Simplified mobility expressions for infinite in-vacuo pipes

In this paper, closed-form expressions for the mobility of the circumferential modes in an infinite in-vacuo thin-walled pipe are derived in terms of the axial wave receptances for each mode. These expressions are valid below the ring frequency. By using simplified expressions for the wavenumbers, low-frequency approximations for the point and transfer mobilities are also derived. These new mobility expressions are validated experimentally, and are used to examine the dynamic behaviour of an in-vacuo pipe.     

Vectorial Hermite--Laguerre--Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh--Sommerfeld integrals, the free-space propagation expressions for vectorial Hermite--Laguerre--Gaussian (HLG) beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.     

Multiquantum incoherent neutron scattering from molecular solids

General expressions are obtained for the scattering of neutrons from molecular solids with the exchange of m-quanta. Explicit expressions are obtained for the total cross section, when both the phonon and the torson modes are given by the Einstein distribution functions. The expressions can be readily utilized to understand neutron scattering from a molecular crystal.     

Correct determination of net gain in Er-doped optical waveguide amplifier from pump-on/off measurement

Starting with evolution equation of signal optical power in an Er-doped channel waveguide, rigorous theoretical expressions used for correct determination of net gain from signal enhancement measured by using pump-on/off method are derived. These expressions allow to clarify the argument on relationships between net gain, internal gain and signal enhancement in some earlier literatures. Physical implications of net gain, internal gain and signal enhancement expressions are analyzed. Standardized definitions for the three physical quantities are proposed. The definition for net gain is proposed on the basis of practical application of an EDWA in optical fiber communication and the definitions for the latter two are suggested based on the physical implication analysis of their expressions.     

Harmonic and intermodulation performance of Josephson junctions

In this paper a simple mathematical model is presented for the inherent resistive nonlinearity of a Josephson junction. By incorporating this model in the RSJ model of the Josephson junction, series expressions are obtained for the harmonic and intermodulation performance of Josephson junctions irradiated by multisinusoidal signals. Special cases are considered where the series expressions can be reduced to simple analytical expressions.     

高能激光准直传输远场斯特雷尔比与数值验证

利用扩展惠更斯-菲涅耳原理对高能激光在大气中的传输进行了分析,获得了高能激光准直传输轴上及峰值斯特雷尔比的积分表达式,并使用激光大气传输四维仿真程序对该表达式的适用范围进行了分析及数值模拟验证。结果表明,积分表达式可以很好地适用于无自适应光学系统补偿时的高能激光湍流热晕传输问题,可以用于自适应光学系统补偿时弱热晕条件下的湍流热晕角非等晕问题和弱热晕及中等热晕条件下的湍流热晕聚焦非等晕问题。     

Nonparaxial elegant Laguerre-Gaussian beams

Closed-form nonparaxial expressions for optical beams are useful to calculate the fields produced by tightly focused laser beams. Such expressions for elegant Laguerre-Gaussian (eLG) beams that are exact solutions of the Helmholtz equation are introduced. These solutions are expressed as linear combinations of a finite number of analytic functions that involve spherical Bessel functions and associated Legendre functions of complex arguments. In the paraxial limit, the expressions proposed have the property to reduce to the well-known eLG beams.     

Radar cross sections of a random medium layer

Analytic expressions are derived for the normalized radar cross sections (NRCS) of a random medium layer. These are calculated from the first-order solutions for diffuse intensities which are based on a multiple-scattering wave theoretical analysis. The permittivity fluctuations are assumed to be small and to obey stationary Gaussian statistics. On studying the expressions for the NRCS, some of their characteristics are pointed out. Three different correlation functions are considered and expressions for the coherent propagation constants are provided. Numerical examples are used to verify theoretical results and highlight some interesting characteristics of NRCS.     

Mass and spin of Poincaré Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincaré Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.     

