Classical Method Of Moments Research Articles

A hybrid method for an inverse scattering problem related to cylindrical bodies buried in a half-space

A hybrid method which is suitable to find numerical solutions for two-dimensional inverse scattering problems connected with cylindrical bodies buried in a half-space with the known orientation is established. The mentioned hybrid method is based on the classical moment method in connection with vertical coordinate while it involves the horizontal coordinate through a spectral expansion. The structure of the spectral expansion which is imposed by the Green's function contributes to improvement of the ill-posedness of the problem along with Tikhonov regularization. By taking this particular structure into consideration one determines the basis functions such that the effect of the ill-posedness is reduced to a minimum. Some illustrative examples show the applicability and accuracy of the method.

Electromagnetism of one-component plasmas of massless fermions

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

Transient dispersion in a channel with crossflow and wall adsorption

We consider a setting with two infinite parallel plates, where the diffusive substance is adsorbed at the lower plate, simultaneously advected longitudinally by a main flow and vertically by a crossflow. We utilize the classical method of moments along with the eigenfunction expansion to calculate the moments up to fourth-order, and thus the effects of non-Gaussian properties can be reflected. Compared with the result of Brownian dynamics simulations, the present work is shown sufficient to cover the pre-asymptotic dispersion regime out of reach of the generalized Taylor dispersion (GTD) method and dual-perturbation method.

Soot particle size distribution reconstruction in a turbulent sooting flame with the split-based extended quadrature method of moments

The Method of Moments (MOM) has largely been applied to investigate sooting laminar and turbulent flames. However, the classical MOM is not able to characterize a continuous particle size distribution (PSD). Without access to information on the PSD, it is difficult to accurately take into account particle oxidation, which is crucial for shrinking and eliminating soot particles. Recently, the Split-based Extended Quadrature Method of Moments (S-EQMOM) has been proposed as a numerically robust alternative to overcome this issue [Salenbauch et al., “A numerically robust method of moments with number density function reconstruction and its application to soot formation, growth, and oxidation,” J. Aerosol Sci. 128, 34–49 (2019)]. The main advantage is that a continuous particle number density function can be reconstructed by superimposing kernel density functions (KDFs). Moreover, the S-EQMOM primary nodes are determined individually for each KDF, improving the moment realizability. In this work, the S-EQMOM is combined with a large eddy simulation/presumed-probability density function flamelet/progress variable approach for predicting soot formation in the Delft Adelaide Flame III. The target flame features low/high sooting propensity/intermittency and comprehensive flow/scalar/soot data are available for model validation. Simulation results are compared with the experimental data for both the gas phase and the particulate phase. Good quantitative agreement has been obtained especially in terms of the soot volume fraction. The reconstructed PSD reveals predominantly unimodal/bimodal distributions in the first/downstream portion of this flame with particle diameters smaller than 100 nm. By investigating the instantaneous and statistical sooting behavior at the flame tip, it has been found that the experimentally observed soot intermittency is linked to mixture fraction fluctuations around its stoichiometric value that exhibits a bimodal probability density function.

The Generalized Method of Moments for Multi-Reference Alignment

This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator maintains its asymptotic optimality for statistical models with group symmetry, including MRA. Then, we conduct a comprehensive numerical study and show that the GMM substantially outperforms the classical method of moments, whose application to MRA has been studied thoroughly in the literature. We also formulate the GMM to estimate a three-dimensional molecular structure using cryo-electron microscopy and present numerical results on simulated data.

Adaptive Multilevel Nonuniform Grid Algorithm for the Accelerated Analysis of Composite Metallic–Dielectric Radomes

An adaptive multilevel nonuniform grid (MLNG) algorithm is developed for the accelerated computation of fields radiated through composite metallic–dielectric radomes as well as antenna-radome interactions. The MLNG approach is applied to the mixed potential formulation of the coupled surface and volume electric field integral equations. The radome is decomposed into a hierarchy of subdomains (SDs) by an adaptive algorithm that closely follows the radome geometry, allowing significant savings in memory and CPU time. In the MLNG algorithm, only local generalized impedance matrices of the finest level SDs are evaluated. Far-zone potentials and fields are indirectly evaluated through a multilevel aggregation involving phase-and amplitude-compensated interpolation on nonuniform grids (NGs), requiring considerably fewer calculations as compared with the classical method of moments (MoM). The MLNG algorithm is incorporated in a preconditioned iterative solver. Accuracy as well as memory consumption and computation times of the algorithm are studied on realistic examples. The radome effect on the antenna input impedance and electric current density distribution is demonstrated. The method is validated by comparison with a commercial MoM software and shown to exhibit a computational complexity (CC) of O(NlogN), N being the number of unknowns.

