Moments Formulation Research Articles

Enthalpy-based cascaded lattice Boltzmann method for conjugate heat transfer

Lattice Boltzmann (LB) methods for conjugate heat transfer are widely studied because of the simplicity and efficiency in dealing with complex boundary conditions. Recently, cascaded (or central-moments-based) LB (CLB) method has shown the potential to improve the stability of LB method. For conventional CLB method which is constructed through the continuous equilibrium distribution function, the temperature-based energy equation is recovered and solved. The continuity of temperature and heat flux at conjugate interface is unable to be accurately enforced without special treatment. To circumvent this deficiency, an enthalpy-based CLB method for conjugate heat transfer is developed in this work. In the proposed method, the enthalpy-based formulation of equilibrium moments is directly designed in the central-moment space, and the macroscopic quantity solved is converted from temperature to enthalpy. As demonstrated by the Chapman-Enskog multiscale analysis, the enthalpy-based energy equation can be recovered by the CLB equation. Compared with the conventional CLB method, the continuity condition for temperature and heat flux on the conjugate interface can be enforced automatically without special treatment. In addition, the proposed CLB method provides a new way to develop a CLB equation that can recover to a general convection-diffusion equation. Finally, the accuracy and stability of the temperature field are validated by benchmarks for the proposed enthalpy-based CLB method.

Moment-SoS methods for optimal transport problems

Most common optimal transport (OT) solvers are currently based on an approximation of underlying measures by discrete measures. However, it is sometimes relevant to work only with moments of measures instead of the measure itself, and many common OT problems can be formulated as moment problems (the most relevant examples being Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}-Wasserstein distances, barycenters, and Gromov–Wasserstein discrepancies on Euclidean spaces). We leverage this fact to develop a generalized moment formulation that covers these classes of OT problems. The transport plan is represented through its moments on a given basis, and the marginal constraints are expressed in terms of moment constraints. A practical computation then consists in considering a truncation of the involved moment sequences up to a certain order, and using the polynomial sums-of-squares hierarchy for measures supported on semi-algebraic sets. We prove that the strategy converges to the solution of the OT problem as the order increases. We also show how to approximate linear quantities of interest, and how to estimate the support of the optimal transport map from the computed moments using Christoffel–Darboux kernels. Numerical experiments illustrate the good behavior of the approach.

Reliability-based topology optimization of fractionally-damped structures under nonstationary random excitation

This contribution proposes an effective reliability-based topology optimization (RBTO) framework for the layout of viscoelastic dampers of energy-dissipating structures under nonstationary seismic excitation, in which the constitutive behavior of viscoelastic damper is described by the novel fractional derivative models. To formulate the RBTO problem, the installation number of fractional viscoelastic dampers is minimized under the constraints of dynamic reliability, and the design variables are chosen as the damper parameters and the existence variables of the potential fractional viscoelastic dampers. The explicit responses are first established for the fractionally-damped structure, and the explicit response sensitivities with respect to the design variables are further derived through the adjoint variable method (AVM). On this basis, an explicit time-domain method (ETDM) is developed for explicit formulation of the statistical moments of responses and the moment sensitivities of the fractionally-damped structure, which are further employed to analytically derive the first-passage dynamic reliabilities and the reliability sensitivities of the structure based on the classical level-crossing process theory. Finally, the RBTO problem for the layout of fractional viscoelastic dampers is solved with the gradient-based method of moving asymptotes (MMA), in which the existence variables of fractional viscoelastic dampers can be driven to binary solutions by the solid isotropic material with penalization (SIMP) technique. An engineering application involving a building frame structure installed with fractional viscoelastic dampers is presented to validate the feasibility of the proposed ETDM-based RBTO framework.

Q-Factor Bounds for Microstrip Patch Antennas

Antenna bounds are a useful tool in assessing the feasibility or performance of an antenna design. Microstrip patch antennas are often limited by their relatively narrow bandwidth, and therefore Q-factor is an important design parameter, as it is related to the inverse of the fractional bandwidth. This article presents the first tight lower Q-factor bounds on microstrip patch antennas supported by an infinite dielectric substrate. The derived lower Q-factor bounds are orders of magnitude tighter than the Chu limit and introduce a new scaling rule. These bounds consider all possible geometries on the predefined design region. Moreover, it is shown that well-known patch antennas have Q-factors near the bounds and have thus a near-optimal bandwidth. The computation of the bounds is done using a method of moments (MoM) formulation. However, an approximation to these bounds using commonly available simulation tools is provided.

