A NEW MATRIX METHOD FOR SOLVING VIBRATION AND STABILITY OF CURVED PIPES CONVEYING FLUID

This paper proposes a new matrix method for calculating critical flow velocity of curved pipes conveying fluid, which have arbitrary centerline shape and spring supports. Its main advantage over other methods is that the corresponding characteristic equation can be reduced to a third order one, no matter how many elements are discretized in calculation. This will lead to saving computer time and obtaining a solution with good precision.     

Evaluating the topological charge density with the symmetricmulti-probing method

We evaluate the topological charge density of SU(3) gauge fields on a lattice by calculating the trace of the overlap Dirac matrix employing the symmetric multi-probing(SMP) method in 3 modes. Since the topological charge Q for a given lattice configuration must be an integer number, it is easy to estimate the systematic error(the deviation of Q to the nearest integer). The results demonstrate a high efficiency and accuracy in calculating the trace of the inverse of a large sparse matrix with locality by using the SMP sources when compared to using point sources.We also show the correlation between the errors and probing scheme parameter r_(min), as well as lattice volume N_L and lattice spacing a. It is found that the computational time for calculating the trace by employing the SMP sources is less dependent on N_L than by using point sources. Therefore, the SMP method is very suitable for calculations on large lattices.     

轴对称构件受力分析的插值粒子法

面对土木工程与机械工程中广泛存在的轴对称力学问题, 采用具有离散点插值特性的无网格方法形函数, 结合弹性力学空间轴对称问题的最小势能原理, 建立了轴对称构件力学分析的插值粒子法. 本文无网格法方法构造形函数不依赖网格, 也具有像有限元法一样可直接施加边界条件的优点. 本方法能直接获得全域连续应力场, 避免了有限元法应力后处理二次拟合带来的计算误差. 最后通过实例分析, 验证了所建立的无网格方法的有效性.     

A density matrix formulation of the theory of magnetic resonance spectra in slowly reorienting systems

When a spin system is coupled to a molecule or part of a molecule which is reorienting at a rate comparable to the width of the powder spectrum, the line shape can be calculated from a density matrix which is a function both of spin operators and of the Euler angles describing the molecular orientation. The problem of calculating such line shapes is eased by using the super-operator formalism and choosing symmetry adapted basis operators in the Liouville space of spins and orientations. Diffusion and strong collision models for molecular reorientation are discussed.     

Fast Estimation of Scatter Components Using the Ordered Subset Expectation Maximization Algorithm for Scatter Compensation

In this work we propose a method for scatter compensation in single photon emission computed tomography imaging, by which we can estimate the scatter components in projections in high speed with good accuracy. The method is that we first estimate the scatter components in projections based on scatter response kernels by one time of ordered subsets expectation maximization iterative reconstruction, and then subtract the estimated scatter components from the projections and complete reconstruction by filtered back-projection method. The principle is that the image corresponding to the scatter components in projections consists largely of low-frequency components of an activity distribution; these low-frequency components will converge faster than the high ones in iterative reconstruction. Therefore, we can estimate the low-frequency component image before the image converges with the high-frequency ones, and obtain the scatter components by re-projecting the low-frequency component image with scatter response kernels. The effects of the proposed method were compared with the dual- and triple-energy window methods using experimental measurements. The results show that good accuracy in estimated scatter components, good uniformity of scatter compensation at the center and the side of an object, and good noise property can be acquired by this method.     

On the polarizability of a pair of cylinders in a transverse electric field

A sequential scheme for calculating the polarizability of a pair of parallel cylinders with an arbitrary (but fairly symmetric) form is suggested. An infinite set of algebraic equations is derived for coefficients involved in an expression for the potential. The numerical solution of this set makes it possible to find the polarizability with any degree of accuracy. This method is unrelated to the cylinder shape. The electrostatic properties of the cylinders are described in terms of the multipolar polarizability matrix.     