The general theory for calibrating two arbitrarily oriented phase plates

The general expressions for the retardances of two phase plates arbitrarily oriented between two polarizing prisms are presented. It is shown that more accurate results are obtained if measurements are performed at particular orientations of the plates. Compact formulas for the retardances at these orientations are directly derived as special cases from the general expressions. Also, some aspects related to the calibration model like the sensitivity of measurements to the relative orientations of the plates can only be treated using the general expressions.     

电容器通过变压器对脉冲形成线充电过程

 从T模型等效电路出发,在等效电路中磁化电感两端的电压在形成线等效电容充电到第一个峰值之前变化较小这一假设之下,推导了电容器通过变压器对脉冲形成线充电的解析表达式,给出了考虑回路存在电阻和杂散电感下的表达式。最后利用电路模拟来验证解析表达式,结果表明:给出的解析表达式能够较好地分析电容器通过变压器对脉冲形成线充电过程;在形成线充电的第一个半周期内,解析理论得到的结果与模拟结果比较吻合,在原边电容和形成线等效电容可比较的情况下,从变压器耦合系数较低（不超过0.7）到耦合系数接近于1的情况都适用。     

On the cryogenic magnetic transition and martensitic transformation of the austenite phase of 7MoPLUS duplex stainless steel

The magnetic behaviour and martensitic transformation at cryogenic temperatures (down to 4 K) of the austenite phase of the duplex stainless steel (DSS), 7MoPLUS, were studied. As regards the prediction of Neel temperature, the empirical expressions for austenitic stainless steels are not applicable to the austenite phase of 7MoPLUS, although the composition of the austenite phase falls within the composition ranges within which the expressions were developed. Regarding the prediction of martensitic point Ms, the applicability of ‘old’ and recently developed expressions has been examined. The recently developed expressions, which take into account more alloying elements and their interactions, are not suitable for the austenite phase of 7MoPLUS. But for the ‘old’, simpler expressions, they seem to be valid in the sense that they all predict high stability of the austenite phase. Results obtained from 7MoPLUS were qualitatively the same as those obtained from another DSS, designated as 2205. Reasons for the applicability and inapplicability of these empirical expressions are suggested.     

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan--Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus--Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of Percus-Yevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.     

Harmonic and intermodulation performance in an R-LED series network

Analytical expressions are obtained for predicting the harmonic and intermodulation performance of R-LED series networks. These expressions are in terms of the ordinary Bessel functions with arguments depenedent on the modulation index.     

Equivalence of the angular forces in the lattice dynamics of fcc metals

The expressions for the Clark, Gazis and Wallis type of angular forces are rederived in the caseof fcc metals. These expressions are now foundtobe equivalent to the deLauney type of angular forces.     

Polarizability of two conducting spheres

Exact series expressions are obtained for the longitudinal and transverse polarizabilities of a system of two conducting spheres, for arbitrary sphere radii and separation. In the important case of close approach, where the exact series converge slowly, approximate analytical expressions are obtained. These analytical expressions become more accurate as the distance between the spheres gets small compared to the sphere radii, and reduce to the known analytic values at sphere contact.     

Validity of local density kinetic energy expressions for electronic structure calculations

Local density expressions provide a simple and flexible means of calculating kinetic energies. Recently it has been ascertained that such expressions can be quite accurate (to within 1%) in obtaining the total kinetic energy of an atomic system. However, we shall demonstrate that local density kinetic energy expressions, as presently formulated, are not appropriate for molecular or solid state calculations. In particular, these expressions do not properly describe trends appropriate for valence electron charge density configurations.     

Breit-Pauli哈密顿的正确张量表达式

采用不同的方法,对Breit-Pauli哈密顿中的自旋-其它轨道相互作用和轨道-轨道相互作用的球张量形式重新进行了推导,给出了自旋-其它轨道相互作用和轨道-轨道相互作用哈密顿的球张量形式的正确表达式,指出了文献中所列出的这类表达式的错误,提供了导出这些表达式的中间步骤.