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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Exact formulation of multiple scattering in a three-dimensional cylindrical geometry

Exact expressions for the source function, flux, and scattered intensity normal to the surface are developed in cylindrical coordinates for a three-dimensional, absorbing, emitting, isotropically scattering medium exposed to both diffuse and collimated radiation. Simplifications of these expressions for certain important geometries and uniform loading are presented. Also, superposition of these equations and radiative equilibrium are discussed. The generalized three-dimensional equations are shown to reduce to the familiar one-dimensional results. Also, the equations for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function are expressed in terms of the isotropic expressions.     

Radar cross sections of a random medium layer

Abstract

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.     

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.     

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.     

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.     

Multiple-order derivatives of a waveguide acoustic field with respect to sound speed, density, and frequency

An adjoint perturbative method is used to derive expressions for the first- through third-order derivatives of a pressure field with respect to sound speed, density, and frequency, for the restricted case of a laterally homogenous waveguide in which environmental parameters are only a function of depth. By using a normal-mode Green's function, the three-dimensional spatial correlation required by the standard acoustic adjoint equation can be reduced to a set of one-dimensional depth integrals. The resulting expressions for the first-order derivative are similar to those obtained by previous perturbative approaches based on the depth-separated wave equation, but the approach followed here permits straightforward extension to higher-order derivatives. Explicit evaluations of the expressions for a representative shallow-water waveguide model are in excellent agreement with numerical finite-difference computations. An analysis of the expressions as a function of source-receiver range finds the contributions to the mode amplitude derivatives to be non-negligible at ranges less than a few modal interference lengths, for parameters associated with the ocean bottom. Therefore, linear perturbative inversion methods that perturb only horizontal wavenumbers and not mode amplitudes should either be used with caution or modified to incorporate the expressions presented here.     

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.     

Universal LCAO parameters for III–V compound semiconductors

A set of semi-empirical expressions for the two-center integrals which enter the Slater-Koster parameters are constructed for Group III–V compound semiconductors These expressions show their explicit dependence on the atomic characteristics, on the dielectric constant, on the lomcity of solids, and also on the interatomic separations, and they are valid for atomic separations as far as second-neighbor distances For zero ionicity they reduce to those obtained previously by us for Group IV semiconductors The Slater-Koster parameters are then constructed from these expressions for the two-center integrals The band structures of various gallium and indium compounds are obtained and are compared with other theoretical calculations and with experimental photoemission results     

Resonant excitation of evanescent spatial harmonics in medium formed by parallel metallic nanorods

The results of analytical modeling of the resonant excitation of evanescent harmonics in a medium formed by parallel metallic nanorods taking into account the spatial dispersion are presented. Analytical expressions are derived for the reflection and transmission coefficients, as well as for the amplitudes of electromagnetic waves inside the medium. These expressions are compared to similar expressions that were previously obtained using a local model of an ultimately anisotropic material without taking into account the spatial dispersion. The obtained expressions are simplified for various partial cases, including the superresolution imaging of a source that is located at a considerable distance from the metamaterial layer. A layer of a medium composed from finitesized wires is numerically simulated and it is demonstrated that, due to the effect of resonant excitation of evanescent spatial harmonics in the layer, subwavelength details of an object that is considerably distant from the layer can be distinguished inside of the layer.