Low-order Moments Research Articles

Implementation of CHyQMOM in OpenFOAM for the simulation of non-equilibrium gas-particle flows under one-way and two-way coupling

The modeling of dilute gas-particle flows is challenging due to particle-trajectory crossing (PTC). Lagrangian particle tracking can be used, but requires a large number of parcels resulting in high computational costs. A less costly method is the Eulerian number density function (NDF) approach, based on the Boltzmann equation, often solved in terms of lower-order moments of the NDF. In this context the conditional hyperbolic quadrature method of moments (CHyQMOM) was developed and is here implemented for the first time in the OpenFOAM-7, together with high-order advection schemes and a new operator splitting procedure. The resulting solver is used to simulate different test cases: phase segregation problems, collision-less and weakly-collisional PTC flows, asymmetric and symmetric Taylor-Green vortex flow and a dilute gas-particle riser. Results, validated against analytical solutions and predictions obtained with Lagrangian particle tracking, show that the implemented CHyQMOM can be used to handle highly non-equilibrium flows.

Cosmic Flow Measurement and Mock Sampling Algorithm of Cosmicflows-4 Tully−Fisher Catalog

Abstract Measurements of cosmic flows enable us to test whether cosmological models can accurately describe the evolution of the density field in the nearby universe. In this paper, we measure the low-order kinematic moments of the cosmic flow field, namely bulk flow and shear moments, using the Cosmicflows-4 Tully−Fisher catalog (CF4TF). To make accurate cosmological inferences with the CF4TF sample, it is important to make realistic mock catalogs. We present the mock sampling algorithm of CF4TF. These mocks can accurately realize the survey geometry and luminosity selection function, enabling researchers to explore how these systematics affect the measurements. These mocks can also be further used to estimate the covariance matrix and errors of the power spectrum and two-point correlation function in future work. In this paper, we use the mocks to test the cosmic flow estimator and find that the measurements are unbiased. The measured bulk flow in the local universe is 376 ± 23 (error) ± 183 (cosmic variance) km s−1 at depth d MLE = 35 Mpc h −1, to the Galactic direction of (l, b) = (298° ± 3°, −6° ± 3°). Both the measured bulk and shear moments are consistent with the concordance Λ Cold Dark Matter cosmological model predictions.

DOA Estimation for Coprime Array With Mixed Noise Scenario via Phased Fractional Low-Order Moment

Direction of arrival (DOA) estimation with coprime array is an important topic in array signal processing. In this letter, the coprime array technique is extended to mixed noise (white Gaussian noise and impulsive noise). Since the second order covariance matrix does not exist in presence of mixed noise, the phased fractional low-order moment (PFLOM) is used to replace the data covariance matrix of the received signals from coprime array, and then a DOA estimation approach based on toeplitz method with coprime array is applied. The feasibility of PFLOM with mixed noise scenario of coprime array is theoretically derived, and the simulation results show that the proposed method has better estimation performance than that of the existing methods, especially in the low generalized signal-to-noise ratio (GSNR) environment.

On the Adequacy of Some Low-Order Moments Method to Simulate Certain Particle Removal Processes

The population balance is an indispensable tool for studying colloidal, aerosol, and, in general, particulate systems. The need to incorporate spatial variation (imposed by flow) to it invokes the reduction of its complexity and degrees of freedom. It has been shown in the past that the method of moments and, in particular, the log-normal approximation can serve this purpose for certain phenomena and mechanisms. However, it is not adequate to treat gravitational deposition. In the present work, the ability of the particular method to treat diffusional and convective diffusional depositions relevant to colloid systems is studied in detail.

First post-Newtonian generation of gravitational waves in Einstein-Cartan theory

In this paper we investigate the gravitational-wave generation problem at the first post-Newtonian order in the context of Einstein-Cartan theory by exploiting the Blanchet-Damour formalism. The quantum intrinsic spin carried by slowly moving, weakly stressed, weakly self-gravitating sources is described geometrically by means of the torsion tensor. We obtain the expression of the source multipole moments with the required accuracy. The analysis of the physical meaning of the lowest-order non-radiative moments and of the asymptotic gravitational waveform is also performed. Eventually, we draw our conclusions and estimate the order of magnitude of the spin contributions in the gravitational-wave signal.

