Coefficient Functions Research Articles

Double-virtual NNLO QCD corrections for five-parton scattering. II. The quark channels

We complete the computation of two-loop helicity amplitudes required to obtain next-to-next-to-leading order QCD corrections for three-jet production at hadron colliders, including all contributions beyond the leading-color approximation. The analytic expressions are reconstructed from finite-field samples obtained with the numerical unitarity method. We find that the reconstruction is significantly facilitated by exploiting the overlaps between rational coefficient functions of quark and gluon processes, and we display their compact generating sets. We implement our results in a public code, and demonstrate its suitability for phenomenological applications. Published by the American Physical Society 2024

Analysis of pipeline leakage in unsaturated stratum: A new seepage-diffusion model

Accurate prediction of the spread of fluids leaking from underground pipelines is crucial for risk assessment. In this study, we developed a method for predicting the diffusion range of pipeline seepage fluids within an unsaturated stratum. First, we derived a seepage–diffusion equation based on the generalized Darcy’s law and subsequently analyzed the mechanism of fluid diffusion in the unsaturated stratum. We then constructed a model for the seepage–diffusion of a pipeline leakage fluid, incorporating variables such as the saturation, permeability coefficient, diffusion pressure, and diffusion distance of soil microelements across various time intervals, using a stepwise algorithm in tandem with the Green–Ampt model and VG–Mualen permeability coefficient function. We investigated the influence of fluid self-gravity, saturated permeability coefficient, initial saturation, and intra-pipe pressure on the diffusion distance of the pipeline leakage fluid in an unsaturated stratum, focusing on specific cases. The results indicate that an increase in the saturated permeability coefficient, initial saturation, and intra-pipe pressure leads to an increase in the fluid diffusion distance. A simulation test was conducted to validate the proposed seepage–diffusion model. The findings of this study can be employed to predict the diffusion range of pipeline leakage fluids in various formation types, providing a vital foundation for pipeline leakage accident management.

Insight into the Physical Properties of the Chalcogenide XZrS3 (X = Ca, Ba) Perovskites: A First-Principles Computation

AbstractThis study investigates the structural, mechanical, optical, thermal, and electronic properties of the ionic semiconducting materials XZrS3 (X = Ca, Ba) within the framework of density functional theory (DFT). Here, the elastic constants, modulus (bulk, shear, Young's), ratios (Pugh, Poisson) and elastic anisotropy for XZrS3 (X = Ca, Ba) are studied. Furthermore, the electronic, optical, and thermal properties for XZrS3 (X = Ca, Ba) are regenerated and designed using the values obtained with Cambridge Serial Total Energy Package (CASTEP) software. The calculated lattice parameters show excellent agreement with theoretical and experimental values. The elastic stiffness constants confirm the mechanical stability of both compounds. Although XZrS3 (X = Ca, Ba) is elastically anisotropic, it has little optical anisotropy. The electronic band structures of the material exhibit direct-bandgap semiconducting behavior, with values of 1.3 eV (CaZrS3) and 1.1 eV (BaZrS3) using the generalized gradient approximation (GGA), respectively, which is ideal for solar cell (0.9–1.56 eV) and optoelectronic device applications. Bandgap values of 1.9 eV and 1.6 eV are found for CaZrS3 and BaZrS3, respectively, using the Heyd–Scuseria–Ernzerhof HSE06 functional, which is consistent with previous theoretical and experimental bandgap results. The optical properties including dielectric function, refractive index, absorption coefficient, reflectivity, and loss function are characterized using the GGA of Perdew–Burke–Ernzerhof (GGA-PBE) and HSE06 methods and are discussed in detail. Because of the relatively low Debye temperature (D), thermal conductivity of the lattice (kph), and minimum thermal conductivity (Kmin), the studied materials can be used as thermal barrier coating (TBC) materials. The capacity of heat, Debye temperature, and thermal coefficient of expansion are all computed.

A review of the flow characteristics of shale oil and the microscopic mechanism of CO2 flooding by molecular dynamics simulation

Shale oil is stored in nanoscale shale reservoirs. To explore enhanced recovery, it is essential to characterize the flow of hydrocarbons in nanopores. Molecular dynamics simulation is required for high-precision and high-cost experiments related to nanoscale pores. This technology is crucial for studying the kinetic characteristics of substances at the micro- and nanoscale and has become an important research method in the field of micro-mechanism research of shale oil extraction. This paper presents the principles and methods of molecular dynamics simulation technology, summarizes common molecular models and applicable force fields for simulating shale oil flow and enhanced recovery studies, and analyzes relevant physical parameters characterizing the distribution and kinetic properties of shale oil in nanopores. The physical parameters analyzed include interaction energy, density distribution, radial distribution function, mean-square displacement, and diffusion coefficient. This text describes how molecular dynamics simulation explains the mechanism of oil driving in CO2 injection technology and the factors that influence it. It also summarizes the advantages and disadvantages of molecular dynamics simulation in CO2 injection for enhanced recovery of shale oil. Furthermore, it presents the development trend of molecular dynamics simulation in shale reservoirs. The aim is to provide theoretical support for the development of unconventional oil and gas.

