Electron scattering with open-shell molecules: R-matrix method

Many molecules with an even number of electrons belong to open-shell systems due to π ² ground state electronic configuration. This configuration gives rise to three low-lying states X ³ Σ ⁻, a Δ ¹ and b ¹ Σ ⁺. The inclusion of these target states in a trial wave function of the entire scattering system have important implications in the resonances that may be detected in these open-shell molecules. Various molecules like O₂, PX (X = H and halogens), SO, Si₂, BF have π ² ground state configuration. The R-matrix method is a well established ab initio formalism to calculate differential, integral and momentum-transfer cross sections for the elastic scattering of electrons by molecules. We have calculated these cross sections for PH and SO molecules in the incident electron energy range 0–10 eV. The results are obtained by using the R-matrix method in which the closecoupling expansion of the wave function of the scattering system includes only the ground state. This target state is described by configuration interaction wave function that includes correlation effects. The cross section for electron impact on PH and SO are presented.     

运用R矩阵方法研究低能电子与NO_2分子的散射

基于静电-交换和密耦合两种模型,采用R矩阵方法,研究了低能电子与二氧化氮自由基分子的积分散射截面和动量迁移散射截面,包括弹性散射和从电子基态到电子激发态的非弹性散射.采用aug-cc-pVTZ基组进行靶分子结构优化和散射研究.在密耦合模型中,包含6个电子的最低三个占据轨道1b_2,1a_1,2a_1被冻结,其余17个电子自由运动在活化空间中,并给活化空间增加了2b_1和7a_1两个虚轨道.包含了所有垂直激发能小于20 eV的靶分子电子组态,得到了收敛的散射截面,并与最新理论和实验值进行了比较.当入射能量小于4 eV时,本文结果与实验值符合得更好,校正了以往部分理论结果在极低能量处过高的现象,表明关联效应对于极低能量散射是非常重要的.     

Analytic method of arbitrary cross section open groove guide

Groove guide is one of the waveguides that have been used at millimeter and submillimeter waveband. This paper analyzes arbitrary groove guides by means of the eigen-weighted boundary integral equation method that uses the eigenfunctions of a fictitious regular boundary as weighting functions. In comparison with the theoretical and experimental results published, the numerical results for rectangular, circular and V-groove guides using this method are exact enough with fast convergence and less calculation.The Project Supported by National Natural Science Foundation of P.R. China     

A semi-analytical calculation method of bending loss for large-mode-area fibers with arbitrary refractive-index profile

Predicting mode-dependent bending loss is important for large-mode-area (LMA) fibers to strip out unwanted modes. In order to seek a reasonable calculation method, a new bending loss formula that allows for both mode field distortion and weaker mode confinement was derived in detail. Based on the formula, a semi-analytical method was introduced to calculate the mode bending loss for LMA fibers. By combining the applications of the finite element method, discrete Fourier transforms and numerical integral, the method is valid for LMA fibers with arbitrary refractive index profile. The obtained loss characteristics are basically consistent with the previous results. This accordance demonstrates the feasibility and generality of the semi-analytical method.     

Influence of groove depth and surface profile on fluorescence enhancement by grating-coupled surface plasmon resonance

The fluorescence intensity of a sample placed on a metal grating pattern is enhanced due to excitation by the electric field of the grating-coupled surface plasmon resonance (GC-SPR). The dependence of the enhancement on groove depth and surface profile was studied with the aim of improving the sensitivity of fluorescence detection. The enhancement was found to depend on the groove depth, with intensity most enhanced on grating substrate of about 20 nm depth, which produced an intensity about 30 times greater than that on a flat borosilicate glass substrate. Rigorous coupled wave analysis calculation showed that the shape of the groove influenced GC-SPR, suggesting that controlling not only the depth but also the shape of the grating surface profile can be an important factor in improving the sensitivity of detection by fluorescence microscopy.     