Hydrodynamics of simple active liquids: the emergence of velocity correlations

We derive the hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the probability density distribution of their positions, velocities, and orientations, while at a mesoscopic level we switch to a coarse-grained description introducing an appropriate set of hydrodynamic fields given by the lower-order moments of the distribution. In addition to the usual density and polarization fields, the hydrodynamics developed in this paper takes into account the velocity and kinetic temperature fields, which are crucial to understanding new aspects of the behavior of active liquids. By imposing a suitable closure of the hydrodynamic moment equations and truncation of the Born–Bogolubov–Green–Kirkwood–Yvon hierarchy, we obtain a closed set of mesoscopic balance equations. At this stage, we focus our interest on the small deviations of the hydrodynamic fields from their averages and apply the methods of the theory of linear hydrodynamic fluctuations. Our treatment sheds light on the peculiar properties of isotropic active liquids and their emergent dynamical collective phenomena, such as the spontaneous alignment of the particle velocities. We predict the existence within the liquid phase of spatial equal-time Ornstein–Zernike-like velocity correlations both for the longitudinal and the transverse modes. At variance with active solids, in active liquids, the correlation length of the transverse velocity fluctuations is sensibly shorter than the length of the longitudinal fluctuations. In particular, the latter depends on the sound speed and increases with the persistence time, while the former displays a weaker dependence on these parameters. Finally, within the same framework, we derive the dynamical structure factors and the intermediate scattering functions and discuss how the velocity ordering persists in time. We find that the velocity decorrelates on a time-scale much longer than the one characteristic of passive fluids.

Estimation of Parameters of Pert Distribution by Using Method of Moments

Abstract: The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

Neat, Simple, and Wrong: Debunking Electrostatic Fallacies Regarding Noncovalent Interactions.

Multipole moments such as charge, dipole, and quadrupole are often invoked to rationalize intermolecular phenomena, but a low-order multipole expansion is rarely a valid description of electrostatics at the length scales that characterize nonbonded interactions. This is illustrated by examining several common misunderstandings rooted in erroneous electrostatic arguments. First, the notion that steric repulsion originates in Coulomb interactions is easily disproved by dissecting the interaction potential for Ar2. Second, the Hunter-Sanders model of π-π interactions, which is based on quadrupolar electrostatics, is shown to have no basis in accurate calculations. Third, curved "buckybowls" exhibit unusually large dipole moments, but these are ancillary to the forces that control their intermolecular interactions, as illustrated by two examples involving corannulene. Finally, the assumption that interactions between water and small anions are dictated by the dipole moment of H2O is shown to be false in the case of binary halide-water complexes. These examples present a compelling case that electrostatic explanations based on low-order multipole moments are very often counterfactual for nonbonded interactions at close range and should not be taken seriously in the absence of additional justification.

Simulation of collision-induced absorption spectra based on classical trajectories and ab initio potential and induced dipole surfaces. II. CO2-Ar rototranslational band including true dimer contribution.

This paper presents further development of the new semi-classical trajectory-based formalism described in Paper I [Chistikov et al., J. Chem. Phys. 151, 194106 (2019)]. We report the results of simulation and analysis of the low-frequency collision-induced absorption (CIA) in CO2-Ar, including its true dimer component. Our consideration relies on the use of ab initio intermolecular potential energy and induced dipole surfaces for CO2-Ar calculated in an assumption of a rigid CO2 structure using the CCSD(T) method. The theory, the details of which are reported in Paper I [Chistikov et al., J. Chem. Phys. 151, 194106 (2019)], permits taking into account the effect of unbound and quasi-bound classical trajectories on the CIA in the range of a rototranslational band. This theory is largely extended by trajectory-based simulation of the true bound dimer absorption in the present paper. The spectra are obtained from a statistical average over a vast ensemble of classical trajectories restricted by properly chosen domains in the phase space. Rigorous classical theory is developed for two low-order spectral moments interpreted as the Boltzmann-weighted average of the respective dipole functions. These spectral moments were then used to check the accuracy of our trajectory-based spectra, for which both spectral moments can be evaluated independently in terms of specific integrals over the trajectory-based calculated spectral profiles. Good agreement between the spectral moments calculated as integrals over the frequency domain or the phase space largely supports the reliability of our simulated CIA spectra, which conform with the available microwave and far-infrared observations.

Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter.

Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.