A semi-analytic approximation for a single-particle continuum wavefunction

A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.

First-principles study on the structural, elastic, electronic, optical and thermophysical properties of NaNO3 and K-doped NaNO3

Abstract The present work represents the structural, electronic, elastic, and thermophysical properties of pure and K-doped NaNO3 obtained using DFT calculations. The estimated structural properties of NaNO3 correspond well with the existing reported values. Electronic characteristics such as band structure and density of statesof pure and doped NaNO3 are analyzed where the calculated band gaps for pure and K-doped NaNO3 are found to be 3.05 eV and 2.90 eV, respectively. The Berry–phase calculations carried out on both systems showed the existence of ferroelectric polarization, where an enhanced spontaneous polarization value of 36 μC/cm2 for K-doped NaNO3, as compared to 20 μC/cm2 for intrinsic NaNO3. The thermophysical properties such as bulk modulus (B0), Debye temperature (θD), and specific heat capacity (Cv) were calculated over a wide temperature range from 0K to 800 K. The linear optical properties namely the dielectric constant, refractive index, absorption coefficient, extinction coefficient and electron energy loss function are calculated in wide energy range from 0 to 30 eV and discussed in detail.

Evaluation Approach for Residual Stress in Drilling of Aluminum Alloy

Residual stress is one of the critical evaluation factors as well as machining accuracy and surface finish in cutting. From the perspective of the fastening strength of parts, residual stress in drilling has an influence on the product or part life. Especially in the aircraft manufacturing, the tensile residual stress is crucial as it can cause major accidents. However, few studies have focused on residual stress in drilling so far. Most of them investigated the characteristics of residual stress based on the experimental data. This paper discusses residual stress in drilling in terms of its mechanical effect. The residual stresses in the inner surfaces of holes were measured in the depth direction from the top of the plate. The change in the residual stress has good correlation with the chip flow direction and the load applied to the inner surface, which acts as a counter force to the cutting force near the outermost ends of the lips. The cutting force is determined using an analytical model based on the minimum cutting energy. The correlation between the residual stress and the direction of the load applied to the inner surface depends on the margin width and back taper on the peripheral sides of a drill. The effect of the margin contact on the residual stress is characterized by linear regression analysis. Finally, an analysis-neural network hybrid system was developed to estimate the residual stresses in drilling. In the system, the mechanical effects of the drilling process, which are the magnitude and direction of the load applied to the inner surface, are obtained through analytical simulation. Meanwhile, the margin effects are expressed as the coefficients in the linear functions, which are associated with the margin width and back taper angle by a neural network. Then, another neural network, working as a post process, estimates the residual stresses using the information of mechanical and margin effects. The developed system is validated by presenting a comparison between the estimated and the actual residual stresses.

Data-Driven Initial Gap Identification of Piecewise-Linear Systems Using Sparse Regression and Universal Approximation Theorem

Abstract This paper proposes a method for identifying an initial gap in piecewise-linear systems from data. Piecewise-linear systems appear in many engineered systems such as degraded mechanical systems and infrastructures, and are known to show strong nonlinearities. To analyze the behavior of such piecewise-linear systems, it is necessary to identify the initial gap, at which the system behavior switches. The proposed method identifies the initial gap by discovering the governing equations using sparse regression and calculating the gap based on the universal approximation theorem. A key step to achieve this is to approximate a piecewise-linear function by a finite sum of piecewise-linear functions in sparse regression. Equivalent gap is then calculated from the coefficients of the multiple piecewise-linear functions and their respective switching points in the obtained equation. The proposed method was first applied to a numerical model to confirm its applicability to piecewise-linear systems. Experimental validation of the proposed method has then been conducted with a simple mass-spring-hopping system, where the method successfully identified the initial gap in the system with high accuracy.

