Numerical Coefficients Research Articles

Modern tensor–spinor symbolic algebra algorithms and computing non-closure geometry and holoraumy in 11D, 𝒩=1 supergravity

The Supersymmetry Genomics project aims to classify supermultiplets by properties like adinkras and holoraumy. The project’s protocol is: (1) set up the SUSY transformation rules (and action) with unknown numerical coefficients, (2) solve those coefficients and (3) compute desired properties, e.g. non-closure geometry (the non-closure functions in the anticommutator of supercovariant derivatives) and holoraumy (the commutator of supercovariant derivatives). This paper provides the first broadly applicable computer algorithms for completing these computations, comprising a new Cadabra module we call “SusyPy”. We provide a significant extension of the available tensor arithmetic/canonicalization to include spinor-indexed expressions and NW–SE convention, and we provide a new Fierz expansion algorithm for spinor-indexed expressions. On top of this new tensor–spinor symbolic algebra, we have built algorithms for solving for the coefficients of a multiplet and its action, and for computing holoraumy, for both off-shell and on-shell [Formula: see text] multiplets of any dimension. We apply our tools to assimilate linearized 11D, [Formula: see text] supergravity into the Genomics project. We demonstrate solving the 11D, [Formula: see text] multiplet, as in Cremmer, Julia and Scherk, in a few lines of code, and we provide a comprehensive picture of the multiplet’s non-closure geometry. Further, we provide the first-ever computation of the holoraumy of 11D, [Formula: see text] supergravity.

Suitability matching evaluation of the low-carbon regional integrated energy system based on the “resource-demand” balance

The integrated energy system (IES) stands out due to its advantages of multi-energy complementarity, green and efficiency. This paper aims to provide a practical model for suitable region site selection of low-carbon regional IES based on the “resource-demand” balance. A “resource-demand” suitability matching analysis indicator system is established. By using prospect theory and variable precision rough set theory, the decision-making preferences and the cognitive fuzziness influence of expert scoring were corrected respectively, and reasonable subjective weights were obtained. Then, the objective weights are obtained using the entropy method, and the optimal combined weights are obtained through the game theory weighting method. Finally, this paper establishes a “resource-demand” suitability matching model consisting of three sub models: similarity matching degree, numerical matching degree, and suitability matching degree. An empirical study is conducted on 16 regions in Beijing, and the results show that the numerical matching degree of “resource-demand” gradually decrease from the central urban regions to the surrounding regions. The similarity matching degree in most regions reaches the highest range (0.776,1.00). There are 4 regions with a suitability matching rating of perfect, 7 regions with a rating of great, 1 region with a rating of good, and 4 regions with a rating of poor. The suitability matching model established in this paper can guide energy project decision-makers to select regions with greater potential for the development of IES. In addition, adjusting the similarity matching coefficient and numerical matching coefficient can meet the diversified needs of decision-makers for the similarity matching degree and numerical matching degree of the “resource-demand” balance, providing support for energy project planning decisions.

The dual Ginzburg-Landau theory for a holographic superconductor: finite coupling corrections

The holographic superconductor is the holographic dual of superconductors. We recently identified the dual Ginzburg-Landau (GL) theory for a class of bulk 5-dimensional holographic superconductors (arXiv:2207.07182 [hep-th]). However, the result is the strong coupling limit or the large-Nc limit. A natural question is how the dual GL theory changes at finite coupling. We identify the dual GL theory for a minimal holographic superconductor at finite coupling (Gauss-Bonnet holographic superconductor), where numerical coefficients are obtained exactly. The GL parameter κ increases at finite coupling, namely the system approaches a more Type-II superconductor like material. We also point out two potential problems in previous works: (1) the “naive” AdS/CFT dictionary, and (2) the condensate determined only from the GL potential terms. As a result, the condensate increases at finite coupling unlike common folklore.