Nonlinear iterative projection methods with multigrid in photon frequency for thermal radiative transfer

This paper presents nonlinear iterative methods for the fundamental thermal radiative transfer (TRT) model defined by the time-dependent multifrequency radiative transfer (RT) equation and the material energy balance (MEB) equation. The iterative methods are based on the nonlinear projection approach and use multiple grids in photon frequency. They are formulated by the high-order RT equation on a given grid in photon frequency and low-order moment equations on a hierarchy of frequency grids. The material temperature is evaluated in the subspace of lowest dimensionality from the MEB equation coupled to the effective grey low-order equations. The algorithms apply various multigrid cycles to visit frequency grids. Numerical results are presented to demonstrate convergence of the multigrid iterative algorithms in TRT problems with large number of photon frequency groups.

An efficient method for stamps recognition using Haar wavelet sub-bands

The problem facing certain organizations such as insurance companies and government institutions where a huge amount of documents is handled every day, hence an automated stamp recognition system is required. The image of the stamp may be on a different background, with different sizes, and suffers from rotating in different directions, also, the appearance of soft areas (patches) or small points as noise. Thus, the main objective of this paper is to extract and recognize the color stamp image. This paper proposed a method to recognize stamps, by using a technique named Haar wavelet sub-bands. The devised method has four stages: 1) extracts the stamp image; 2) preprocessing the image; 3) feature extraction; and 4) matching. This paper is implemented using C sharp (Microsoft Visual Studio 2012) programming language. The experiments conducted on a stamp dataset showed that the proposed method has a great capability to recognize stamps when using Haar wavelet transform with two sets of features (i.e., 100% recognition rate for energy features and 99.93% recognition rate for low order moment).

Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data

Penalized B-splines are commonly used in additive models to describe smooth changes in a response with quantitative covariates. This is usually done through the conditional mean in the exponential family using generalized additive models with an indirect impact on other conditional moments. Another common strategy is to focus on several low-order conditional moments, leaving the full conditional distribution unspecified. Alternatively, a multi-parameter distribution could be assumed for the response with several of its parameters jointly regressed on covariates using additive expressions. The latter proposal for a right- or interval-censored continuous response with a highly flexible and smooth nonparametric density is considered. The focus is on location-scale models with additive terms in the conditional mean and standard deviation. Starting from recent results in the Bayesian framework, a fast converging algorithm is proposed to select penalty parameters from their marginal posteriors. It is based on Laplace approximations of the conditional posterior of the spline parameters. Simulations suggest that the estimators obtained in this way have excellent frequentist properties and superior efficiencies compared to approaches with a working Gaussian assumption. The methodology is illustrated by the analysis of right- and interval-censored income data.

A non-local fluid closure for modeling cyclotron resonance in collisionless magnetized plasmas

A fluid description for collisionless magnetized plasmas that takes into account the effect of cyclotron resonance has been developed. Following the same approach as the Landau fluid closure, the heat flux components associated with transverse electromagnetic fluctuations are approximated by a linear combination of lower-order moments in wavenumber space. The closure successfully reproduces the linear cyclotron resonance for electromagnetic waves propagating parallel to the ambient magnetic field. In the presence of finite temperature anisotropy, the model gives approximately correct prediction for an instability destabilized via the cyclotron resonance. A nonlinear simulation demonstrates the wave growth consistent with the linear theory followed by the reduction of initial anisotropy, and finally, the saturation of the instability. The isotropization may be understood in terms of quasilinear theory, which is developed within the framework of the fluid model but very similar to its fully kinetic counterpart. The result indicates that both linear and nonlinear collisionless plasma responses are approximately incorporated in the fluid model.

Adaptive blind equalization of fast time‐varying channel with frequency estimation in impulsive noise environment

In this paper, a novel source signal recovery method for fast time-varying channels described by complex exponential-basis expansion model (CE-BEM) in the impulsive noise environment is proposed. This method consists of two phases. The first phase is the equalization of fast time-varying channels, in this phase, a novel algorithm FSE-FLOS-CMA is proposed. The convergence performance of this newly proposed algorithm is much better than that of existing fractionally spaced equalizer-constant modulus algorithm (FSE-CMA) in impulsive noise environment. In the second phase, a novel frequency estimation method is proposed. The estimated frequency in impulsive noise environment is obtained by calculating a specific p-order fractional low-order cyclic moment of the equalized signal. Simulation results show that the proposed FSE-FLOS-CMA and frequency estimation method can effectively estimate the source signals transmitted through the fast time-varying channels in impulsive noise environment.