Modular relations involving generalized digamma functions

Generalized digamma functions ψk(x), studied by Ramanujan, Deninger, Dilcher, Kanemitsu, Ishibashi etc., appear as the Laurent series coefficients of the Hurwitz zeta function. In this paper, a modular relation of the form Fk(α)=Fk(1/α) containing infinite series of ψk(x), or, equivalently, between the generalized Stieltjes constants γk(x), is obtained for any k∈N. When k=0, it reduces to a famous transformation given on page 220 of Ramanujan's Lost Notebook. For k=1, an integral containing Riemann's Ξ-function, and corresponding to the aforementioned modular relation, is also obtained along with its asymptotic expansions as α→0 and α→∞. Carlitz-type and Guinand-type finite modular relations involving ψj(m)(x),0≤j≤k,m∈N∪{0}, are also derived, thereby extending previous results on the digamma function ψ(x). The extension of Guinand's result for ψj(m)(x),m≥2, involves an interesting combinatorial sum h(r) over integer partitions of 2r into exactly r parts. This sum plays a crucial role in an inversion formula needed for this extension. This formula has connection with the inversion formula for the inverse of a triangular Toeplitz matrix. The modular relation for ψj′(x) is subtle and requires delicate analysis.

Optical characterization of La2SrFe2TiO9 triple perovskite: Insights for advanced optoelectronic and solar cell applications

In this work, powdered La2SrFe2TiO9 triple perovskite that was produced by a solid-state reaction is analyzed to determine its optical characteristics. The transmittance and absorbance were measured using UV–visible spectroscopy at room temperature, which allowed for the discovery of promising optical properties. Based on the Tauc technique, the material has been shown to have a direct bandgap of 2.02 eV. Furthermore, the DASF method study has confirmed that the material is a direct bandgap. The absorption coefficient, Urbach energy, refractive index, optical conductivity, and dielectric function were included among the investigated optical properties. Calculations were performed for first- and third-order nonlinear susceptibilities and static and nonlinear refractive indices. These calculations brought to light the material's potential for use in advanced optoelectronic and solar cell applications. The remarkable optical properties of La2SrFe2TiO9, which include both linear and nonlinear characteristics, have made it an attractive candidate for use in advanced optoelectronic and solar cell applications.

Translational motion of a spheroidal drop in a viscous fluid

The problem of translational motion of a spheroidal drop along its axis of revolution in a viscous incompressible fluid is investigated semi-analytically. The flow fields in the exterior and interior of the drop are governed by the Stokes equations. Stream function formulation is adopted to solve the hydrodynamic equations in both regions. The general solution for the stream function in prolate and oblate spheroidal coordinates is expressed in an infinite-series form of semi-separation of variables. The leading order coefficients in the stream function are obtained using suitable boundary conditions. The hydrodynamic drag force experienced by the spheroidal drop is numerically evaluated with adequate convergence behavior for various values of the internal-to-external viscosity ratio and axial-to-radial aspect ratio of the drop. The numerical values of the drag force for the infinite and infinitesimal viscosity ratios agree with the available corresponding results for the slow translation of a slip spheroidal particle in the limiting conditions of no slip and full slip, respectively. At intermediate values of the viscosity ratio, the hydrodynamic force may not be a monotonic function of the aspect ratio. For a spheroidal drop with a fixed aspect ratio, its drag force increases monotonically with an increase in the viscosity ratio.

Research on Expansion Coefficient Based on Water Temperature Density Regression Function

Based on the regression function of water temperature and water density, two expressions of the thermal expansion coefficient function of water are obtained by integrating and differentiating the function. Compared with the measured data, the theoretical formula of the integral method is in good agreement with the measured accumulated thermal expansion coefficient of water obtained by the cumulative step size. The theoretical formula of the differential method is in good agreement with the measured cumulative thermal expansion coefficient of water obtained by equal step size and variable step size. Therefore, no matter the theoretical formula of the integral method or differential method, it can be used for the thermal expansion coefficient of water with cumulative step size or with finite equal step size or finite variable step size. The theoretical formula of the thermal expansion coefficient of water with integral method and differential method is of high precision and easy to use.

Integrating IoT and blockchain for intelligent inventory management in supply chains: A multi-objective optimization approach for the insurance industry

This research aims to develop and optimize an intelligent supply chain framework tailored for the insurance industry by integrating an innovative inventory management policy supported by the Internet of Things (IoT) and blockchain technologies. Through an extensive literature review, key assumptions are established, needs are identified, and objectives are formulated. A multi-objective mathematical planning model is proposed to minimize cost and time within the supply chain, with optimization conducted under deterministic and fuzzy conditions. The model utilizes augmented epsilon constraint and weighted sum methods to address its multi-objectiveness. Noteworthy is the integration of advanced technologies such as Wireless Sensor Networks (WSN), Radio-Frequency Identification (RFID), blockchain, and online sales, distinguishing it from traditional approaches. Initial validation and testing in smaller dimensions demonstrate the model’s adaptability to precise methods, while larger dimensions necessitate the use of meta-heuristic algorithms for efficient problem resolution. Additionally, a comprehensive sensitivity analysis in the insurance industry on objective function coefficients reveals intricate relationships, offering valuable insights into optimization dynamics across diverse conditions.