Calculation of the Gaunt coefficients over real spherical harmonics

The Gaunt coefficients are numerical coefficients that describe the interaction between two different angular momentum quantum states. In the quantum physics, this interaction affects the energy levels and structures of atoms and molecules. The calculation of Gaunt coefficients plays a significant role in molecular integral evaluations, which emerge from the solving Schrödinger equation. This work presents the analytical evaluation methods for the Gaunt coefficients using real spherical harmonics and associated Legendre functions. In this paper, the general integral form of the Gaunt coefficients is written in two main parts as polar and azimuthal integrals. The new analytical relations and symmetry properties are generated for these integrals. The analytical expressions are obtained in terms of the beta functions, and these coefficients are calculated for different atomic orbitals of angular momentum using the Mathematica programming language. The obtained numerical results are compared with the values in the literature and we found completely agreement to 15 digits.

Compensation of staircase-induced boundary absorption errors in FDTD simulation

Finite-difference time-domain (FDTD) methods are popular for wave-based simulations because their regular grid enables highly efficient implementation, especially on parallel processing architectures. On the flip side, these methods exhibit errors caused by the staircase approximations that result when arbitrary boundary geometries are approximated on the fixed grid. Of particular concern in room acoustics is the staircasing of absorptive boundaries, as this has been shown to cause errors as large as 40% in computed reverberation times that do not reduce when the grid is refined. This paper analyses the effectiveness of a previously proposed compensation method that consists of modifying the admittance boundary conditions based on the staircased surface area. A theoretical analysis shows that for special boundary orientations the numerical reflection coefficient converges to the exact result at low frequencies. Numerical tests complement this analysis to show that the compensation yields accurate results at intermediate orientations as well. A spherical resonator case further demonstrates that a close match between numerically and analytically computed relaxation times is also obtained for curved boundaries.

Rapid computation of the plasma dispersion function: Rational and multi-pole approximation, and improved accuracy

The plasma dispersion function Z(s) is a fundamental complex special integral function widely used in the field of plasma physics. The simplest and most rapid, yet accurate, approach to calculating it is through rational or equivalent multi-pole expansions. In this work, we summarize the numerical coefficients that are practically useful to the community. In addition to the Padé approximation to obtain coefficients, which are accurate for both small and large arguments, we also employ optimization methods to enhance the accuracy of the approximation for the intermediate range. The best coefficients provided here for calculating Z(s) can deliver 12 significant decimal digits. This work serves as a foundational database for the community for further applications.

Turbo-RANS: straightforward and efficient Bayesian optimization of turbulence model coefficients

PurposeIndustrial simulations of turbulent flows often rely on Reynolds-averaged Navier-Stokes (RANS) turbulence models, which contain numerous closure coefficients that need to be calibrated. This paper aims to address this issue by proposing a semi-automated calibration of these coefficients using a new framework (referred to as turbo-RANS) based on Bayesian optimization.Design/methodology/approachThe authors introduce the generalized error and default coefficient preference (GEDCP) objective function, which can be used with integral, sparse or dense reference data for the purpose of calibrating RANS turbulence closure model coefficients. Then, the authors describe a Bayesian optimization-based algorithm for conducting the calibration of these model coefficients. An in-depth hyperparameter tuning study is conducted to recommend efficient settings for the turbo-RANS optimization procedure.FindingsThe authors demonstrate that the performance of the k-ω shear stress transport (SST) and generalized k-ω (GEKO) turbulence models can be efficiently improved via turbo-RANS, for three example cases: predicting the lift coefficient of an airfoil; predicting the velocity and turbulent kinetic energy fields for a separated flow; and, predicting the wall pressure coefficient distribution for flow through a converging-diverging channel.Originality/valueTo the best of the authors’ knowledge, this work is the first to propose and provide an open-source black-box calibration procedure for turbulence model coefficients based on Bayesian optimization. The authors propose a data-flexible objective function for the calibration target. The open-source implementation of the turbo-RANS framework includes OpenFOAM, Ansys Fluent, STAR-CCM+ and solver-agnostic templates for user application.