Null-controllability properties of a fractional wave equation with a memory term

We study the null-controllability properties of a one-dimensional wave equation with memory associated with the fractional Laplace operator. The goal is not only to drive the displacement and the velocity to rest at some time-instant but also to require the memory term to vanish at the same time, ensuring that the whole process reaches the equilibrium. The problem being equivalent to a coupled nonlocal PDE-ODE system, in which the ODE component has zero velocity of propagation, we are required to use a moving control strategy. Assuming that the control is acting on an open subset $ \omega(t) $ which is moving with a constant velocity $ c\in\mathbb{R} $, the main result of the paper states that the equation is null controllable in a sufficiently large time $ T $ and for initial data belonging to suitable fractional order Sobolev spaces. The proof will use a careful analysis of the spectrum of the operator associated with the system and an application of a classical moment method.

Null-controllability properties of the wave equation with a second order memory term

We study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus T=R/2πZ. We assume that the control is acting on an open subset ω(t)⊂T, which is moving with a constant velocity c∈R∖{−1,0,1}. The main result of the paper shows that the equation is null controllable in a sufficiently large time T and for initial data belonging to suitable Sobolev spaces. Its proof follows from a careful analysis of the spectrum associated with our problem and from the application of the classical moment method.

Analyzing dwell times with the Generalized Method of Moments.

The Generalized Method of Moments (GMM) is a statistical method for the analysis of samples from random processes. First developed for the analysis of econometric data, the method is here formulated to extract hidden kinetic parameters from measurements of single molecule dwell times. Our method is based on the analysis of cumulants of the measured dwell times. We develop a general form of an objective function whose minimization can return estimates of decay parameters for any number of intermediates directly from the data. We test the performance of our technique using both simulated and experimental data. We also compare the performance of our method to nonlinear least-squares minimization (NL-LSQM), a commonly-used technique for analysis of single molecule dwell times. Our findings indicate that the GMM performs comparably to NL-LSQM over most of the parameter range we explore. It offers some benefits compared with NL-LSQM in that it does not require binning, exhibits slightly lower bias and variance with small sample sizes (N<20), and is somewhat superior in identifying fast decay times with these same low count data sets. Additionally, a comparison with the Classical Method of Moments (CMM) shows that the CMM can fail in many cases, whereas the GMM always returns estimates. Our results show that the GMM can be a useful tool and complements standard approaches to analysis of single molecule dwell times.

Градиентные методы оптимизации в машинном обучении идентификации параметров динамических систем

The article considers one of the possible ways to solve the problem of estimating the unknown parameters of dynamic models described by differential-algebraic equations. Parameters are estimated based on the results of observations of the behavior of the mathematical model. Their values are found as a result of minimizing the criterion that describes the total quadratic deviation of the state vector coordinates from the exact values obtained at measurements at different points in time. The parallelepiped type constraints are imposed on the parameter values. To solve the optimization problem, it is proposed to use gradient optimization methods used in machine learning procedures: the stochastic gradient descent method, the classical moment method, the Nesterov accelerated gradient method, the adaptive gradient method, root mean square propagation method, the adaptive moment estimation method, the adaptive estimation method modification, Nesterov–accelerated adaptive moment estimation method. An example of identification of the parameters of a linear mathematical model describing a change in the characteristics of a chemical process is shown, which demonstrates the comparative effectiveness of the optimization methods of the selected group. The methods used to search for an extremum do not guarantee finding a result – a global extremum, but allow you to get a solution of good enough quality for an acceptable time. The results of calculations by all the listed optimization methods are presented. Recommendations on the selection of method parameters are given. The obtained numerical results demonstrated the effectiveness of the proposed approach. The found approximate values of the estimated parameters slightly differ from the best known solutions obtained by other methods.

Model‐free causal inference of binary experimental data

AbstractFor binary experimental data, we discuss randomization‐based inferential procedures that do not need to invoke any modeling assumptions. In addition to the classical method of moments, we also introduce model‐free likelihood and Bayesian methods based solely on the physical randomization without any hypothetical super population assumptions about the potential outcomes. These estimators have some properties superior to moment‐based ones such as only giving estimates in regions of feasible support. Due to the lack of identification of the causal model, we also propose a sensitivity analysis approach that allows for the characterization of the impact of the association between the potential outcomes on statistical inference.