Numerical visualization of free surface oscillation predicted with arbitrary Lagrangian-Eulerian method

A numerical prediction method has been proposed to predict non-linear free surface oscillation in a three-dimensional container. The fluid motions are numerically predicted with Navier-Stokes equations discretized in a Lagrangian scheme with sufficient numerical accuracy. The profile of a free surface is precisely represented with three-dimensional body-fitted coordinates (BFC), which are regenerated in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) formulation. The computational method was applied to non-linear sloshings and transitions from sloshing to swirling motions. The predicted free surface motions were visualized as sequential image files and animations to understand their dynamic futures     

Analysis of circular fibers with an arbitrary index profile by the Galerkin method

We propose a full-vectorial Galerkin method for the analysis of circular symmetric fibers with arbitrary index profiles. A set of orthogonal Laguerre-Gauss functions is used to calculate the dispersion relation and mode fields of TE and TM modes. Examples are given for both standard step-index fibers and Bragg fibers. For standard step-index fiber with low or high index contrast, the Galerkin method agrees well with the analytical results. In the case of the TE mode of a Bragg fiber it agrees well with the asymptotic results.     

光散射聚集速率测定中T矩阵方法的应用

聚集速率是评估胶体体系特性及稳定性的关键参数, 静态光散射和动态光散射则是测量聚集速率的两个重要方法. 然而, 用静态光散射和动态光散射测量聚集速率时, 需要知道有关单粒子和双粒子聚集体光散射特性的数据. 为此, 通常需要把动、静两种方法结合, 才能消去这个数据. 以前各种近似理论曾用来解决这个问题, 但因粒子尺寸和形状的限制, 结果并不理想. 而T矩阵方法可以不受粒子大小和形状的限制计算其光散射特性. 本工作用T矩阵方法直接计算静态光散射和动态光散射所必须的粒子散射特性, 并将该法得到的聚集速率与动静态光散射结合法得到的聚集速率进行了比较, 两者结果很接近. 本工作为简化静态光散射和动态光散射测量聚集速率, 扩展其应用范围开辟了新途径. 关键词： T矩阵')" href="#">T矩阵 光散射法 聚集速率     

Prediction of sound absorption of a periodic groove structure with rectangular profile

Sound absorption of a periodic groove structure with rectangular profile is studied in this paper. On the basis of De Bruijn’s theory, by conducting matrix manipulation in MATLAB, a good prediction of the sound absorption of a periodic groove structure is obtained. Experiments in the Kundt’s tube are carried out and the results match the calculation well. This series of experiments and computation show that with the same period and the same ratio of absorber, groove structures have a much better sound absorbing ability than flat surface structures. Besides, a parametric survey has been done on the performance of the periodic groove structure and porous absorber as well. The parameters are the period of the surface, the ratio of the absorber, the depth of the groove, and the thickness, the flow resistivity, the open volume porosity and the structure factor of the porous absorber. Based on this survey, a periodic groove structure, as well as the porous absorber, with required sound absorbing capability can be created by arranging these parameters suitably.     

Noise field anisotropy of surface sources in a coastal region with arbitrary bottom relief and sound velocity profile

The noise field anisotropy of surface sources in a coastal region with an arbitrary three-dimensional bottom relief and an arbitrary sound velocity profile is investigated. The results of computations performed by a computer code in two stages are presented. The first stage consists in the computation of horizontal rays, i.e., the projections of the real rays multiply reflected from the bottom and sea surface onto the horizontal plane. The second stage summarizes the contributions of the noise sources lying within the surface elements that are cut out on the sea surface by a narrow ray tube launched from the point of observation in a given direction. The computations show that, in the coastal region, the noise field is essentially anisotropic, and this anisotropy occurs not only in the vertical plane, which is characteristic of the deep ocean, but in the horizontal plane as well.     

Sylvester theorem and the multichannel transfer matrix method for arbitrary transverse potential profile inside a wave guide

Based on the Sylvester and Frobenius theorems, we drastically enhance the feasibility of the transfer-matrix approach to deal with problems involving a large number of propagating and interfering modes, which require the solution of coupled differential equations and the evaluation of functions of matrix variables. We report closed formulas for the spectral decomposition of this type of functions. As specific example, besides the calculation of simple and well-known 1D one channel transfer matrices, we derive the multi-channel transfer matrix for an electron gas in the presence of a transverse electric field.     

Laser pulse transient method for measuring the normal spectral emissivity of samples with arbitrary surface quality

A laser pulse transient method for measuring normal spectral emissivity is described. In this method, a laser pulse (λ=1064 nm) irradiates the top surface of a flat specimen. A two-dimensional temperature response of the bottom surface is measured with a calibrated thermographic camera. By solving an axisymmetric boundary value heat conduction problem, the normal spectral emissivity at 1064 nm is determined by using an iterative nonlinear least-squares estimation procedure. The method can be applied to arbitrary sample surface quality. The method is tested on a nickel specimen and used to determine the normal spectral emissivity of AISI 304 stainless steel. The expanded combined uncertainty of the method has been estimated to be 18%.     