Innovative Date Fruit Classifier Based on Scatter Wavelet and Stacking Ensemble

Dates are essential fruits loaded with vital nutrients that keep bones healthy and prevent bone-related disorders. Approximately 8.46 million tons of different types of dates are cultivated and produced annually around the globe. There are more than 400 types of dates that are time-consuming and expensive to produce. Classifying them using conventional methods is labor-intensive, and this is one of the biggest problems for the date industry. Dataset fruit classification plays a vital role in the food industry. Dates can be classified from a luxury class to a less quality class. Accordingly, the food industry needs an automotive date fruit classifier that can work in food factories. This study proposes a pioneering method to classify date fruit that relies on extracting features from the texture of dates using Scattering Wavelet Transformation (SWT). The SWT yields in numeric coefficients were found to be immune to the deformation of invariants. This feature set trains an ensemble classifier that combines a voting mechanism to eliminate overfitting. The ensemble classifier consists of a random forest, a support vector machine classifier, and a logistic regression hyper-learner. Our novel approach was tested on two benchmarked datasets. The first data set scored F1 between 0.95 and 1.0 at the same time. The second dataset registered F1 between 0.96 and 1.0 in each of the 20 date classes. Some dates are close to each other in texture, resulting in high false positives or recall, causing a lower F1 score accuracy degree. The novelty of this approach comes from the featured representative of each date class, relying on the texture of the fruit as a discriminative feature, not on the fruit shape or color, which may not be robust enough as distinguishable features, especially in date classes that are close to each other in shape. Doi: 10.28991/HIJ-2024-05-02-010 Full Text: PDF

A CFD Analysis of Oscillating Airfoil with Leading Edge Roughness: Comparing Correlations for Equivalent Sand Grain Roughness

Numerical simulations express surface roughness as equivalent sand grain roughness values, so the correlation is required to convert realistic roughness into equivalent sand grain roughness values. The correlations were designed to match the wall velocity distributions for static cases with roughness, and they accurately predicted roughness effects when applied to URANS simulations. Several studies have examined the roughness effect on dynamic pitching airfoils. Still, they have only considered the presence of roughness, neglecting the process of converting the actual roughness to equivalent sand-grain roughness. Thus, in the present study, we apply a static case-based equivalent sand-grain roughness correlation to dynamic pitching analysis to validate the suitability of each correlation and verify the significance of correlation parameters. It was observed from a comparison study between numerical aerodynamic coefficients and experimental data from Ohio State University that physical parameters such as skewness and roughness height were important parameters to predict the dynamic stall behaviour more accurately. It was also observed that dynamic stall prediction accuracy is affected by the frequency and type of airfoil, and through this, it was confirmed that there are additional factors to consider when using an equivalent sand grain roughness correlation on pitching airfoils.

Dependencies for determining heat transfer coefficients and air resistance for heat exchangers with tubular-plate heat exchange surface

Problem. The article analyzes existing generalized dependencies for determining convective heat transfer coefficients and air resistance coefficients for tubular-plate surfaces widely used in the production of modern charge air coolers and radiators. It is established that practical application of such dependencies, in some cases, is associated with significant errors revealed during experimental checks. Consequently, there is a need to adjust such dependencies for corridor bundles of flat-oval tubes with transverse grouped finning by flat fins. Goal. The aim of this study is to correct experimental dependencies for heat exchange and resistance. Numerical coefficients are adjusted on this basis, while the structure of dimensional dependencies remains unchanged. Simultaneously, the study is conducted for further improvement of the methodology for obtaining similar dependencies. Methodology. Adjustment of generalized dependencies for determining convective heat transfer coefficients and air resistance coefficients for tubular-plate heat exchange surfaces is carried out experimentally. Results. New dependencies are proposed for determining heat transfer coefficients and air resistance coefficients for tubular-plate heat exchange surfaces. Their accuracy and efficiency are investigated over a wide range of regimes. Originality and practical value. Unlike known dependencies of a similar nature, the proposed dependencies are provided in a single complex that should be used in modern heat exchanger calculation methods. It is established that the maximum error in determining air temperature according to the proposed dependence does not exceed 0.3 °C for the entire investigated range, and the error in determining aerodynamic resistance does not exceed 8 %, indicating high accuracy of modeling. Such accuracy ensures the possibility of applying the proposed dependencies for engineering calculations.