Numerical Stability Analysis for a Stationary and Translating Droplet at Extremely Low Viscosity Values Using the Lattice Boltzmann Method Color-Gradient Multi-Component Model with Central Moments Formulation

Numerical Stability Analysis for a Stationary and Translating Droplet at Extremely Low Viscosity Values Using the Lattice Boltzmann Method Color-Gradient Multi-Component Model with Central Moments Formulation

Mendidik Toleransi Beragama Siswa; Analisis Tentang Efektivitas Layanan Informasi Menggunakan Media Film

This study aims to analyze teacher activities in educating religious students on religious tolerance, which is packaged through information services using film media. In this research, the film used is The Santri film by director Livi Zheng, released in 2019. The research location is in MTs. Insan Cita Medan, with research informants, focused on class VIII. This study uses quantitative research methods with a quasi-experimental approach. The research sample was 30 students, determined by purposive sampling. Data collection using questionnaires and interviews. Questionnaire to obtain data about information services and consultations to determine student responses to these services. Test the hypothesis made with the Product Moment formulation and for its significance using the t-test. The study results show a significant positive effect of information services using film media on religious tolerance in students VIII MTs. Insan Cita Medan Learning Year 2021/2022 with a correlation index of r-count = 0.7155 > r-table = 0.334 and a significant level of 51.19%. Thus the better the information services provided, the better the changes in the attitude toward religious tolerance of students.

Method of Moments and T-Matrix Hybrid

Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this article. The hybrid methods are particularly efficient when describing the interaction of electrically small complex objects and electrically large objects of canonical shapes such as spherical multilayered bodies where the T-matrix method is reduced to the Mie series making the method an interesting alternative in the design of implantable antennas or exposure evaluations. Method performance is tested on a spherical multilayer model of the human head. Along with the hybrid method, an evaluation of the transition matrix of an arbitrarily shaped object is presented and the characteristic mode decomposition is performed, exhibiting fourfold numerical precision compared to conventional approaches.

The relations between the multipole moments in axistationary electrovacuum spacetimes and the N-soliton solution

A general formulation of the relativistic multipole moments in axistationary electrovac spacetimes is introduced in a closed analytical form. We give a complete description of how the Ernst potentials on the symmetry axis can be completely characterized by these arbitrary multipole moments. Some concrete applications are also developed.

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

Formulation of 8-moment plasma transport with application to the Nernst effect

8-moment plasma models using two different distribution functions are used to study the Nernst effect and heat transport in dense plasma. These models are presented in hyperbolic form in contrast to traditional parabolic systems derived from perturbing the distribution function, as in Braginskii [Rev. Plasma Phys. 1, 205 (1965)]. The hyperbolic moment formulation can be solved implicitly in time with straightforward and fast local solvers. The numerical implementation of 8-moment models with the relaxation method in the PERSEUS code is also presented. To test 8-moment PERSEUS compared to Braginskii's transport equations, a verification test for the Nernst thermo-magnetic wave by Velikovich et al. [Phys. Plasmas 26, 112702 (2019)] is performed that confirms the presence of the same physics, but with slight differences in the transport coefficients, which are tabulated in the limits of high and low magnetization.

Thermodynamic approach to electric quadrupole moments

Higher-rank electric/magnetic multipole moments are attracting attention these days as candidate order parameters for exotic material phases. However, quantum-mechanical formulation of those multipole moments is still an ongoing issue. In this paper, we propose a thermodynamic definition of electric quadrupole moments as a measure of symmetry breaking, following previous studies of orbital magnetic dipole moments and magnetic quadrupole moments. The obtained formulas are illustrated with a model of orbital-ordered nematic phases of iron-based superconductors.

Omni-Zernike Algorithm for Template Matching in Catadioptric System

Image descriptor have been widely applied in many computer visions and image understanding applications including pattern recognition, robotic, video surveillance, camera calibration and image retrieval, etc. Invariants features are robust when apply several transformations of photometry (illumination, blur, noise, JPEG compression) and transformations of geometry (scaling, rotation, translation and viewpoint change). In this study, we present representation and matching region descriptors. Consequently, a set of region used provided by catadioptric system for evaluation of the performance. These regions are normalized by unit circle form with form and size change. In this contribution, the image descriptors of regions used is Moment's Zernike. They are most suitable invariants in omnidirectional context thanks to the polar coordinates used both omnidirectional geometry and Zernike Moments formulation. The aim is realize a robust matching between object's block by using a measure of distance between Zernike's moment descriptors for optimal similarity. Results shown clearly demonstrate the performance of our method and powerful than most important region descriptors (GLOH, SIFT, PCA-SIFT, complex moments and steerable filters) in term of the ROC curve or precision-recall criterion.

