Coefficients Of Equation Research Articles

Twinkle: A GPU-based Binary-lens Microlensing Code with the Contour Integration Method

Abstract With the rapidly increasing rate of microlensing planet detections, microlensing modeling software faces significant challenges in computation efficiency. Here, we develop the Twinkle code, an efficient and robust binary-lens modeling software suite optimized for heterogeneous computing devices, especially GPUs. Existing microlensing codes have the issue of catastrophic cancellation that undermines the numerical stability and precision, and Twinkle resolves them by refining the coefficients of the binary-lens equation. We also devise an improved method for robustly identifying ghost images, thereby enhancing computational reliability. We have advanced the state of the art by optimizing Twinkle specifically for heterogeneous computing devices by taking into account the unique task and cache memory dispatching patterns of GPUs, while the compatibility with the traditional computing architectures of CPUs is still maintained. Twinkle has demonstrated an acceleration of approximately 2 orders of magnitude (≳102×) on contemporary GPUs. The enhancement in computational speed of Twinkle will translate to the delivery of accurate and highly efficient data analysis for ongoing and upcoming microlensing projects. Both GPU and CPU versions of Twinkle are open-source and publicly available.

Determining both leading coefficient and source in a nonlocal elliptic equation

Abstract In this short note, we investigate an inverse (source) problem associated with a nonlocal elliptic equation ( - ∇ ⋅ σ ⁢ ∇ ) s ⁢ u = F {(-\nabla\cdot\sigma\nabla)^{s}u=F} that is given in a bounded open set Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} , for n ≥ 3 {n\geq 3} and 0 < s < 1 {0<s<1} . We demonstrate both the leading coefficient σ and the source F can be determined uniquely by using the exterior Dirichlet-to-Neumann (DN) map in Ω e := ℝ n ∖ Ω ¯ {\Omega_{e}:=\mathbb{R}^{n}\setminus\overline{\Omega}} . The result is intriguing in that analogous theory cannot be true for the local case generally, that is, s = 1 {s=1} . The key ingredients to prove the uniqueness are based on the unique continuation principle for nonlocal elliptic operators and the reduction from the nonlocal to the local via the Stinga–Torrea extension problem.

Fiber-Optic Photoacoustic Gas Microprobe Based on Linear Spot-Type Multipass Cell.

A linear spot-type multipass cell-enhanced fiber-optic photoacoustic gas microprobe is proposed. To further reduce the volume of the gas chamber and enhance the photoacoustic signal, we designed the cross section of the photoacoustic tube as a slit with a height of 10 mm and a width of 1.5 mm. The volume of the gas chamber is only 210 μL. Through theoretical analysis and multiphysical field simulation, the photoacoustic intensity of the slit cross section is more than 6 times that of traditional circular cross section. A cantilever beam is integrated into the photoacoustic microprobe and forms a Fabry-Perot (FP) interferometer with an optical fiber, achieving enhanced photoacoustic detection. By adjusting the angle of the collimator, the light passes through the photoacoustic cell 26 times, and 13 linear spots are formed on the reflecting surface. The photoacoustic signal with multiple linear reflections is 12.4 times that of a single reflection. The gas enters the sensor in a freely diffused manner, and the response time of the sensing system is 54 s. When the averaging time is 400 s, the detection limit of the designed sensor for acetylene gas reaches 1.5 ppb. The minimum detectable absorption coefficient (αmin) and the normalized noise equivalent absorption coefficient (NNEA) are 1.7 × 10-8 cm-1 and 1.9 × 10-9 Wcm-1/Hz1/2, respectively.

Repeated freeze-thaw damage mechanism of asphalt mixture based on equivalent expansive coefficient of air void from mesoscopic perspective

Repeated freeze-thaw damage mechanism of asphalt mixture based on equivalent expansive coefficient of air void from mesoscopic perspective

Condition Analysis for the Effective Use of Identification Algorithms of Solid-State Wave Gyroscope Resonator Mechanical Characteristic Accuracy