Perturbative reheating and thermalization of pure Yang-Mills plasma

We investigate the thermalization of high-energy particles injected from the perturbative decay of inflaton during the pre-thermal phase of reheating in detail. In general, thermalization takes a relatively long time in a low-temperature plasma; therefore, the instantaneous thermalization approximation is not justified, even for the reheating of the Standard Model (SM) sector. We consider a pure Yang-Mills (YM) theory as an approximation of the SM sector or a possible dark sector, considering the Landau-Pomeranchuk-Migdal effect, a quantum interference effect in a finite temperature plasma. We perform the first numerical calculation to solve the time evolution of the system, including the redshift due to the expansion of the Universe, and show the details of the temperature evolution near the maximum and the behavior of the quasi-attractors at later times. The maximal temperature Tmax and time scale tmax are determined quantitatively, such as Tmax ≃ 0.05 × ΓIMPI2/mI32/5mI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left({\\Gamma}_I{M}_{\ extrm{PI}}^2/{m}_I^3\\right)}^{2/5}{m}_I $$\\end{document} and tmax ≃ 2 × 103 × ΓIMPI2/mI3−3/5mI−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left({\\Gamma}_I{M}_{\ extrm{PI}}^2/{m}_I^3\\right)}^{-3/5}{m}_I^{-1} $$\\end{document} in the SM-like system, where mI and ΓI are the mass and decay rate of inflaton. We also provide a similar formula for pure SU(N) and SO(N) YM theories for general values of N and coupling constant α, including Tmax ∝ α4/5 and tmax ∝ N−2α−16/5 behaviors and their numerical coefficients. The thermalization occurs in a finite time scale, resulting in a lower maximal temperature of the Universe after inflation than that under the instantaneous thermalization approximation.

Latent structure and reliability

There are numerous reliability coefficients and α is the most popular. It is known that different coefficients can be appropriate in specific conditions and that α should not be used indiscriminately. However, some coefficients and conditions, particularly regarding the latent structure, lacked attention in previous research. In four Monte Carlo simulations, this study compared α, λ2, maximized λ4, λ4 based on locally optimal splits, μ2, Gilmer-Feldt, Kaiser-Caffrey α, Heise-Bohrnstedt Ω, Joreskog's ρ, ωtotal, algebraic greatest lower bound, greatest lower bound based on minimum rank factor analysis in every condition and also hierarchical ω and asymptotic ω hierarchical in multidimensional conditions. Findings suggest each of these coefficients can be useful at least in some conditions. Most differences in performance were observed in congeneric conditions and conditions with up to moderate loadings. Some coefficients were found to be more useful than previously considered. Results are discussed in the context of existing theory and previous Monte Carlo studies.

Charged particle transport coefficient challenges in high energy density plasmas

High energy density physics (HEDP) and inertial confinement fusion (ICF) research typically relies on computational modeling using radiation-hydrodynamics codes in order to design experiments and understand their results. These tools, in turn, rely on numerous charged particle transport and relaxation coefficients to account for laser energy absorption, viscous dissipation, mass transport, thermal conduction, electrical conduction, non-local ion (including charged fusion product) transport, non-local electron transport, magnetohydrodynamics, multi-ion-species thermalization, and electron-ion equilibration. In many situations, these coefficients couple to other physics, such as imposed or self-generated magnetic fields. Furthermore, how these coefficients combine are sensitive to plasma conditions as well as how materials are distributed within a computational cell. Uncertainties in these coefficients and how they couple to other physics could explain many of the discrepancies between simulation predictions and experimental results that persist in even the most detailed calculations. This paper reviews the challenges faced by radiation-hydrodynamics in predicting the results of HEDP and ICF experiments with regard to these and other physics models typically included in simulation codes.