Optical properties of dense coulomb plasmas

&nbsp;In the present work, we provide a theoretical analysis of the reflection of low-temperature dense plasma for the normal incidence of laser radiation, and the dependence of reflectivity of s - and p - polarized waves in respect to the angle of incidence. In connection with the calculations for large parameters of density, the interpolation approach based on the theory of moment’s method is used for the calculation of the dielectric function. In contrast to the classical method of moments, the characteristic frequencies can be found from the simplified formulas, and the Nevanlinna parameter function is determined as in Phys.Rev.Lett. 119, 045001 (2017). The reflectivity is calculated with using of Fresnel equations. The obtained results were compared with theoretical and experimental data of other authors. It is shown that results of the present work for the reflection coefficient are close to the experimental results, in contrast to other theoretical results, in which a model with several adjustable parameters was used. The patent of RK for the present method was submitted. &nbsp; &nbsp; &nbsp; G M T &nbsp; Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский &nbsp; Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Звуковая функция ограничена 200 символами &nbsp; &nbsp; Настройки : История : Обратная связь : Donate Закрыть

The frequency domain approach to analyse field-scale miscible flow transport experiments in the soils

A new approach to the estimate of the parameters u (advective velocity) and λ (dispersivity) characterizing solute transport in soils is presented. The pair (u, λ) is estimated by matching in the frequency domain (FD) the theoretical expression of moments pertaining to the breakthrough curve (BTC) against to the one evaluated by means of the experimental data. In particular, we demonstrate that to reduce the impact of the random measurement-errors upon such an estimate, it is worth retaining in the Fourier's expansion of the moments only the harmonics associated to the smaller frequencies. This is due to the fact that the Fourier transform moves most of the measurement-errors affecting moments in the high-frequency range. As a consequence, by adopting a relatively small number of harmonics to compute the Fourier transform of the experimental moments, one may filter out most of the noise. It is also shown that the number of harmonics to retain (cut-off) depends upon the soil's water content as well as the magnitude of the characteristic length l E of the error relative to the dispersivity λ. The proposed methodology has been applied to a recently conducted plot-scale transport experiment. For comparison purposes, we have also estimated the pair (u, λ) by the classical method of moments (MM). Both the methods lead to the same value of the advective velocity u. This is explained by recalling that u depends upon the first-order moment, a quantity that is scarcely influenced by the measurement-errors. Instead, the estimate of the dispersivity λ (which is related to the second-order moment) is largely different (with the value achieved by the MM larger than the one obtained by the FD approach). Such a difference is addressed to the fact that in the MM the distortion-effect due to the measurement-errors amplifies with the increasing order of the moments, a phenomenon which is completely avoided in the FD approach by adopting the above mentioned cut-off.

Problems involving the determination of the column-only band broadening in columns producing narrow and tailed peaks

We have investigated which of the different existing peak variance read-out methods (including the effect of a deconvolution pre-treatment method) are most suited to eliminate the system contribution from the total observed band broadening observed in LC systems. Emphasis is put on the most demanding case, i.e., the measurement of non-retained component peaks, which typically are very narrow and tailed. The problem with such peaks is that the method that is generally considered to be the only mathematically correct method (i.e., the method of moments) leads to peak variance values that are so strongly dominated by the tail of the peak that they become highly exaggerated and practically meaningless (i.e., they are dominated by the peak width at 10 or 12σt, which corresponds to resolutions and peak purities that are so high they are never pursued in practice). Interestingly, filtering away the extra-column contribution from the entire peak shape using peak deconvolution (wherein not only the second order moment is corrected but also all other moments) produces corrected 4σt- and half height peak widths that are physically meaningful, i.e., the corrected values allow to make sufficiently accurate predictions of how the peak width at 4σt and at half height changes when the column length changes. This result now allows to navigate away from the classical method of moments to define the column plate height, and resort to plate heights based on the practically much more relevant 4σt- and 5σt-widths, provided theses are corrected via peak deconvolution.

Bacterial foraging optimisation and method of moments for modelling and optimisation of microstrip antennas

A novel technique applying bacterial foraging optimisation (BFO) in conjunction with the method of moments (MOM) is developed to calculate accurately the resonant frequency and bandwidth of rectangular microstrip antenna of any dimension and of any substrate thickness. The resonant frequency results obtained by using (BFO/MOM) algorithm are in very good agreement with the experimental results available in the literature. The computation time is greatly reduced as compared with the classical MOM. Furthermore, the idea of this paper can be used for calculating the various parameters of microstrip antennas of different structures and geometries.

Calculation of eddy-current probe signal for a 3D defect using global series expansion

Purpose – The purpose of this paper is to present a novel eddy-current modeling technique of volumetric defects embedded in conducting plates. This problem is of great interest in electromagnetic non-destructive evaluation and has already been exhaustively studied. Design/methodology/approach – The defect is modeled by a volumetric current dipole density which satisfies an integral equation. The latter is solved by the classical method of moments. The authors propose the use of globally defined, continuous basis functions for the expansion of the current dipole density. Findings – The proposed global expansion provides an improvement of the numerical stability and the performance of the simulation, over classical approaches. The proposed method is tested against both measured and synthetic data obtained by a different defect model. Originality/value – The new discretisation scheme – in contrast to the classical approaches – does not need the discretisation of the defect volume. This involves numerous adva...

