Representation of the Helmholtz equation solution in the form of a series based on backscattering multiplicity

Abstract

The representation of the Helmholtz equation solution in the form of a series based on backscattering multiplicity is considered. New methods for calculating wave fields propagating in inhomogeneous media, which have been developed on the basis of this series, are presented. The results that have been obtained using these new methods are briefly described.     

RC串联电路相移测量方法的研究

利用电压法、李萨茹图形法和双轨迹法分别测量了RC串联电路的相移,并将实验值与理论值进行了比较。研究表明,在所选择的频率波段内,这三种方法测量的实验值与理论值符合的很好,具有高精度、测量装置简单、操作方便等优点。通过对以上三种测量方法的研究,能够让学生从直观上更深入地理解对RC串联电路的特性。     

干涉条纹的处理方法研究

论述了干涉图的图像处理方法,提出了干涉图反高斯变换的光强平均分布处理,保证了干涉图信号的完整性,同时将基于视觉零交叉理论的边缘检测方法应用于干涉条纹的边缘检测中,精确地检测了干涉条纹的边缘,减小了上干涉条纹提取相位差的误差,并与常用的二值化方法进行比较,最后给出了一个有效的干涉条纹细化方法,并与其它处理方法进行了比较 。     

Testing statistical significance of multivariate time series analysis techniques for epileptic seizure prediction

Nonlinear time series analysis techniques have been proposed to detect changes in the electroencephalography dynamics prior to epileptic seizures. Their applicability in practice to predict seizure onsets is hampered by the present lack of generally accepted standards to assess their performance. We propose an analytic approach to judge the prediction performance of multivariate seizure prediction methods. Statistical tests are introduced to assess patient individual results, taking into account that prediction methods are applied to multiple time series and several seizures. Their performance is illustrated utilizing a bivariate seizure prediction method based on synchronization theory.     

Determination of the orientational order parameter of the homologous series of 4-cyanophenyl 4-alkylbenzoate (n.CN) by different methods

The orientational order parameters of a homologous series of 4-cyanophenyl 4-alkylbenzoates have been determined at different temperatures from (13)C-NMR, x-ray diffraction, optical birefringence, high resolution density and diamagnetic susceptibility anisotropy measurements. To determine the temperature dependence of the orientational order parameter from the (13)C chemical shift values, the two-dimensional polarization inversion spin exchange at the magic angle (PISEMA) method was also used for the measurement of (13)C-(1)H dipolar couplings at different sites in the oriented phase. The nematic order parameters determined from each of these methods have been compared. Apart from a slight shift in their values their trends with temperature are very similar. The differences among the results obtained by these five different methods have been discussed. From the high resolution density data, the values of the critical exponents near the T(N-I) transition are found to lie between the Ising model and tricritical behaviour.     

A study of the contrast on growth striations in silicon by X-ray double crystal topography in the Laue case

The image of growth striations in Si formed by the double crystal X-ray topography in the Laue case (DCTL) is investigated. The results of the dynamical diffraction theory for crystals with small microdefects have been compared with the contrast behaviour determined experimentally. It has been found that the theory explains qualitatively the contrast on the striations and it has been demonstrated that the DCTL method is suitable for detection of the presence of small microdefects in growth striations. Since the paper completes a series of papers on X-ray topography of growth striations, some general conclusions are formulated concerning the applicability of the X-ray topographical methods to the investigation of the structure of the growth striations     

Representation of a Monotone Curve by a Contour with Regular Change in Curvature

The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.     

Fourth-Order Rotational Corrections to the Effective Dipole Moments of Nonrigid Asymmetric Rotors

An expression for the fourth-order rotational correction terms of the effective dipole moments of nonrigid asymmetric rotors has been derived using the method of contact transformation. The treatment takes into account the large-amplitude bending motion. The correction terms have been calculated for the different bending states of the H(2)O molecule. A poor convergence of the rotational series for this molecule has been obtained and some different nonpolynomial forms for these series, obtained by different summation methods, have been proposed and tested. Copyright 2001 Academic Press.     

Classification of the Phenomenological Models of Phase Transitions with Two Interacting Order Parameters Using the Catastrophe Theory: <Emphasis Type="Italic">L</Emphasis> = <Emphasis Type="Italic">C</Emphasis><Subscript>2<Emphasis Type="Italic">v</Emphasis></Subscript>

The phenomenological models of phase transitions for two one-component interacting order parameters have been classified using the methods of the equivariant catastrophe theory. The models have been constructed based on the number of control parameters, which depend on the thermodynamic parameters varied in experiments (temperature, pressure, chemical potentials of impurities, etc.), rather than by simple expansion of the thermodynamic potential in series of order-parameter powers. The models with the order-parameter symmetry group L = C_2v are classified in terms of the number of control parameters from two to five. An infinite series of the phenomenological models with biquadratic interaction of the order parameters was also obtained.     