Effect of the conditional scalar dissipation rate in the conditional moment closure

In the context of modeling turbulent scalar mixing using probability density function (PDF) methods, the treatment of molecular mixing is of paramount importance. The conditional moment closure (CMC) offers a high-fidelity description for molecular mixing in nonpremixed flows. Recent work has demonstrated that first-order CMC can be implemented numerically using the moments of the conditioning variable and first-order joint moments of the scalar of interest. When solving the CMC using, for example, quadrature-based moment methods (QBMM), a functional form must be chosen for the conditional scalar dissipation rate (CSDR) of the conditioning variable. In prior work, the CSDR was chosen to produce a β-PDF for the conditioning variable (mixture fraction) at steady state. This choice has the advantage that the system of moment equations used in QBMM-CMC can be written in closed form. In this work, an alternative choice for the CSDR is investigated, namely, the amplitude mapping closure (AMC). With the AMC, the moment equations can be closed using the quadrature method of moments incorporated into a realizable ordinary differential equation solver. Results are compared with the β-CSDR closure for binary, passive scalar mixing in homogeneous single- and disperse-phase turbulent flows. It is also demonstrated that the moment formulation of CMC provides a straightforward method for modeling the effect of differential diffusion in the context of CMC.

The influence of Frayer model strategy towards students’ vocabulary mastery at the eighth class of SMPN 26 Bandar Lampung in 2017/2018

Students’ vocabulary mastery is influenced by many factors. One of them is the technique, which the teachers use in teaching. In this research, the writer applied Frayer Model Strategy to teach vocabulary in the classroom. Then the writer analyzed the result of the technique in order to know its influence. The research was conducted at the eighth class of SMPN 26 Bandar Lampung in 2017/2018. The students of X1 were as the sample that was taught by using Frayer Model Strategy and X2 that was taught by using conventional technique. In this case, the writer used two classes as the sample, the first class as experimental class (29 students) and the second class as a control class (28 students) from 265 students of eight classes. The sample was gotten by random sampling technique and the research based on the experiment method. In collecting, the writer used objective test that was multiple-choice test contained 40 questions. The technique of analysis data in this research used product moment formulation. The result of the research shows that there is a significant influence of Frayer Model Strategy towards Students’ Vocabulary Mastery at the eighth class of SMPN 26 Bandar Lampung in 2017/2018. It showed from the distribution list with df = 55 obtained the t ratio t0.95 or significance level of 5% and t - ratio to 0.99 or significance level of 1% is equal to 2.02 and 2.70. They are less than t-test 7.16. Finally, the writer concluded that there is a significant influence of Frayer Model Strategy towards students’ vocabulary mastery at the eighth class of SMPN 26 Bandar Lampung in 2017/2018. dx.doi.org/10.23960/aksara/v21i2.pp145-155

An iterative equivalent linearization approach for stochastic sensitivity analysis of hysteretic systems under seismic excitations based on explicit time-domain method

The sensitivity analysis of hysteretic systems under nonstationary random excitations is of great concern to the stochastic optimal design and control of structures. The equivalent linear equation of motion is first constructed for the hysteretic system by the equivalent linearization method (ELM), and the sensitivity equation of the equivalent linear system is then derived by the direct differentiation technique. These two equations are further combined into an overall equivalent linear equation, which depends on the statistical moments and sensitivities of responses of the system and should be solved on an iterative basis. The analysis problem is thus transformed to a series of nonstationary random vibration analyses of the iterative linearized systems, which can be solved with the explicit time-domain method (ETDM) recently proposed for linear random vibration problems. The ETDM has high computational efficiency owing to the explicit formulations of statistical moments of responses. Therefore, a numerical algorithm is developed by combining ELM and ETDM for efficient stochastic sensitivity analysis of hysteretic systems. A 100-degree-of-freedom hysteretic system is investigated to illustrate the accuracy and efficiency of the proposed method, and a 10-degree-of-freedom base-isolated system is further analyzed to show the feasibility of the proposed method for stochastic structural optimization.

Stochastic sensitivity analysis of energy-dissipating structures with nonlinear viscous dampers by efficient equivalent linearization technique based on explicit time-domain method

