Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

Measurement of remanent magnetic moment using a torsion pendulum with single frequency modulation method

In Tian Qin spaceborne gravitational-wave detectors, the stringent requirements on the magnetic cleanliness of the test masses demand the high resolution ground-based characterization measurement of their magnetic properties. Here we present a single frequency modulation method based on a torsion pendulum to measure the remanent magnetic moment mr of 1.1 kg dummy copper test mass, and the measurement result is(6.45 ± 0.04(stat) ± 0.07(syst)) × 10^(-8)A · m^(2). The measurement precision of the mr is about 0.9 n A · m^(2), well below the present measurement requirement of Tian Qin. The method is particularly useful for measuring extremely low magnetic properties of the materials for use in the construction of space-borne gravitational wave detection and other precision scientific apparatus.

An analysis of the radar backscatter from oil-covered sea surfaces using moment method and Monte-Carlo simulation: preliminary results

An analysis of the radar backscattering from the ocean surface covered by oil spill is presented using a mi- crowave scattering model and Monte-Carlo simulation. In the analysis, a one-dimensional rough sea sur- face is numerically generated with an ocean waveheight spectrum for a given wind velocity. A two-layered medium is then generated by adding a thin oil layer on the simulated rough sea surface. The electric fields backscattered from the sea surface with two-layered medium are computed with the method of moments （MoM）, and the backscattering coefficients are statistically obtained with N independent samples for each oil-spilled surface using the Monte-Carlo technique for various conditions of surface roughness, oil-layer thickness, frequency, polarization and incidence angle. The numerical simulation results are compared with theoretical models for clean sea surfaces and SAR images of an off-spilled sea surface caused by the Hebei （Hebei province, China） Spirit oil tanker in 2007. Further, conditions for better oil spill extraction are sought by the numerical simulation on the effects of wind speed and oil-layer thickness at different inci- dence angles on the backscattering coefficients.

A NEW MOMENT METHOD FOR THE FAST AND ACCURATE ANALYSIS OF NORMAL MODE HELICAL ANTENNAS

In this letter, a new moment method using helical segments is presented to model Normal Mode Helical Antenna (NMHA). Using this method, the NMHA can be modeled by a few segments. The current distributions and radiation patterns of some NMHAs are calculated.A comparison is made between results obtained using this helical segment algorithm and a linear segment algorithm, and the results of the two algorithms agree fairly well. When calculating the impedance matrix [Z], all the elements of the matrix can be obtained by only calculating a few elements with the application of the symmetric and periodic characteristics of the NMHA.Therefore, the CPU time and the memory storage are significantly reduced, with the accuracy and speed enhanced.

APPLICATION OF THE MOMENT METHODS TO ANALYSIS OF X-RAY DIFFRACTION LINE PROFILE FOR PA1010-BMI SYSTEM

Pure X-ray diffraction profiles have been analysed for polyamide 1010 and PA1O1O-BMI system by means of multipeak fitting resolution of X-ray diffraction. The methods of variance and fourth moment have been applied to determine the particle size and strain values for the paracrystalline materials. The results indicated that both variance and fourth moment of X-ray diffraction line profile yielded approximately the same values of the particle size and the strain. The particle sizes of (100) reflection have been found to decrease with increasing BMI content, whereas the strain values increased.

Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the num- ber concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimoda/and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter- modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.

Quadrature Method of Moments for Nanoparticle Coagulation and Diffusion in the Planar Impinging Jet Flow

把大旋涡模拟与照时刻方法相结合的一个计算模特儿被雇用在一口限制侵犯的喷气学习 nanoparticle 进化。调查粒子尺寸在短暂政体被限制，并且粒子碰撞核被使用流动匹配的理论获得。模拟被把它与试验性的结果作比较验证。协调结构扮演统治粒子数字紧张的数字结果表演，尺寸和多分散性分布，和它也导致粒子沉重的喷气被冲淡由周围。在侵犯的喷气流动的粒子动力学的进化是强烈，与雷纳兹有关，数字和 nozzle-to-plate 距离，和他们的关系被分析。

THE CALCULATION METHOD OF FLYWHEEL MOMENT OFINERTIA OF CRANE MECHANISM

The origin and substance of the tlywheel moment calculation method of inertia mo ment of crane mechanism are set forth comprehensively and systematically in this paper, that is, the nucleus or the focus ofmoment of inertia calculation is the problem of calculating convertible tlywheelmoment. It is much better for the calculation of flywheel moment of loading move mass of lifting, traveling and rotating mechanism using the low of conservation of energy, the theorem of kinetic energyfor that of radius - changing mechanism, and the law of conservation of energy for that of all parts of gearing mechanism.