Analyzing the Time Evolution of a Particle by Decomposes the Initial State Confinement in 1D Well into the Lowest Eigenstates Energy

In this work, we obtained the time evolution of the wave function of a limited quantum system (1D Box), hence getting a mathematical model to describe the system. By using programming computes, it performs a time evolution that decomposes the initial state into the 2,10, and 20 lowest energy eigenstates. Finally, by comparing numerical de-composition coefficients for the wave function to the analytical values, it found the number of knots increases directly versus the energy of the particle's quantum state. As a result, the mean bending given by the second derivative which is proportional to the kinetic energy operator should increase. We found there is a negligible mean and standard deviation of the energy in units of the ground state energy.

Analytical Confirmation of the Calculated Dependencies for Heat Exchange in a Plate Recuperator when Humidifying the Auxiliary Flow

The relevance of the study is related to the need to ensure maximum reduction of energy consumption while ensuring the calculated parameters of the indoor climate in buildings under the Law of the Russian Federation “On Energy Saving...” and the updated version of SP 131. The purpose of the study is to obtain an approximate analytical expression of this dependence, which makes it possible to additionally confirm the results of field and numerical experiments previously performed by the authors for this flow treatment scheme. The objective of the study is to build a simplified mathematical model of the processes of changing the heat and humidity state of the air in the recuperator, identify the main factors affecting the increasing multiplier to the coefficient of temperature efficiency of the device and obtain the necessary numerical coefficients in formulas linking the desired and initial parameters. The general equation of thermal balance and heat transfer for the heat exchanger as a whole is used, including the integral characteristics of the apparatus in a dimensionless form, as well as standard techniques of algebraic transformations. An approximate analytical expression is obtained for an increasing multiplier to the coefficient of thermal efficiency of the recuperator taking into account the additional cooling of the inflow due to the heat consumption for evaporation. It is shown that the general structure of this ratio coincides with the one found by the authors earlier by processing the results of numerical modeling of a two-dimensional temperature field in a heat exchanger, taking into account experimental data on the amount of moisture carried away, which confirms their correctness and reliability.

On the possibility of changing the trajectory of a projectile or rocket based on aerodynamic impact in the shock wave zone

A physical hypothesis is proposed that it is possible to change the design trajectory of the projectile on the basis of mechanical action on the entire volume of shockwave zones with a unilateral, asymmetric presence of the second projectile. Deviating from the original trajectory results in a positive result when it comes to a defensive task. A new semi-empirical model has been developed and compiled, which allows you to calculate the trajectory of the projectile taking into account the air resistance to movement. In the new model, it is recommended that only four easily detectable values​ ​ be used in upcoming experiments: the initial departure speed , the maximum altitude , the maximum flight range and the full time. The calculation scheme uses iterative calculations. On the basis of which the values ​ ​ of numerical coefficients in the semi-empirical model are specified. The physical idea that external powerful laser radiation can heat the side surface of the projectile and the entire zone of wave jumps of the seal is justified. On one side of the semi-plant, that is, it is one-way heating. The asymmetrical thermal state on both sides of the missile may cause the missile or projectile to deviate from the previously assigned heading. This circumstance is also in favor of the proposed idea.

Validation of a RANS Turbulence Model for a S833 Wind Turbine Airfoil With a Trailing Edge Flap Using Oil Visualization and Pressure Taps

Abstract The aerodynamics of a small wind turbine blade was captured using a γ–Reθ k–ω shear stress transport transitional turbulence model tuned with production limiter coefficients at a Reynolds number of 1.70×105. The computational fluid dynamics simulations were validated against wind tunnel experiments that included airfoil pressure tap measurements and surface oil flow visualization (SOFV) to capture the flow field. The uniqueness of this blade included a trailing edge flap that was 20% of the chord controlled using a servomotor. The test matrix included angles of attack (AOA) between 1 deg and 7 deg with flap angles of 10 deg in the upward and downward position. Two locations were always observed on the airfoil: a leading edge region of high shear and a midsection of flow separation. Within the flow separation section, two distinct regions existed: a complete detachment of flow from the airfoil surface creating a stagnation region which was followed by a reverse flow region. A third location of flow reattachment near the trailing edge was observed for all cases excluding a downward angled trailing edge flap. The utilization of the flap resulted in changes to the size of the separation zone and the movement of the separation zone along the chord. The numerical skin friction coefficient, oil residue profiles from the SOFV, and pressure tap measurements all showed onset of separation locations on the chord within 10%. The computational fluid dynamics model also predicted the coefficient of pressure across the chord of the airfoil within 10% in comparison to the experimental measurements.