The article is aimed at analyzing the conditions for the effective use of algorithms to measure the resonator mechanical characteristicaccuracyof integrating solid-state wave gyroscopes, which include the residual values of the resonatorfrequency and quality parameters. At the same time, the main measurement modes are the free oscillation modesof the stationary gyroscoperesonator. The considered algorithms for measuring the residual values of the frequency and quality resonatorparameters are implemented via standard computational procedures for identifying the differential equationcoefficients of resonatorfree oscillations. The resonatoroscillationequations in the axes of the working and quadrature standing waves,recorded for their slowly changing amplitudes, were chosenas a basic identification model. Initial signals for the primary information preparation for identification tasks are generated in a measuring device similar to the standard one of an integrating solid-state wave gyroscope. Various problemformulations to identify the parameters of residual different-quality and multi-frequency resonators both separately and simultaneously are discussed. As a result, well-conditioned computational schemes that do not require the introduction of additional regularization of inverse identification problems are proposed and analyzed. These schemes are reasonably linked to mathematical algorithms for the primary information preparation for the identification problems to be solved, being formed in the form of arrays of intermediately calculated amplitudes of and quadrature standing waves at work. The effect of calculationerrors these amplitudes on the accuracy of identification of the parameters of different-quality and multi-frequency resonators is shown. In addition, the possibilities of improving the accuracy of amplitudecalculation under measurement noise are discussed. The revealed accuracy conditions for the application of algorithms for identifying the parameters of residual different-quality and multi-frequency resonators of gyroscopes through finding the coefficients of differential equations and their free oscillations make it possible to increase the efficiency of setting up production control methods.

Position analysis of the tripod joint: An alternative approach

The position analysis, which is the most challenging phase of the kinematic analysis of a mechanism, was solved for the tripod joint, in exhaustive form, a few decades ago. The method proposed at the time was supposed to be able to find all possible assembly configurations of the joint. Regrettably, it becomes useless when the angle that parametrizes the position of one of the connected shafts reaches some specific values, which happens several times for each turn of the shaft; moreover, an error in the expression of a coefficient of a pivotal equation hampers adoption of the method. This paper presents a new procedure whose steepest step is finding the roots of a fourth order algebraic equation. It is shown that eight assembly configurations do exist for the adopted kinematic model of tripod joint, in the complex domain. The proposed procedure has a more direct approach than the previous one and is not affected by its singularities. Moreover, because no arbitrarily-selected movable reference frame is introduced, it leads to equations whose coefficients reveal the periodicity of the dependence of some parameters of the joint configuration on the angular position of one of the connected shafts. This means that some aspects of the tripod joint behavior can be hinted even without solving the equations. A numerical example shows application of the new procedure to a case study.

An asymptotically optimal two-sample instrumental variables estimation using many instruments

AbstractWe investigate the statistical estimation of the coefficients in a linear structural equation within a simultaneous equation system, utilizing two-sample data and a large number of instrumental variables. Specifically, we derive the asymptotic properties of the two-sample least variance ratio (2SLVR) estimator, an extension of the limited information maximum likelihood (LIML) estimator designed for one-sample contexts, in the two-sample setting with numerous instruments. It is well-documented that the one-sample two-stage least squares (TSLS) estimator and the generalized method of moments (GMM) suffer from non-negligible bias. Despite their widespread practical use, these methods often lose consistency when a large number of instruments are employed. In contrast, our findings demonstrate that the variance–covariance matrix of the limiting distribution of the 2SLVR estimator and its modifications frequently achieve the asymptotic lower bound, even when the disturbance terms deviate from a normal distribution. The results of this study hold significant potential for applications in econometrics and biometrics, particularly in contexts such as Mendelian Randomization (MR) analyses using DNA data.

USE OF VECTOR APPROACH FOR STUDYING COMPLEX CHEMICAL PROCESSES ON THE EXAMPLE OF BLACK POWDER

The paper demonstrates the possibilities of a vector approach for calculating stoichiometric coefficients of chemical equations using the example of black powder. An approach is proposed for selecting and limiting intermediate interactions between reactants and determining final products. It is shown that even a small number of components can lead to a large number of final and intermediate products. Using real calculations, the relationship between the number of possible chemical equations and the number of reactants is shown. A method is proposed for calculating all possible chemical equations in a reaction system for an arbitrary ratio of components, which allows obtaining all possible chemical reactions, and a method for calculating the chemical composition for a fixed set of reactants, which allows estimating the set of products of possible chemical interactions for a given initial composition