Nonlinear fluid viscous dampers have been widely used in energy-dissipating structures due to their stable and high dissipation capacity and low maintenance cost. However, the literature on stochastic optimization of nonlinear viscous dampers under nonstationary excitations is limited. This paper is devoted to the stochastic response and sensitivity analysis of large-scale energy-dissipating structures equipped with nonlinear viscous dampers subjected to nonstationary seismic excitations. The analysis procedure is developed in the frame of the equivalent linearization method (ELM) in conjunction with the explicit time-domain method (ETDM). The equivalent linear system and the corresponding statistical moments of responses at a specific time instant are first obtained through a series of stochastic response analyses of the linearized systems. Then the sensitivities of the statistical moments of responses are determined via a series of stochastic sensitivity analyses of the equivalent linear system at the corresponding time instant. The above two iterative procedures are facilitated at high efficiency using ETDM with explicit formulations of the statistical moments of responses and the sensitivities of the statistical moments. This process is repeated for different time instants, and the time histories of the statistical moments and their sensitivities can be obtained. The stochastic response and sensitivity results are further utilized to conduct the stochastic optimal parametric design of the nonlinear viscous dampers. A one-storey building model equipped with a nonlinear viscous damper is analyzed to demonstrate the accuracy of the proposed method, and a suspension bridge with a main span of 1200 m equipped with 4 nonlinear viscous dampers is further investigated to illustrate the feasibility of the proposed method for stochastic optimal design of large-scale structures.

Risk-sensitive control of Markov decision processes: A moment-based approach with target distributions

In many revenue management applications risk-averse decision-making is crucial. In dynamic settings, however, it is challenging to find the right balance between maximizing expected rewards and minimizing various kinds of risk. In existing approaches utility functions, chance constraints, or (conditional) value at risk considerations are used to influence the distribution of rewards in a preferred way. Nevertheless, common techniques are not flexible enough and typically numerically complex. In our model, we exploit the fact that a distribution is characterized by its mean and higher moments. We present a multi-valued dynamic programming heuristic to compute risk-sensitive feedback policies that are able to directly control the moments of future rewards. Our approach is based on recursive formulations of higher moments and does not require an extension of the state space. Finally, we propose a self-tuning algorithm, which allows to identify feedback policies that approximate predetermined (risk-sensitive) target distributions. We illustrate the effectiveness and the flexibility of our approach for different dynamic pricing scenarios.

Analysis of a rectangular waveguide transverse slot using MoM and image method

A waveguide fed transverse slot has been analysed using the Method of Moments (MoM) formulation, wherein the internal admittance matrix elements have been evaluated from image theory and using the images of the slot due to waveguide walls. The contribution from all the images not in the same row as the slot has been evaluated using a closed-form expression and a rapidly converging series with negligible contribution. The contribution from the row containing the reference slot has been evaluated by adding the mutual admittance between a few images and the reference slot using some recently developed simple and accurate approximations. The formulation has been extended to transverse slots radiating between the baffles. The results calculated using this simple, efficient and intuitive method are in excellent agreement with other theoretical as well as measured results. The technique can be extended to other slot configurations such as an inclined slot and for other slot aperture distributions such as with an edge condition in configurations permitting image formation.

New and extended design moment formulations for slender columns in frames with sway

Present first-order based design code formulations for slender columns in frames with sway, employ sway magnification factors (for global second-order effects) also as moment magnifiers for the individual columns of the frame (storey). This approach ignores differences in magnification of individual column moments caused by local second-order effects in the columns. This difference can be significant. Better understanding of this aspect will strengthen approximate first-order based elastic methods, for which the important superposition principle is valid. Towards this end, local second-order effects are considered for shears, end moments and maximum moments, applicable over the full range of axial loads. Specifically, end moment and maximum moment expressions of columns with sway are derived. These represent novel contributions that are suitable in typical design code formats, and in practical design work. They will allow more rational column assessments, and will allow more economical designs than present structural code procedures. Proposals are verified by comparison with results from second-order in-plane elastic analyses of single restrained columns and columns in frame panels. Also, extensions to the general case of load combinations that include both gravity and sideways loading are briefly presented.

On the Use of Fractional-Order Quadrature-Based Moment Closures for Predicting Soot Formation in Laminar Flames

ABSTRACT The accurate numerical prediction of soot formation in practical combustion devices remains a challenge. Several new quadrature-based moment closures based on fractional-order moments of soot particle volume are proposed for the prediction of soot formation in laminar diffusion flames at atmospheric and elevated pressures. Both univariate Quadrature Method of Moments (QMOM) models based on a classical particle volume formulation and bivariate Conditional Quadrature Method of Moments (CQMOM) models based on a new particle volume/primary particle number formulation are proposed. The soot models include detailed gas-phase chemistry along with nucleation, surface growth, oxidation, and coalescence/coagulation soot chemistry source terms. Initial comparisons to predictions of a sectional method for space homogeneous simulations illustrate well the improved predictions of soot number density and volume fraction are provided by the fractional-order moment closures compared to integer-order moment approaches. Furthermore, additional comparisons of soot prediction of methane/ethanol laminar diffusion flames at elevated pressures indicate that the proposed bivariate CQMOM, with a specified soot inception size, offer significantly improved results when compared to the other variants and available experimental data.