Track fitting in the OPAL vertex detector with stereo wires

The geometry of the vertex chamber for the OPAL detector at LEP is reviewed and expressions for the coordinates of the hits are given in terms of the measured drift distance and z-coordinate. The tracks are fitted by a procedure based on the Lagrange multipliers method. The increase in the accuracy of the fit due to the use of the stereo wires is discussed.     

An estimation procedure for the disposition of fitting parts

This article deals with the estimation of the functional parameters of a (normal-)distribution from grouped samples. In contrast to the well-known problem, in the present investigation the data are classified into several noncontiguous and overlapping intervals (i.e., the classes arenot mutually exclusive). Therefore, conventional methods cannot be applied. Of course, this grouping is not done intentionally, but is due to certain “production requirements”. Two methods, based on maximum-likelihood and minimum-X ², are derived in order to handle this awkward situation and to render an estimation possible. Numerical results of a simulation study show that both methods lead to fair results, provided that the sample size is large enough.      

A fast method for direction-of-arrival estimation

In many eigenvalue-eigenvector-based direction-of-arrival estimation algorithms, one finds orthogonal basis vectors for the noise subspace. We propose a circulant basis for the noise space which can be calculated more efficiently than an orthogonal basis. The new method for high signal-to-noise ratio (SNR) has a performance similar to the well-known MUSIC algorithm but can be implemented much more efficiently.     

Incoherent beam combining using fast steering mirrors

Incoherent beam combining (ICBC) is a promising technique that can increase the total power of the lasers without decreasing the beam quality. Fast steering mirror (FSM) can be used in ICBC system to overlap the laser beams as well as suppress the jitter of the platform and the tip-tilt component of the turbulence. In this paper, a method using FSMs for incoherent beam combining is proposed and the relationship between the emergent light and the control voltages is derived, then the stochastic parallel gradient descent algorithm is adopted to calculate the optimal control voltages applied to the FSMs. A series of simulations combining two laser beams are carried on under static and dynamic turbulence. In order to verify the feasibility of this scheme, the dynamic turbulence is simulated under the hypothesis of Taylor’s frozen turbulence. The results of simulations show that the turbulence would severely degrade the result of combining and the correction process would resist the influence and assure the evaluation function can reach the ideal situation at last. The model of the scheme used in this paper can be easily utilized for arbitrary amount of the lasers.     

Three-dimensional track and vertex fitting in chambers with stereo wires

A formalism has been developed, and used in the TASSO experiment, for track fitting and geometrical vertex fitting in a uniform magnetic field. A two-dimensional fit, suitable for many detectors, has been extended into three dimensions in the case of cylindrical drift chambers with small-angle stereo measurements. Error matrices are calculated which are suitable for input to subsequent calculations. Multiple scattering is approximated by a model.     

A model for fitting peaks induced by fast neutrons in an HPGe detector

Inelastic neutron scattering in the HPGe detector produces wide, triangular-shaped peaks in the spectrum. We develop an accurate model for the peak shape and show that the inclusion of the model in the gamma spectrum analysis makes it possible to quantify fast neutron scattering in the Ge crystal and improves the estimation of the baseline. This in turn facilitates the detection of fission products present at trace levels in environmental samples. The model, together with simulations, is used to deduce some properties of the underlying neutron energy distribution. The neutron evaporation temperature of 1.1 MeV is obtained from the analysis of environmental monitoring gamma spectra.     

A surface fitting method for three dimensional scattered data

A method is presented that may be used to empirically establish the type of relationship that is present between a response variable and its influencing factors, by fitting a mathematical model to three dimensional scattered data. The generated response surface is composed of continuous triangular planes that are fitted to the corresponding data in the least squares sense. The method may be easily implemented. It requires some fairly large number of scattered data, two initial boundary conditions and a desired accuracy for the band-wise partitioning of the data. The proposed surface fitting technique has been successfully applied to solar radiation modelling for a number of different data combinations.     

A fast wavelet-multipole method for direct BEM

A fast wavelet-multipole method (WMM) has been developed to achieve further speedup for the boundary element method in solving the direct boundary integral equations. The main idea is to compute the right-hand-side vector by the fast multipole method and to solve the linear system by the wavelet compression method. By using the variable order moments, almost linear complexity can be obtained. The primary advantages of the present WMM lie in that it (1) permits efficient implementation; (2) is universal in handling practical problems with complicated geometries. Numerical examples with around 1 million unknowns, performed on nontrivial geometries, clearly show that the WMM can shorten the total computational time by reducing the time for computing the right-hand-side.     

A fast numerical procedure for steady capillary flow in open channels

The surface evolver (SE) algorithm is a valued numerical tool for computations of complex equilibrium interfacial phenomena. In this work, an iterative procedure is implemented such that SE can be employed to predict steady-state flows along capillary channels of arbitrary cross-section. As a demonstration, a one-dimensional stream filament flow model is solved that approximates the pressure changes inside the channel. Despite its simplicity, the precision, stability, and speed of the method affirm it as an efficient and unique design tool for a variety of capillary flow problems. The procedure is ideally suited for slender column flows such as open wedge channel flows, several of which are validated herein via parabolic flight and drop tower experiments.     