Experimental study of rainwater grate blocking and submergence of outfall on drainage network capacity

Accurately evaluating the performance of urban underground drainage network and its influencing factors is a challenging problem, as this process is affected by many complex factors. In this study, based on an overland flow experiment considering drainage process of pipe network, a series of physical model experiments were conducted to investigate the influences of different surface slopes, rainwater grate blockage and the submergence of outfall on the performance of the drainage pipe network system. The hydrographs of surface runoff and pipe network flow were recorded in collection tanks by precise digital pressure sensors to provide comprehensive information about the characteristics of drainage performance in the pipe network. Through a series of experimental data collection and analysis, the following conclusions are drawn from this study: (1) The longitudinal slope of the road decreases the pipe drainage capacity by 1.68%–8.94%, and this reduction effect is more significant with the increase of slope. (2) The blockage of rainwater grate at different locations has different impacts on the road drainage system, the downstream rainwater grate blockage has the most obvious impact on the performance of the drainage system, which reduces the drainage capacity by 22.59%–25.38%. (3) Different submergence degrees of rainwater outlet have different impacts on the drainage system. Under different slopes, the drainage capacity of the pipe network decreases by 1.88%–23.46% with the increase of the submergence degree of the outfall. These experimental results are helpful in understanding the working conditions of urban road drainage system and the influencing factors of the system's drainage capacity, and also provide measured data for verification of relevant numerical models and coefficient calibration.

Socioeconomic Determinants of Genetic Disorder in Disabled Persons of Punjab, Pakistan

This study investigates the relationship among family history, genetic markers, family income, occupation, and the presence of genetic disorders in disabled persons in Punjab, Pakistan. The research study uses cross-sectional primary data from 5040 individuals collected with online and manual research questionnaire. The study employs Structural Equation Modeling (SEM) for rigorous assessment of numerical coefficients and also examines reliability, validity, and discriminant validity among the constructs to ensure their distinctiveness within the model. With R-square (0.541) and adjusted R-square (0.529), the results show that Socioeconomic indicators (Family income & employment, and Occupation) and family history have significant positive while genetic indicators like genetic markers have a negative impact on the presence of genetic disorder in disabled persons. The results also showed that mediation effects (the access to education and access to healthcare) demonstrate a significant negative impact on the presence of genetic disorders in disabled persons, where we safely say that with the increase in access to education and access to healthcare, genetic disorders in disabled persons can be removed or overcome in Punjab, Pakistan. Based on findings, recommendations are proposed for better decisions of officials and policymakers in the betterment and favor of disabled persons in Punjab, Pakistan.

Assessment of the Possibility of Excluding Secondary Heating of the Inflow During the Warm Period in Modern Climatic Conditions

The subject of the study is the dependence on the required indoor air temperature and the accepted inflow temperature for a minimum heat and humidity ratio in the room, in which secondary heating of inflow can be excluded. The purpose of the study is to obtain an analytical expression of this dependence, which allows an engineering assessment of the possibility of eliminating secondary heating in the process of designing air conditioning systems without the use of graphical constructions. The objective of the study is to represent an adequate flow processing scheme on the I–d diagram, identify the main factors affecting the minimum heat and humidity ratio in the room and obtain the necessary numerical coefficients in formulas linking the desired and initial parameters. Research results. An analytical dependence is obtained that allows calculating the minimum possible value of the heat and humidity ratio in a room in which secondary heating is not required, and only cooling of the inflow with drying in a surface air cooler is sufficient if it has a bypass channel. The presentation is illustrated with numerical and graphical examples.