDQ method are capable of solving the initial boundary value problem for spatial-temporal partial differential equations with high accuracy and efficiency.     

A Meshless Local Petrov-Galerkin Method for the Analysis of Cracks in the Isotropic Functionally Graded Material

A meshless local Petrov-Galerkin method (MLPG) [[Atluri and Zhu (1998)] for the analysis of cracks in isotropic functionally graded materials is presented. The meshless method uses the moving least squares (MLS) to approximate the field unknowns. The shape function has not the Kronecker Delta properties for the trial-function-interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular integrals to generate the global effective stiffness matrix if body force is ignored; it only involves a regular boundary integral. The material properties are smooth functions of spatial coordinates and two interaction integrals [Rao and Rahman (2003a,b)] are used for the fracture analysis. Two numerical examples including both mode-I and mixed-mode problems are presented to calculated the stress intensity factors (SIFs) by the proposed method. Example problems in functionally graded materials are presented and compared with available reference solutions. A good agreement obtained show that the proposed method possesses no numerical difficulties.     

Experimental determination of the limits and conditions of applicability of pairwise aggregation of radiometric instruments for the detection of sources of ionizing radiation

The method of pairwise aggregation of radiometric devices for the detection of radioactive substances is studied. The limits of applicability of the method for gamma-neutron fields are determined.