Finite-element analysis of dispersion and loss characteristics of groove guide with arbitrary shapes

The dispersion and loss characteristics of groove guide with arbitrary shapes are analyzed with high-order finite element method. The effectiveness and the reliablity of the method are verified by the experiments and the results obtained by other methods. Groove guides with various groove shapes, such as rectangular, triangular, parabolic, elliptic and cosine functions, are investigated systematically. The calculating results show that the dispersion of groove guide with different groove shape is almost the same, however, the loss characteristics is rather different; among them, V-shape groove guide has the lowest loss which is about half of the rectangular one. All the curves and the data given in this paper can be used in designing elements and circuits of the groove guide.     

金刚石刀具nm级表面轮廓质量多参数集成测量方法

为有效解决金刚石刀具表面轮廓质量评价指标分散、无法进行全面系统测量的难题,基于原子力显微镜和超精密回转轴系,提出了实现前后刀面粗糙度、刃口锋利度和刃口微豁三个关键指标的集成测量方法。根据金刚石刀具表面轮廓质量的测量要求,以原子力显微镜扫描系统、气浮隔振平台、二维移动平台以及精密回转轴系为基础构建测量系统,精确测量了金刚石刀具刃口附近的表面微观形貌;采用基于MATLAB开发的专用测量软件对原始数据进行处理,得到金刚石刀具前后刀面粗糙度值、刃口锋利度值和刃口微豁范围;并对测量误差进行了分析,提出了控制要求。通过上述自主开发的测量仪器,可以高效、完整地描述金刚石刀具表面轮廓质量,能够实现nm级粗糙度、亚m级锋利度以及m级微豁的准确测量。     

A fundamental theory of the half-shell t-matrix for nucleon-nucleon scattering

A dispersion-theoretic approach to the half-shell t-matrix is presented and applied to the ¹S₀- and ¹P₁-Reid interactions. This approach is shown to provide interesting dynamical insights about these half-shell t-matrices.     

Propagation of surface acoustic waves in a piezoelectric medium with a periodic groove structure

A system of equations is formulated to describe the propagation of surface acoustic waves in a piezoelectric substrate whose surface has a periodic structure formed by transverse grooves. Dependences of the reflection coefficient and the wave velocity on the geometry of the periodic structure (the width and the depth of the grooves) are obtained in a wide range of variation of these parameters for five different orientations in various piezoelectric crystals (quartz, lithium niobate, lithium tantalate, and langasite).     

Frequency selective surface with better polarization-independency for arbitrary incident angle

This paper investigates the frequency-selective property of a planar layer consisting of period arrays both theoretically and experimentally for different polarizations at arbitrary incident angle. The novel element is designed by loading the rectangular microstrip element with L-shaped conducting patch at its two ends. Based on the spectral-domain method, the frequency response including angle effect and polarization effect of the frequency selective surface (FSS) structure are analysed and the plots of the frequency versus transmission coefficient are obtained. As a result of the numerical analysis, it is shown that if the source polarization is changed, polarization-independence of previous FSS design can be achieved only for normal incidence, which limits most FSS applications. But in our proposed structure, the better polarization-independency for arbitrary incident angle can be achieved. It is observed that the simulated result comes very close to the experimental result.     

Analytical investigations of planar optical waveguides with arbitrary index profile

We present here an improvement of the existing equivalent attenuated vector (EAV) method. It is shown that our study gives not only analytical dispersion equation with clear physical insight, but also the extremely accurate propagation constants for planar waveguides with arbitrary index profiles.     

Channel plasmon-polariton in a triangular groove on a metal surface

One-dimensional localized plasmons (channel polaritons) guided by a triangular groove on a metal substrate are investigated numerically by means of a finite-difference time-domain algorithm. Dispersion, existence conditions, and dissipation of these waves are analyzed. In particular, it is demonstrated that the localization of the predicted plasmons in acute grooves may be substantially stronger than what is allowed by the diffraction limit. As a result, the predicted waves may be significant for the development of new subwavelength waveguides and interconnectors for nano-optics and photonics.     

Admittance of a groove on a rigid surface under a grazing flow

The problem of sound diffraction by a groove on a rigid surface in the presence of a grazing flow is considered. The input admittance of the groove is calculated, and its real part is shown to be negative.