Heat equation-based temperature profiles retrieval in frozen tundra soil using dual-polarized multi-angular brightness temperature observations in L-band

ABSTRACT In this theoretical paper, a method for temperature profile retrieval in frozen tundra soil is proposed based on the thermoevolutionary relationship between polarimetric multi-angular brightness temperature (TB) at 1.4 GHz, observed in sliding time window with a fixed duration, and the time series of soil temperature profiles, predicted by the heat equation. For TB modelling, the profiles of volumetric moisture, dry bulk density, and organic matter content in the active layer, measured at the Franklin Bluffs test site (North slope of Alaska, U.S.) from 12 December 2022 to 5 May 2023, were used. When solving the inverse problem, the retrieving temperature profiles were specified as a linear interpolation function between four known depths 0 cm, 25 cm, 50 cm, and 95 cm. The thermodynamic properties of the frozen active layer were considered independent of soil temperature, time, and vertical coordinates, which made it possible, based on weather station data, to determine the apparent value of the thermal diffusivity coefficient in the heat equation. The practically significant accuracy of retrieving soil temperature up to a depth of 70 cm with a root-mean-square error of 0.5–1.8°C and a coefficient of determination of 0.877–0.988 was demonstrated by the proposed method. The pursued research shows the advantage of the synergy of the heat equation and polarimetric multi-time compared to only single-moment TB observations for temperature profile retrieval in frozen tundra soil.

Effectiveness of betel and kaffir lime combination form of leaf infusion as an in-vitro antiseptic candidate

Background: Natural antiseptics can be alternatives to reduce the adverse effects of alcohol. An antiseptic is classified as effective if it has an inhibitory ability and a phenol coefficient value ≥ 1. Betel plants (Piper betle L.) and kaffir lime (Citrus hystrix DC.) contain a variety of antibacterial compounds and have the potential to act as an antiseptic.Objective: To analyze the in vitro effectiveness of a combined leaf infusion preparation of betel (PB) and kaffir lime (CH) as potential antiseptic candidates.Methods: This quasi-experimental research employed a post-test-only control group design. We utilized diffusion (measuring inhibition zone) and dilution (determining phenol coefficients) methods. The treatments, performed in triplicate, included PB+CH infusion at concentrations 6.25%, 12.5%, 25%, 50%, 75%, and 100%, with 70% alcohol and 5% phenol as control. They were tested against five types of ATCC standard bacterial isolates.Results: Phytochemical screening of the tested infusion revealed the presence of phenolic compounds, flavonoids, alkaloids, tannins, saponins, and terpenoids. The inhibition zone area increased with concentration, with PB+CH 100% producing the most significant effect. ANOVA and post-hoc Duncan test analysis (p < 0.05) showed significant differences between treatment groups. PB+CH infusion at 75-100% produced antibacterial effects exceeding the control for all bacteria tested, except S. typhi. Phenol coefficient tests (dilution 1:20-1:250) showed the effectiveness of PB+CH infusion as a potential antiseptic. The infusion had a phenol equivalent coefficient of 5% against S. aureus, S. epidermidis, E. coli, and P. aeruginosa but only 0.99 ± 0.07 for S. typhi. The 70% alcohol coefficient value was < 1. Conclusion: The combined infusion of betel leaves and kaffir lime demonstrates significant antibacterial activity and shows a potential candidate as an effective natural antiseptic.

The problem of satellite attitude stabilization in the geomagnetic field

A satellite moving along a circular Keplerian orbit in near-Earth space was explored, focusing on its attitude stabilization in the orbital coordinate system using the intrinsic magnetic and Lorentz force moments. Fluctuations in geomagnetic induction that occur as the satellite orbits cause the coefficients in the dynamical equations governing the satellite’s attitude motion to vary over time. The results show that, although the linearized system of differential equations of the satellite’s motion is non-stationary, it can be reduced to a stationary system of higher order, which holds even for high-precision multipole models of the geomagnetic field. Thus, a control law design was proposed to stabilize the satellite. The controllability of the system was analyzed, and an optimal stabilization algorithm based on the LQR method was developed. The effectiveness of the proposed approach was validated by computer modeling.