The New Application of Multilevel Method of Moments in Analysis of Wire-Antenna Arrays

This paper introduces the principle of the multi-level method of moments (MoM) and its application in the analysis of the wire-antenna arrays. The multi-level MoM broadens the usage of the iterative methods in the MoM. Our numerical results show that when applying it to the wire-antenna array analysis with the consideration of the mutual coupling between elements, it can allow a rapid and accurate evaluation of the current distribution on the antennas, and the computational cost is less, especially when the number of antennas is large.

The moment-method form of Pocklington's integral equation above ground

Pocklington’s integral equation is presented for analysis of current distributions on wire antenna above ground. Sommerfeld type integrals, the kernel functions of the integral equation, can be approximately expressed as the elementary functions using the Fresnel plane wave reflection coefficients method; and the Pocklington’s integral equation will be rearranged into a linear equation with solution easily obtained by using the method of moments, when the sinusoidal sub domain expansion is chosen to express the current distributions.

A method of moments for calculating dynamic responses beyond linear response theory

A method of moments for calculating the dynamic response of periodically driven overdamped nonlinear stochastic systems in the general response sense is proposed, which is a modification of the method of moments confined within linear response theory. The calculating experience suggests that the proposed technique is simple and efficient in implementation, and the comparison with stochastic simulation shows that the first three orders of susceptibilities calculated by the proposed technique have high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and another observed phenomenon of stochastic resonance in the systems induced by the location of a single periodic orbit is disclosed and explained.

Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.

Investigation of Thermodynamic Properties of Zirconia Thin Films by Statistical Moment Method

The moment method in statistical (SMM) dynamics is used to study the thermodynamic quantities of ZrO2 thin films taking into account the anharmonicity effects of the lattice vibrations. The average lattice constant, thermal expansion coefficient and specific heats at the constant volume of ZrO2 thin films are calculated as a function of temperature, pressure and thickness of thin film. SMM calculations are performed using the Buckingham potential for the ZrO2 thin films. In the present study, the influence of temperature, pressure and the size on the thermodynamic quantities of ZrO2 thin film have been studied using three different interatomic potentials. We discuss temperature and thickness dependences of some thermodynamic quantities of ZrO2 thin films and we compare our calculated results with those of the experimental results.

Two-Stream Approximation to the Radiative Transfer Equation:A New Improvement and Comparative Accuracy with Existing Methods

Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

Series expansion feasibility of singular integral in method of moments

When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.

Quadrature-based moment methods for the population balance equation: An algorithm review

The dispersed phase in multiphase flows can be modeled by the population balance model(PBM). A typical population balance equation(PBE) contains terms for spatial transport, loss/growth and breakage/coalescence source terms. The equation is therefore quite complex and difficult to solve analytically or numerically. The quadrature-based moment methods(QBMMs) are a class of methods that solve the PBE by converting the transport equation of the number density function(NDF) into moment transport equations. The unknown source terms are closed by numerical quadrature. Over the years, many QBMMs have been developed for different problems, such as the quadrature method of moments(QMOM), direct quadrature method of moments(DQMOM),extended quadrature method of moments(EQMOM), conditional quadrature method of moments(CQMOM),extended conditional quadrature method of moments(ECQMOM) and hyperbolic quadrature method of moments(Hy QMOM). In this paper, we present a comprehensive algorithm review of these QBMMs. The mathematical equations for spatially homogeneous systems with first-order point processes and second-order point processes are derived in detail. The algorithms are further extended to the inhomogeneous system for multiphase flows, in which the computational fluid dynamics(CFD) can be coupled with the PBE. The physical limitations and the challenging numerical problems of these QBMMs are discussed. Possible solutions are also summarized.

Efficient PO-MOM Method for Analysis of the Radiation Characteristics of a Large Antenna-Radome System

An efficient hybrid method based on the method of moments （MOM） and physical optics （PO） for the analysis of radiation characteristics of an electrically large antenna-radome system is presented. Specifically, MOM is first applied to the antenna to find the current on its surface, and then the equivalent PO currents produced by the antenna radiation are assumed on the radome wall. When the coupling of the PO currents and antenna current is considered, the coupling matrix is divided into a series of partial matrices, in order to deduce the memory requirement and accelerate the evaluation process. Numerical results indicate that the proposed hybrid PO-MOM method is accurate and efficient.

Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The non-linear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge-Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance （10^-5）. The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.