Threshold dynamics of a reaction–advection–diffusion schistosomiasis epidemic model with seasonality and spatial heterogeneity

Most water-borne disease models ignore the advection of water flows in order to simplify the mathematical analysis and numerical computation. However, advection can play an important role in determining the disease transmission dynamics. In this paper, we investigate the long-term dynamics of a periodic reaction–advection–diffusion schistosomiasis model and explore the joint impact of advection, seasonality and spatial heterogeneity on the transmission of the disease. We derive the basic reproduction number R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}_0$$\\end{document} and show that the disease-free periodic solution is globally attractive when R0<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}_0<1$$\\end{document} whereas there is a positive endemic periodic solution and the system is uniformly persistent in a special case when R0>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}_0>1$$\\end{document}. Moreover, we find that R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {R}}_0$$\\end{document} is a decreasing function of the advection coefficients which offers insights into why schistosomiasis is more serious in regions with slow water flows.

First principles study of chromium-based hydrides for optoelectronics and hydrogen storage applications

The first-principles study employed on chromium-based hydride XCrH3 (X: Na, K) is the first time studied and investigated different physical properties incorporated for optoelectronics and hydrogen storage applications. The structural properties results revealed that these materials have cubic phases, with lattice constants are 3.54 Å (NaCrH3), and 3.74 Å (KCrH3), which was also confirmed by the XRD analysis. The XRD results revealed that the intensity of KCrH3 is shifted towards to lower angle (2θ) degree due to high lattice constants and inter-planner distance. Moreover, both materials exhibited thermodynamically and mechanically stable due to negative formation energy, and elastic constants, and obeyed the Born approximation criteria. The phonons dispersion curve shows that XCrH3 is dynamically stable due to no imaginary frequency presence. Electronic properties found that current materials have metallic characteristics, due to zero band-gap energy, which plays a vital role in hydrogen storage applications. Magnetic properties exhibited paramagnetic behavior of current materials highly contributed to hydrogen storage application due to unpaired electrons and studied materials have spin-polarized magnetic nature. However, elastic properties confirmed that these materials are found hard, and brittle, with an ionic bonding nature between the atoms, and an anisotropic character. Besides this, different optical parameters have studied like as conductivity, absorption coefficient, refractive index, reflectance, and loss function and the results revealed that the examined materials dominated the role in LED, sensors, solar cells, and optoelectronics applications. Thermal analysis revealed that increasing temperature increases energy and entropy but decreases free energy. Among the studied materials, NaCrH3 has a high gravimetric ratio of 3.87 wt%, and KCrH3 is 3.21 wt%. These materials provided new potential for hydrogen storage applications.

An AFD-based adaptive impulse response model of time series

In this paper, an adaptive impulse response model of time series is proposed based on adaptive Fourier decomposition (AFD), which characterizes the data-driven impulse response model with “energy-resolution” and is applied to the effect analysis of shocks on time series. First, according to the observed time series, the frequency points of impulse response function are estimated, and the approximate expression of impulse response function in frequency domain is given. Second, AFD is carried out on the approximate impulse response function level by level, and the poles and coefficients of basis function of each level are obtained adaptively by using the criterion of energy maximization. Third, when the goodness of fit is greater than a certain threshold, all decomposition levels are determined and the adaptive impulse response model is established. Each decomposition level depicts the energy-based resolution characteristics of the impulse response model. Based on gold price return and US dollar index return in daily frequency from 2017 to 2022, this paper carried out AFD-based effect analysis with energy-resolution year by year. Results show that the proposed AFD-based adaptive impulse response model in this paper can describe the persistence effect of shocks of gold price on the US dollar index, and further measure the plainness of linkage relationship between these two time series. Decomposing impulse response to each decomposition level reveals consistence, convergency, and sufficiency of the impulse response model. The AFD-based adaptive data-driven model provides a new way for the analysis of time series in time-frequency domain.