A least squares method for fitting head fields by parametricequations

Models of magnetic recording systems generally require the field of the record head to be calculated. In the interests of speed a simple, but accurate, analytic expression is desirable. In this paper the method of minimization of squared residuals is used to obtain parameters defining a parametric approximation to the head field. As an example parameters are obtained which give best fits to finite pole tip head fields produced by conformal mapping. It is found that a good set of parameters is obtained by separately characterizing the infinite pole length head field and correction terms due to the outer pole edges evaluated at the medium surface. The same method could be used to fit measured data or fields obtained using numerical models     

一种快速求解宽频简正波的方法

针对宽带信号的简正波解,传统的求解简正波数值方法常常需要重复计算本征值方程,计算效率低。文中将频率的变化当作扰动,提出利用微扰理论得到参考频率附近的简正波解。该方法具有直接、精确、高效的特点,计算得到的水平波数和本征函数与KRAKENC程序计算结果吻合较好,两种方法计算得到的脉冲波形最大相关系数大于0.97。     

快速控制反射镜系统中的传递函数辨识

提出一种传递函数辨识方法。该方法使用非线性最小二乘曲线拟合法,结合控制对象的传递函数模型选取参数初始值,针对不同的频率特性分段拟合。使用该方法可以将复杂的控制系统频率特性转化为高精度的传递函数。在系统的中低频段内获得幅频±1dB和相频±1°的传递函数辨识精度。由此设计的数字补偿器有效补偿了机械谐振带来的影响,扩宽了控制系统的闭环带宽。传递函数辨识方法摆脱了数字补偿器设计依赖手工调试的状况,并可以提供复杂的数字补偿器以得到高性能的控制系统。     

A procedure for approximation of the error in the EFG method

In this paper, we present a procedure to estimate the error in elliptic equations using the element‐free Galerkin (EFG) method, whose evaluation is computationally simple and can be readily implemented in existing EFG codes. The estimation of the error works very well in all numerical examples for 2‐D potential problems that are presented here, for regular and irregular clouds of points. Moreover, it was demonstrated that this method is very simple in terms of economy and gives a good performance. The results show that the error in EFG approximation may be estimated via the error estimator described in this paper. The quality of the estimation of the error is demonstrated by numerical examples. The implemented procedure of error approximation allows the global energy norm error to be estimated and also gives a good evaluation of local errors. It can, thus, be combined with a full adaptive process of refinement or, more simply, provide guidance for redesign of cloud of points. Copyright © 2001 John Wiley & Sons, Ltd.     

Equivalent-strain method and crack vertex advance

Summary An approximate approach is proposed for determining the opening of a crack and the size of the plastic zone arising ahead of the crack front for bounded bodies. The basis of the approach is the equivalent loaded-state method. The method has been tested in solving various standard problems and has been found very effective.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 25, No. 2, pp. 16–19, March–April, 1989.     

一种快速检测光滑半球表面缺陷的方法

针对具有镜面反射特性的光滑球面,提出了一种利用反光带的镜像变形来对表面缺陷进行快速检测的新方法。这种方法通过漫反射反光带增强图像上的缺陷信息,克服了背景噪声在图像处理中会造成较大误差的缺点,也降低了照明系统的设计难度。根据缺陷引起的反光带镜像变形获取缺陷特征,使图像处理软件的工作量大大减少。通过实验,给出了缺陷尺寸和扫描间隔等因素对检测结果影响的分布曲线,为合理提取缺陷尺寸提供了参考。实验表明,该方法的鲁棒性好、效率高,能识别0.5mm以上的全部缺陷,定位误差在 1之内。     

A fast wavelet-based moment method for solving thin-wire EFIE

Solving the thin-wire electric field integral equation (EFIE) by the multiresolution wavelet expansion method involves a time-consuming double numerical integration for each nonzero element of the moment matrix which in turn can outweigh the advantages of achieving a sparse matrix. To speed up the matrix fill process in wavelet-based moment method codes, first, the triangular scaling functions of a nonorthogonal piecewise liner wavelet at the finest spatial resolution are appropriately replaced by sinusoidal dipoles for which mutual impedances are available in closed-form analytical expressions. The fast wavelet bases transform is then exploited to effectively transfer the resultant matrix equation to multiresolution wavelet domain. Numerical results obtained by the compactly supported semi-orthogonal linear B-spline wavelet demonstrate dramatic reduction of the overall solution time without any degradation in the accuracy of the final solution.     

A new procedure for lifetime determination using the Doppler-shift attenuation method

A new procedure for lifetime determination in singles measurements performed by means of the Doppler-shift attenuation method is proposed. An explicit separation of the shifted and unshifted fractions of the line-shape is achieved employing a summation over recoil histories calculated using a Monte-Carlo simulation. The lifetime is derived according to the Differential decay-curve approach. Tests with simulated data and experimental data analyzed earlier by a different method confirm the applicability of the procedure. Practical aspects of the new approach are investigated and discussed.