On the theory of conductivity of anisotropic composites: A linear-concentration approximation of inclusions

A general approach is proposed for calculating the conductivity of anisotropic composites with a low concentration of inclusions of an arbitrary shape. The contribution to effective conductivity [^(s)] _e\hat \sigma _e, which is linear in concentration, is expressed in terms of the polarizability of the inclusion defined in a certain transformed system in which the inclusion is surrounded by an isotropic matrix. A transition to this system is performed using a symmetry transformation that does not change the equations for direct current.     

稀土掺杂固体发光材料的光谱分析

光谱分析是评价稀土发光材料光谱性质的主要依据,Judd-Ofelt(J-O)理论是光谱分析的基础。详述了采用J-O模型拟合三个强度参量和估算一些重要辐射参量的操作细节,讨论了相关公式的合理应用,总结了计算中误差的主要来源,并推荐了一种通过低温实验获得较可靠光谱参量的途径。建议采用透射光谱数据计算实验跃迁振子强度,吸收系数和吸收截面的计算应该扣除光反射、散射和基质本身吸收的影响,平均波数和平均波长的取值须考虑线形因子。并建议通过发射光谱的实测线形计算各波长的发射截面。由于J-O模型涉及许多近似和假设,计算结果误差较大,可能导致结果不可靠。通过分析指出,采用低温下测得的能级寿命和荧光分支比进行相关参量的估算可获得较可靠、较有意义的结果。     

同位素Tl-201的单光子发射CT影像的康普顿散射校正

给出一种基于康普顿散射理论的Tl-201 SPECT影像的散射校正方法,此方法仅考虑一次散射和二次散射的影响.计算中将散射介质分成散射小元,然后积分求出每一小元内所有电子的散射光子数,一个电子的散射几率由Klein-Nishina公式确定,散射光子被分配至散射小元中心对应的探测器接收孔位置.辐射源的奇点问题也通过这种积分方法解决.误差主要来自于计算中有限的散射元体积和受限制的散射介质,但计算的线源响应函数和散射比与Monte Carlo计算结果相符,计算时间缩短40倍.     

Modeling elastic wave forward propagation and reflection using the complex screen method.

Formulation for calculating forward propagation and reflection in a 3D elastic structure based on the complex-screen method is given in this paper. The calculation of reflections is formulated based on the local Born approximation. When using a small angle approximation, the backscattering operator reduces to a screen operator which is similar to the forward screen propagator. Combining the forward propagator and backscattering operator together, the new method can properly handle the multiple forward scattering and single backscattering in a 3D heterogeneous model. Using a dual-domain technique, the new method is highly efficient in CPU time and memory savings. For models where reverberation and resonance scattering can be neglected, this method provides a fast and accurate algorithm. Synthetic seismograms for two-dimensional elastic models are calculated with this method and compared with those generated by the finite-difference method. The results show that the method works well for small to medium scattering angles and medium velocity contrasts.     

Minimum-Covariance Estimates of Signal Parameters

We show the existence of the only procedure ensuring the absolute minimum of an arithmetic mean covariance in a certain parameter-variation range and coinciding identically with the algorithm for calculating the estimate minimizing the mean risk for a quadratic loss function and a uniform a priory distribution of parameters. This procedure is compared with the standard method for obtaining maximum likely estimates. In particular, it is shown that the procedure ensures a significantly smaller random scatter of estimates during the estimation of deterministic-signal parameters against the background of Gaussian interference. In the case where the estimate covariance is independent of the parameter estimated for physical reasons, the use of the above procedure with an arbitrary sample size allows us to reach the actual attainable variance bound.     

Improved analysis of dispersion penalty in optical fibre systems

Based on the model presented by Campbell [1], simple and convenient formulae are developed for calculating the dispersion penalty with consideration of the system pulse shaping, the laser diode spectrum and the different statistics of mode partition noise within and between baud periods. Numerical calculations show that they are good approximations of the complex expressions given by Campbell. Furthermore, we show that Ogawa's mode partition noise expressions in [2] should be corrected by a factor of about 2 and the wave shape at decision should be carefully designed to minimize the mode partition noise.     