System frequency response model and droop coefficient setting considering renewable energy participation in frequency regulation

The highly uncertain and uncontrollable power output of renewable energy sources (RES), when integrated into power systems at high penetration levels, reduces system inertia and introduces uncertain changes in system structure, parameters, and frequency response characteristics. This renders traditional frequency regulation analysis methods and frequency response models inapplicable, lacking a generalized model to describe renewable energy’s participation in frequency regulation. Thus, this paper proposes a method where RES utilize suitable means to reduce load, thereby contributing to frequency regulation. Furthermore, employing Virtual Synchronous Machine (VSM) technology, these renewable energy units emulate the inertia and droop characteristics of Synchronous Generators (SG), enabling their equivalent modeling alongside traditional generators within a single-machine aggregate model. An SFR (System Frequency Response) model integrating renewable energy’s frequency regulation has been established. This model enables the analysis of the relationships between the system’s equivalent droop coefficient and the frequency nadir, nadir time, and quasi-steady-state point. Furthermore, the required equivalent droop coefficients are proposed for various sending-end system capacities and operating conditions. Finally, the model’s validity and accuracy are confirmed through a modified WSCC 4-machine 10-bus system, offering theoretical underpinnings for stable system operation and optimized operational planning.

The mediating role of problematic TikTok use and loneliness in the relationship between mindfulness and psychological resilience in adolescents

Throughout life, individuals encounter many different upsetting events. The concepts of psychological resilience and mindfulness come to the fore in the situations encountered. The dynamics of these concepts and the extent to which they are related to loneliness and problematic TikTok use demonstrate the importance of the research. The aim of this study was to test the mediating role of problematic TikTok use and loneliness in the relationship between mindfulness and psychological resilience in adolescents. In the study, Mindfulness Scale, UCLA Loneliness Scale, Brief Psychological Resilience Scale, and Problematic TikTok Use Scale were administered to 354 students (236 girls and 118 boys) with an average age of 14.7 years who were studying in different high schools in Turkey. The data were tested using Pearson product-moment correlation coefficient and structural equation modeling analyses. The results of the study showed that problematic TikTok use and loneliness had a partial mediating role in the relationship between mindfulness and psychological resilience in adolescents. In the model with serial mediation, it was concluded that individuals with high levels of mindfulness had low levels of loneliness and problematic TikTok use and high levels of psychological resilience. Mindfulness predicts psychological resilience directly and indirectly through problematic TikTok use and loneliness. This situation can be interpreted as the impairment of psychological resilience, the level of mindfulness can be impaired by TikTok use and individuals can become lonely. This result was discussed in the light of theoretical and empirical data.

Using the exponential distribution as a synthetic curve volume of runoff to determine the volume of surface runoff

The paper analyzes the problem of determining the amount of surface wastewater that has formed on the territory of the drainage area as a result of precipitation and snowmelt, and enters the surface sewage disposal systems, for which the flow coefficient is used, which reflects the relationship between waterproofness and flow. Comparison of regression models used to estimate runoff coefficients showed a significant variation of its values ​​over the entire range of the total impervious area. For the samples of the generated values ​​of the total runoff coefficient with the corresponding proportion of waterproofness, statistical indicators were calculated and box diagrams were constructed. Regression equations of the total runoff coefficient from the share of the total impervious area with the corresponding soil filtration coefficient were obtained for the conditions of Kyiv, which more fully take into account the infiltration potential of the soil and the moisture level of the catchment before the rain starts.

Cooperative maximum adhesion tracking control for multi-motor electric locomotives

PurposeThis study aims to propose a cooperative adhesion control method for trains with multiple motors electric locomotives. The method is intended to optimize the output torque of each motor, maximize the utilization of train adhesion within the total torque command, reduce the train skidding/sliding phenomenon and achieve optimal adhesion utilization for each axle, thus realizing the optimal allocation of the multi-motor electric locomotives.Design/methodology/approachIn this study, a model predictive control (MPC)-based cooperative maximum adhesion tracking control method for multi-motor electric locomotives is presented. Firstly, train traction system with multiple motors is constructed in accordance with Newton’s second law. These equations include the train dynamics equations, the axle dynamics equations, and the wheel-rail adhesion coefficient equations. Then, a new MPC-based multi-axle adhesion co-optimization method is put forward. This method calculates the optimal output torque through real-time iteration based on the known reference slip speed to achieve multi-axle co-optimization under different circumstances.FindingsThis paper presents a MPC system designed for the cooperative control of multi-axle adhesion. The results indicate that the proposed control system is able to optimize the adhesion of multiple axles under numerous different conditions and achieve the optimal power distribution based on the reduction of train skidding/sliding.Originality/valueThis study presents a novel cooperative adhesion tracking control scheme. It is designed for multi-motor electric locomotives, which has rarely been studied before. And simulations are carried out in different conditions, including variable surfaces and motor failing.