Experimental test of the EEC wind climatology model in a Mediterranean coastal area

Summary The analysis of 18 months of meteorological measurements collected in three stations located in Sardinia (Italy), is presented. The experimental wind distributions for 12 sectors of 30 degrees each have been fitted with the Weibull distribution function. The experimental Weibull parameters have been compared with the ones simulated by using the model produced within the EEC programme ?Wind Atlas for Europe?. Discrepancies between the experimental and simulated wind distributions have been discussed. Time series of the three stations have been compared to study the modification of the characteristics of the air flow from the coast to inland. Statistics of the atmospheric stratification, based on the concept of Pasquill stability classes has been produced by using semi-empirical methods. Further developments have been suggested.     

Wavelength dependence of the numerical aperture of optical fibers

Wavelength resolved measurements of the numerical apertures and the profiles of graded index fibers have been performed by the far- and near-field methods, respectively. Quantitative results for the spectral dispersion of the numerical aperture of fibers are in very good agreement with theoretical results, which are obtained by using a 3-term Sellmeier series. Together with spectral attenuation measurements these results allow the approximate determination of fiber dopants.     

Application of Computer Algebra in Solving Chaffee--Infante Equation

In this paper, a series of two line-soliton solutions and double periodic solutions of Chaffee-Infante equation have been obtained by using a new transformation. Unlike the existing methods which are used to find multiple soliton solutions of nonlinear partial differential equations, this approach is constructive and pure algebraic. The results found here are tested on computer and therefore their validity is ensured.     

在WBEPM理论中受扰里德堡能级研究

在最弱受约束电子势模型理论下,研究了外来微扰能级对里德堡能级系列的影响,给出了确定外来微扰能级位置的方法.依此计算了钡原子6snp(n≥15).P1和6snd(n≥9)3D3两个里德堡能级系列的量子数亏损和能级.计算结果和实验值的绝对误差在1 cm-1以内,达到了较高的精度.     

等离子体色散函数的计算方法

本文推出了复宗量ξ=x+iy的误差函数的级数表达式。在这一基础上,对0≤y≤1,|x|≤10宗量区,给出了较高精度的等离子体色散函数Z及其微商Z'的计算方法。进而,对复平面ξ的各个区域,系统地研完了等离子体色散函数和相应的计算方法;在VAX—11/750计算机上得到了满意的结果,文章对这些结果,所用方法及其精度作了讨论;分别对y≥0和y<0,描述了Z和Z'的基本行为。     

A prediction method for the effects of flight on subsonic jet noise

The noise of a single-stream circular jet and that of a coaxial jet with coplanar nozzles of 2·5 area ratio have been measured under simulated flight conditions in the RAE 24 ft wind-tunnel. The majority of tests were conducted with the single-stream jet and primary section of the coaxial jet at a nominal temperature of 880 K. The data have been used to quantify the effect of jet temperature and were combined with measurements from an earlier test series to establish a prediction method for the effect of flight on the noise of single-stream subsonic jets. This method is based on jet noise theory modified by experimentally derived constants. For coaxial jets it is concluded that the noise reductions, which are independent of the secondary stream velocity, are predicted to an acceptable degree by the method suggested for unheated single-stream jets. The prediction methods are suitable for both OASPL's and spectra.     

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane–air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.     

On spectral methods for solving nonlinear acoustics equations

Two very efficient methods for obtaining approximate solutions to nonlinear acoustics equations are discussed. I proposed these methods earlier, but they are still little known. The first method is based on expanding an unknown function into a Taylor series with respect to the coordinate (evolution variable) and on approximate summation of the terms of this series in all orders up to the infinite order. This series can be summed completely only in particular cases, e.g., for a simple wave. It has been noted that the partial summation technique is implemented more easily if all the terms of the series are represented as corresponding topological diagrams. The second method is based on introducing a “nonlinear” phase delay (proportional to the wave amplitude) for the temporal variable in linear solutions of the problem. The application technique of these methods is illustrated by obtaining approximate solutions of the Burgers equation.     

高电荷态ECR离子源的金属离子产生

简单介绍了采用炉子加热、 挥发性金属化合物和溅射产生ECR离子源的金属离子的3种方法和实验结果, 主要研究了铜、 锌、 镍和铁等多种电荷态离子的产生．　对3种方法分别进行了探讨．To satisfy the requirements of HIRFL (Heavy Ion Research Facility in Lanzhou), series of experiments have been done to produce metallic ion beams. By now, numerous methods have been tested, in which MIVOC (Metallic Ion from Volatile Compounds), heating oven methods and plasma sputter methods are all included. According to the experiments, the results of using MIVOC methods and heating oven methods are very good. In most of our researches, emphasis was put upon the ion production of iron, Nickel, Tantanum, copper of different charge states. Among the ion beams we have obtained, 210 μA Fe11+, 175 μA Fe12+, 142 μA Fe13+, 25 μA Fe16+, 64 μA Ni10+, 57 μA Ni13+, 31 μA Ni15+ and 15 μA Ni16+ are representative results.