Tailoring the optoelectronic properties of MoS2 for broadband photodetection: Showcasing an Ab-into study involving the quasi-particle correction within the Green’s function-based approximation

In this study, the electronic and structural characteristics of both bulk and monolayer hexagonal MoS2 material are studied within and beyond density functional theory (DFT) by considering one-shot GW corrections for an accurate band gap prediction. Interestingly, our computed quasiparticle (QP) bandgap of 1.36 eV and 3.33 eV for bulk and monolayer, respectively, is in excellent agreement with the experimental finding. The elucidation of the optical properties was estimated with the aid of the Bethe–Salpeter equation within the many-body perturbation theory (MPB). The computed optical transitions such as absorption coefficient, extinction coefficient, refractive index, reflectivity, and electron energy loss function are in better agreement with the experimental data. Moreover, the new approach allows for the efficient inclusion of all conduction bands in GW calculations, significantly reducing computational costs compared to traditional methods. A good agreement of the lattice parameters, as well as the interlayer distance with the experimental findings, is observed by the inclusion of van der Waals (vdW) corrections. Besides the agreement with previously reported values, the evaluated band structure determined with the quasiparticle corrections shows that both bulk and monolayer MoS2 material exhibit semiconducting properties with direct and indirect band gaps, respectively. The calculation of the density of states reveals that the s-orbitals of S atoms and the d-orbitals of Mo are predominantly at the origin of the essential material properties secured at the Fermi level. The results of the study also point to the possibility of a foundation for creating physical structures with swift, decisive, directed, and long-range broadband photodetection capabilities.

On α-Pseudo Spiralike Functions Associated with Exponential Pareto Distribution (EPD) and Libera Integral Operator

The present study aims at investigating some characterizations of a new subclass Gα(μ,τ) and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a compound function Lx,nσ(z) is derived from the convolution of the analytic function f(z) and a modified exponential Pareto distribution G(x) in conjunction with the famous Libera integral operator L(ζ). With the aid of the derived function, the aforementioned subclass Gα(μ,τ) is introduced, while some properties of functions belonging to this subclass are considered in the open unit disk.

Combined spin orientation and phase function of asteroids

Large sky surveys provide numerous non-targeted observations of small bodies of the Solar System. The upcoming LSST of the Vera C. Rubin Observatory will be the largest source of small body photometry in the next decade. With non-coordinated epochs of observation, colors -- and therefore taxonomy and composition -- can only be computed by comparing absolute magnitudes obtained in each filter by solving the phase function (evolution of brightness of the small body against the solar phase angle). Current models in use in the community ( and however, fail to reproduce the long-term photometry of many targets due to the change in the aspect angle between apparitions. We aim to derive a generic yet simple phase function model accounting for the variable geometry of the small bodies over multiple apparitions. As a spinoff of the model, we propose the phase function model in which we introduce a term describing the brightness changes due to spin orientation and polar oblateness. We applied this new model to finkObs observations of finkTotObjFilteredSSO Solar System objects (SSOs). These observations were acquired in the and filters with the Zwicky Transient Facility between November 1, 2019 and December 1 2023. We retrieved them and implemented the new model in a broker of alerts designed for the LSST. The model leads to smaller residuals than other phase function models, providing a better description of the photometry of asteroids. We determined the absolute magnitude, $H$, and phase function coefficients ( in each filter, the spin orientation ($ and the polar-to-equatorial oblateness, $R$, for finkSampleUnion SSOs, which constitutes about a tenfold increase in the number of characterized objects compared to the current census. The application of the model to ZTF alert data using the FINK broker shows that the model is appropriate for extracting physical properties of asteroids from multi-band and sparse photometry, such as the forthcoming LSST survey.

Simulation of acquisition shifts in T2 weighted fluid-attenuated inversion recovery magnetic resonance images to stress test artificial intelligence segmentation networks.

To provide a simulation framework for routine neuroimaging test data, which allows for "stress testing" of deep segmentation networks against acquisition shifts that commonly occur in clinical practice for T2 weighted (T2w) fluid-attenuated inversion recovery magnetic resonance imaging protocols. The approach simulates "acquisition shift derivatives" of MR images based on MR signal equations. Experiments comprise the validation of the simulated images by real MR scans and example stress tests on state-of-the-art multiple sclerosis lesion segmentation networks to explore a generic model function to describe the F1 score in dependence of the contrast-affecting sequence parameters echo time (TE) and inversion time (TI). The differences between real and simulated images range up to 19% in gray and white matter for extreme parameter settings. For the segmentation networks under test, the F1 score dependency on TE and TI can be well described by quadratic model functions (). The coefficients of the model functions indicate that changes of TE have more influence on the model performance than TI. We show that these deviations are in the range of values as may be caused by erroneous or individual differences in relaxation times as described by literature. The coefficients of the F1 model function allow for a quantitative comparison of the influences of TE and TI. Limitations arise mainly from tissues with a low baseline signal (like cerebrospinal fluid) and when the protocol contains contrast-affecting measures that cannot be modeled due to missing information in the DICOM header.