非线性反馈控制强流加速器中的束晕—混沌现象

 基于Poincare-Lyapunov定理, 应用定性分析,提出用非线性反馈法实现对束晕-混沌的控制。矩阵传输理论研究已发现：质子束的空间电荷效应导致质子束径向发散及束晕现象。因此, 构造一类正弦等形式的非线性反馈函数去抵消质子束空间电荷非线性效应。PIC数值模拟结果证实该方法的可行性,为实验提供一定理论依据。     

卫星平台高光谱复杂运动成像伪互相关退化仿真研究

针对具有推扫机制的狭缝体制成像光谱仪受卫星平台俯仰、侧滚、偏航等复杂运动的影响,导致光谱数据精度降低的问题,在成像光谱仪运动成像光谱微分动态成像退化仿真方法的基础上,提出基于点扩散矩阵的光谱退化理论。按照八邻域掺杂模型,考虑卫星平台运动的时变性,不同目标像元的点扩散矩阵不同,符合伪互相关运算的概念,因此提出运动成像的伪互相关光谱退化理论。其中,点扩散矩阵由星上POS数据运用微分像移理论计算八邻域掺杂像元的平均掺杂比得到,在用模拟POS数据曲线仿真计算点扩散矩阵时,发现依据掺杂影响的大小,点扩散矩阵可以简化以便减小运算量。明确阐述光谱运动成像的伪互相关退化理论的表述和计算方法,对退化仿真和计算的结果从图像维和光谱维分别进行了定性和定量的效果评价,并使用结构相似度参数展示了退化图像与原始图像的相似性。运动成像的伪互相关光谱退化理论完善了已有的基于卫星平台复杂运动的光谱数据退化问题,仿真结果表明此种退化理论完全适用于解决卫星平台复杂运动条件下的光谱数据退化问题。     

Anomalous diffraction effects observed on the x-ray diffraction patterns of decomposing supersaturated solid solutions

The basic purpose of an x-ray study of the initial stage of the decomposition of a supersaturated solid solution is to determine the shape, size, and relative orientation of the anomalous-scattering regions in the reciprocal lattice (in reciprocal space) from the anomalous diffraction effects observed on the diffraction patterns. From the size, shape, and relative orientation of the various anomalous-scattering regions in reciprocal space one can draw quite reliable conclusions regarding the nature of the same distortions in the matrix lattice, due to the observed anomalous diffraction effects. An analytic method is proposed for calculating the anomalous-scattering regions in reciprocal space for the most general case of an unknown crystal orientation.     

Is the detailed shape of the nuclear charge distribution relevant to the ft values of superallowed Fermi transitions?

The uniform nuclear charge distribution remains a satisfactory model for calculating electron radial wave functions and nuclear matrix elements even in the case of the superallowed Fermi transitions of light nuclei up to ⁵⁴Co, where high accuracy is needed to determine the vector coupling constant of nuclear β-decay. The modifications due to the deviation of the realistic charge distribution from this simple model are found to be smaller than previously thought and therefore are negligible, provided that the nuclear radius, which is the most important shape parameter, has its correct value (i.e. the r.m.s. radii of the realistic and the model distribution are the same). Moreover, the dependence on the nuclear radius is fairly small for the light nuclei under consideration.     

Isotropic matrix elements of the collision integral for the Boltzmann equation

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.     

An interpolating reproducing kernel particle method for two-dimensional scatter points

An interpolating reproducing kernel particle method for two-dimensional(2D) scatter points is introduced. It eliminates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating reproducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.     

Synthesis and Spectroscopy of Silica Nanoparticles as Scatter Centers in Random Gain Porous Media

This work was carried out to synthesis a silica matrix by sol-gel technique, which used as host to Kiton Red laser dye doped with silica nanoparticles, which also prepared by sol-gel technique, to obtain KR-SiO₂ nanoparticles confined in silica xerogel matrix. The rods at different pH values were successfully synthesized. The different values of pH cause different size of obtained nanoparticles, these nanoparticles act as scatter centers in the matrix. Amplified spontaneous emission (ASE), threshold pumping energy (E_th), and mean free path (l_t) for photons in the rods have been reported. the results show that the values of bandwidth at full width half-maximum (FWHM) and the threshold energy are about 8.7 nm and 12 mJ respectively.