Anti-plane deformations around arbitrary-shaped canyons on a wedge-shape half-space:moment method solutions

The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied. Nunerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals (moment method). The wave displacement fields are computed by the residual mcthod for the cases of elliptic, circular, rounded-rectangular and flat-elliptic canyons. The analysis demonstrates that thc resulting surface displacemcnt depends, as in similar previous analyses, on several factors including, but not limited, to the angle of thc wedge, thc geometry of thc vertex, the frcquencies of thc incident waves, the angles of incidence, and the material properties of the media. The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.

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.

Nanoparticle Transport and Coagulation in Bends of Circular Cross Section via a New Moment Method

Transport of nanoparticles and coagulation is simulated with the combination of CFD in a circular bend. The Taylor-expansion moment method(TEMOM)is employed to study dynamics of nanoparticles with Brownian motion,based on the flow field from numerical simulation.A fully developed flow pattern in the present simulation is compared with previous numerical results for validating the model and computational code.It is found that for the simulated particulate flow system,the particle mass concentration,number concentration,particle polydispersity, mean particle diameter and geometric standard deviation over cross-section increase with time.The distribution of particle mass concentration at different time is independent of the initial particle size.More particles are concen-trated at outer edge of the bend.Coagulation plays more important role at initial stage than that in the subsequent period.The increase of Reynolds number and initial particle size leads to the increase of particle number concentration.The particle polydispersity,mean particle diameter and geometric standard deviation increase with decreasing Reynolds number and initial particle size.

Nanoparticle coagulation in a planar jet via moment method

Large eddy simulations of nanoparticle coagulation in an incompressible pla- nar jet were performed.The particle is described using a moment method to approximate the particle general dynamics equations.The time-averaged results based on 3000 time steps for every case were obtained to explore the influence of the Schmidt number and the Damkohler number on the nanoparticle dynamics.The results show that the changes of Schmidt number have the influence on the number concentration of nanoparticles only when the particle diameter is less than 1 nm for the fixed gas parameters.The number concentration of particles for small particles decreases more rapidly along the flow di- rection,and the nanoparticles with larger Schmidt number have a narrower distribution along the transverse direction.The smaller nanoparticles coagulate and disperse easily, grow rapidly hence show a stronger polydispersity.The smaller coagulation time scale can enhance the particle collision and coagulation.Frequented collision and coagulation bring a great increase in particle size.The larger the Damkohler number is,the higher the particle polydispersity is.

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.

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 number 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 intermodal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimodal and shifts to a larger particle size range. In the free molecular regime and transition regime, the intermodal 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.

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 PA1010--BMI system by means of multipeak fitting resolution of X-ray diffraction.The methods ofvariance and fourth moment have been applied to determine the particle size and strainvalues for theparacrystalline materials.The results indicated that both variance and fourthmoment of X-ray diffraction line profile yielded approximately the same values of theparticle size and the strain.The particle sizes of(100)reflection have been found todecrease with increasing BMI content,whereas the strain values increased.

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 microwave scattering model and Monte-Carlo simulation. In the analysis, a one-dimensional rough sea surface 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 oil-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 incidence angles on the backscattering coefficients.

Adsorption and Transfer Properties for Toluene and pDichlorobenzene in Dense CO_2/Silica Gel Packed Bed System by Moment Method and Time-Domain Analysis

Based on chromatographic theory, the moment method and the time-domain fitting analysis were applied to measure and evaluate the adsorption equilibrium constant and mass transfer properties (axial dispersion coefficient and effective intra-particle diffnsivity) for toluene and p-dichlorobenzene on silica gel adsorbent in the subcritical and supercritical CO2. An apparatus based on supercritical fluid chromatography was established and the experiments were performed at temperatures of 298.15-318.15 K and pressures of 7.5-17.8 MPa. The two methods have been compared. The results show that for the systems studied here the moment method can give reasonable values for both adsorption equilibrium constant and mass transfer properties, but the time-domain analysis only can obtain the adsorption equilibrium constant. The dependence of adsorption equilibrium constant and mass transfer properties on temperature and pressure was investigated.