Non-intrusive reduced-order modeling for uncertainty quantification of space–time-dependent parameterized problems

We propose a non-intrusive reduced-order modeling method for space–time-dependent parameterized problems in the context of uncertainty quantification. In the offline stage, proper orthogonal decomposition (POD) is used to extract the spatial modes based on a set of high-fidelity time-parameter-dependent snapshots and then to extract the temporal modes of the projection coefficients of the spatial modes. Finally, parameter-dependent combination coefficients are approximated using polynomial chaos expansions (PCEs). Cubic spline interpolation is used to evaluate the temporal modes at any other given time. In the online stage, a fast evaluation is provided at any given time and parameter by simply estimating the values of the polynomials and temporal modes. To validate the numerical performance of the proposed method, three time-dependent parameterized problems are tested: a one-dimensional (1-D) forced Burger’s equation with a random force term, a 1-D diffusion–reaction equation with a random field force term, and a two-dimensional incompressible fluid flow over a cylinder with a random inflow boundary condition. The results indicate that the proposed method is able to approximate the full-order model very inexpensively with a reasonable loss of accuracy for problems with uncorrelated or correlated input parameters. Furthermore, the proposed method is effective in estimating low-order moments, indicating that it has great potential for use in uncertainty quantification analysis of space–time-dependent problems.

Robust and discriminative image representation: fractional-order Jacobi-Fourier moments

Robust and discriminative image representation is a long-lasting battle in the computer vision and pattern recognition. Moment-based image representation model is effective in satisfying the core conditions of semantic description, due to its geometric invariance and independence. However, moment-based descriptors suffer from a contradiction between the robustness and discriminability, which limits the further improvement of description quality. In this paper, a set of generic moments along with a novel representation framework are proposed to mitigate this troublesome contradiction. We first define a new set of orthogonal moments, named Fractional-order Jacobi-Fourier Moments (FJFM), which is characterized by the generic nature and time-frequency analysis capability. We then develop a new framework to improve both the robustness and discriminability of image representation, called Mixed Low-order Moment Feature (MLMF), by fully exploiting the time-frequency property of FJFM. Extensive experimental results and a real-world application are provided to demonstrate the superior performance of our FJFM-based MLMF, with respect to robustness and discriminability.

On moments of folded and truncated multivariate Student-t distributions based on recurrence relations

The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques allow for fast computation of arbitrary-order product moments of folded and truncated multivariate Student-t distributions and offer explicit expressions of low-order moments of folded and truncated multivariate Student-t distributions. A real data example containing positive censored responses is applied to illustrate the effectiveness and importance of the proposed methods. An R MomTrunc package is developed and publicly available on the CRAN repository.

Scalogram-Based Instantaneous Features of Acoustic Emission in Grinding Burn Detection

Time-frequency methods are effective tools in identifying the frequency content of a signal and revealing its time-variant features. This paper presents the use of instantaneous features (i.e. instantaneous energy and signal phase) of acoustic emission (AE) in the detection of thermal damage to the workpiece in grinding. Both the instantaneous energy and mean frequency are obtained using the low-order frequency moments of a scalogram. While the zero-order frequency moment yields the instantaneous energy, the first-order frequency moment gives the instantaneous frequency by which the signal phase is recovered. The grinding process is monitored using acoustic emission for various operating conditions, including the regular grinding, grinding at a higher cutting speed and larger infeed, and small dressing depth of cut. It has been found that both the instantaneous energy and phase deviation indicate the presence of burn damage and serve as robust and reliable indicators, providing a basis for detecting the grinding burn.

Time Delay Estimation Method Used Median Filter in Low Signal to Noise Ratio Pulse Environment

In practice, the collected signal often contains impulsive noise. The classical time delay estimation algorithm based on the second-order statistics of Gaussian distribution will degrade or even be unreliable, so that it cannot be used. Although the fractional low-order signal processing method can be better adapted to signal processing in the impulse noise environment, the determination of the order p value of the fractional low-order moment depends on the prior knowledge or estimation of the characteristic index α value of the pulse, and when the pulse is stronger or the signal-to-noise ratio is low, the performance cannot meet the requirements well. The paper adopted the method of median filter preprocessing. First, the abnormal points (pulse points) are removed in the noise and return the noise to the Gaussian model distribution; next, use the time delay estimation algorithm under the second-order statistics to avoid the estimate of p-value. Computer simulation experiments show that the method proposed in this paper has better estimation performance in low snr pulse environment.