A Three-Dimensional Adaptive Integral Method for Scattering From Structures Embedded in Layered Media

A 3-D extension of the adaptive integral method (AIM) is presented for fast analysis of scattering from electrically large perfect electrically conducting structures embedded inside a single layer of a planar layered medium. The proposed scheme accelerates the iterative method-of-moments (MOM) solution of the combined-field integral equation by employing a 3-D auxiliary regular grid. It uses the auxiliary grid to execute the standard four-stage AIM procedure; unlike the procedure for free space, two different sets of matrices are obtained for the AIM propagation stage by decomposing the Green functions to terms that are in convolution or correlation form in the stratification direction. These matrices are in (three level) block-Toeplitz and Hankel-(two level)-block-Toeplitz forms and can be multiplied by using 3-D FFTs. The dominant computational costs of the scheme are the evaluation of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(N)$</tex></formula> different layered-medium Green functions, which is accelerated by extracting asymptotic terms and using interpolation tables, and the matrix multiplications in the propagation stage, which require only <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(N_{\rm C}\log N_{\rm C})$</tex></formula> per iteration; these should be contrasted to the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(N^{2})$</tex></formula> Green function evaluations and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$O(N^{2})$</tex></formula> operations per iteration required by the classical MOM. Here, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$N_{\rm C}$</tex></formula> denotes the number of nodes on the auxiliary grid, and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$N$</tex></formula> denotes the number of degrees of freedom of the surface current density. Numerical results validate the proposed method's complexity, demonstrate its accuracy for several large-scale structures in layered media, and compare its computational costs to those of its counterpart for free space.

Quantifying reliability uncertainty from catastrophic and margin defects: A proof of concept

We aim to analyze the effects of component level reliability data, including both catastrophic failures and margin failures, on system level reliability. While much work has been done to analyze margins and uncertainties at the component level, a gap exists in relating this component level analysis to the system level. We apply methodologies for aggregating uncertainty from component level data to quantify overall system uncertainty. We explore three approaches towards this goal, the classical Method of Moments (MOM), Bayesian, and Bootstrap methods. These three approaches are used to quantify the uncertainty in reliability for a system of mixed series and parallel components for which both pass/fail and continuous margin data are available. This paper provides proof of concept that uncertainty quantification methods can be constructed and applied to system reliability problems. In addition, application of these methods demonstrates that the results from the three fundamentally different approaches can be quite comparable.

A Novel Integration Method for Weak Singularity Arising in Two-Dimensional Scattering Problems

In this paper, we introduce a novel mechanical quadrature method for an efficient solution of weakly singular integral equations arising in two-dimensional electromagnetic scattering problems. This approach is based on and adapted from the recently proposed mechanical quadrature methods in [Extrapolation algorithms for solving mixed boundary integral equations of the Helmholtz equation by mechanical quadrature methods, SIAM J. Sci. Comput., vol. 31, 4115-4129, 2009]. We report experiments for solving TM-polarized induced currents and scattered fields to show its superiority to the classical method of moments when accuracy is a concern. Moreover, additional numerical experiments made with an extrapolation algorithm suggest that the accuracy of the present method can be further improved dramatically by means of the extrapolation algorithm to some extent.

Adaptive Noise Mitigation in Impulsive Environment: Application to Power-Line Communications

In this paper, we address the general issue of asynchronous impulsive noise mitigation and its application over coded power-line communications (PLC). As is well known, PLC channels usually suffer from significant degradation due to impulsive interference generated by electrical appliances. The use of a level limiter is a simple and intuitive technique, widely used to mitigate the noxious effect of impulsive noise in these channels. However, the determination of the clipping threshold remains, most of the time, empirical, and the impulse statistics are usually assumed to be known. In a previous study, we proposed an original threshold determination based on signal detection theory, using the well-known false alarm and good detection tradeoff. Here, we further investigate the proposed optimization method in closed form. We compare two tradeoff criteria by means of a receiver operating curves analysis. We clearly show that the resulting decision fits well with encountered bit-error rate performances. We also evaluate the influence of impulsive noise statistics estimation on the performance of the proposed approach. To do so, we assess the robustness of the classical method of moments on Gaussian mixture estimation. It clearly appears that the estimation method is reliable for reasonable values of the impulse occurrence. As one of the main results of this paper, we make a proposal for impulse statistics estimation under ¿severe¿ conditions (i.e., for very rare impulse events, based on impulse detection over corrupted OFDM symbols). Subsequently, we propose a general scheme of automatic impulse mitigation, according to the disturbance ratio of the environment. Finally, the performance of the approach is evaluated over the Home-Plug AV (HPAV) physical layer.