THE MOMENT METHOD ON RESONANT QUADRIFILAR HELICAL ANTENNAS

An efficient measure is taken to rearrange Nakano’s kernels of integral equationsfor an antenna system composed of arbitrarily bent wires.By means of the moment method,great efforts are made to analyze and compute the circularly polarized patterns,directivity,axialratio,front-to-back ratio and beam-shaping characteristics of resonant quadrifilar helical antennasas well as the feeding technique and the effect of an electrically large conducting body on theperformance of the antennas.

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.

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.

NUMERICAL SIMULATION OF NANOPARTICLE COAGULATION IN A POISEUILLE FLOW VIA A MOMENT METHOD

Numerical simulations of coagulating nano-scale aerosols in a two dimensional Poiseuille flow between fixed plates are performed. Evolution of the particle field is obtained by utilizing a moment method to approximate the aerosol general dynamic equation. A moment method is used, which assumes a lognormal function for the particle size distribution and requires knowledge of the first three moments. A Damk?hler number is defined to represent the ratio of the convection time scale to the coagulation time scale. Simulations are performed based on three Reynolds numbers, 100, 500 and 1000, and on three initial particle volume fractions corresponding to Damk?hler numbers 0.1, 0.2 and 1.0. Spatio-temporal evolution of the first three moments along with the geometric mean volume and standard deviation are discussed.

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。

Artificial moment method for swarm robot formation control

The purpose of this paper is to develop a general control method for swarm robot formation control. Firstly,an attraction-segment leader-follower formation graph is presented for formation representations. The model of swarm robot systems is described. According to the results and two kinds of artificial moments defined as leader-attraction moment and follower-attraction moment,a novel artificial moment method is proposed for swarm robot formation control. The principle of the method is introduced and the motion controller of robots is designed. Finally,the stability of the formation control system is proved. The simulations show that both the formation representation graph and the formation control method are valid and feasible.

Moment Method Based on Fuzzy Reliability Sensitivity Analysis for a Degradable Structural System

为有模糊失败区域的一个可能减解的结构的系统，一个片刻方法基于模糊可靠性敏感算法被介绍。根据性能功能的值赋值，为计算模糊失败概率的不可分的区域首先被分成性能的会员函数值在模糊失败区域以内在工作的一系列分区能被一套常数接近。模糊失败概率然后在分区被转变成随机的失败可能性的产品和会员功能的近似常数的和。而且，模糊可靠性敏感分析被转变成一系列随机的可靠性敏感分析，和随机的可靠性敏感能被构造时刻方法获得。介绍方法的主要优点与低、中等的维数和宽适用性为含蓄的表演功能包括更高的效率到多重失败模式和 nonnormal 基本随机的变量。限制是要求的计算努力随基本随机的变量的维数的增加指数地成长；因此，它不对高维数问题合适。与可得到的方法相比，介绍的在维数比 10 低的情况中是相当有竞争力的。举的例子被用来验证优点并且显示限制。

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 well 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.

An analytical solution for the population balance equation using a moment method

Brownian coagulation is the most important inter-particle mechanism affecting the size distribution of aerosols.Analytical solutions to the governing population balance equation(PBE) remain a challenging issue.In this work,we develop an analytical model to solve the PBE under Brownian coagulation based on the Taylor-expansion method of moments.The proposed model has a clear advantage over conventional asymptotic models in both precision and efficiency.We first analyze the geometric standard deviation(GSD) of aerosol size distribution.The new model is then implemented to determine two analytic solutions,one with a varying GSD and the other with a constant GSD.The varying solution traces the evolution of the size distribution,whereas the constant case admits a decoupled solution for the zero and second moments.Both solutions are confirmed to have the same precision as the highly reliable numerical model,implemented by the fourth-order Runge-Kutta algorithm,and the analytic model requires significantly less computational time than the numerical approach.Our results suggest that the proposed model has great potential to replace the existing numerical model,and is thus recommended for the study of physical aerosol characteristics,especially for rapid predictions of haze formation and evolution.