Analyzing the Dynamics and Friction Forces on Spheres in Fluid Flows: Applications Across Engineering and Sports Science

This study explores the dynamics and friction forces of spherical objects in fluid flows, emphasizing their applications across engineering and sports science. By examining key theoretical concepts such as drag coefficient, Reynolds number, and fluid dynamics equations, the research highlights how these principles influence the motion of spheres in various fluid environments. The analysis encompasses computational fluid dynamics (CFD) and experimental approaches, addressing applications in ocean, aerospace, and vehicle engineering, as well as sports science. The findings demonstrate the critical role of understanding drag and friction characteristics in optimizing designs, improving performance, and driving technological innovation. Challenges such as multi-scale phenomena, nonlinear dynamics, and measurement techniques are identified, suggesting future research directions to refine theoretical models and enhance practical applications. The study not only advances the theoretical understanding of fluid dynamics but also provides essential insights for engineering optimization and sports performance enhancement.

Shear Elastic Buckling and Resistant Behavior of Single-Side-Stiffened Steel Corrugated Shear Walls

Stiffened steel corrugated shear walls (SSCSWs) have achieved extensive applications in building structures and serve as efficient lateral force-resisting members. Single-side-stiffened steel corrugated shear walls (SS-SCSWs) are more flexible in terms of their structural configuration compared to conventional SSCSWs because this novel structural member effectively reduces wall thickness and simplifies the construction process. In this paper, numerical analyses were carried out to investigate the shear elastic buckling and resistant behavior of SS-SCSWs. A formula for the equivalent flexural stiffness of single-side stiffeners was given based on theoretical analysis. The elastic buckling and elastoplastic analyses of SS-SCSWs were carried out by finite element (FE) models to determine the value of the equivalent flexural stiffness coefficient. Meanwhile, the elastic and elastoplastic transition stiffness ratios of single-side stiffeners were proposed to predict the minimum stiffness required for the stiffener to provide sufficient constraint. The accuracy of the above formulas was verified by calculating the shear elastic buckling loads, the ultimate shear resistance, and the out-of-plane displacements of the SS-SCSWs. Furthermore, parametric analyses were performed to reveal the influences of the aspect ratio and plate thickness on shear resistance capacity. The equivalent flexural stiffness coefficients in both the elastic and elastoplastic analyses were determined to be 0.45 and 0.7, respectively, through curve fitting. The results indicated that the theory of BS-SCSWs could accurately predict the shear elastic and elastoplastic behavior of SS-SCSWs after modifying its expression for flexural stiffness. Consequently, the modified theoretical formulas were demonstrated to be suitable for SS-SCSWs in practical designs.

Разработка методики планирования эксперимента для исследования параметров мельниц горно-обогатительного комбината

The article presents the results of studying the process parameters of ball mills at a mining and processing plant during the development and implementation of a complete factorial experiment. A methodology for conducting this experiment has been developed that takes into account the specific features of mining production. The main process factors have been established, i.e. productivity, hardness of the ore fed for grinding, density of the classifier discharge, which have the greatest impact on power consumption. An analysis of the input parameters for the grinding process was carried out, the ranges of their variation were determined, a planning matrix was built, the coefficients of the linear regression equation were calculated, and their significance was assessed. Along with this, a transition was made from code values of variables to natural values, and a mathematical model was designed, with the help of which it is possible to calculate and forecast power consumption depending on the most significant process parameters. The obtained results allow to control the operating modes of the mills at mining and processing plants in on-line mode and are planned to be included in the automated process control systems of the enterprises.

Research on the approximate equation inversion method for the physical properties parameters of OA media with decoupling of stress and fracture effects

Pre-stack seismic inversion is an effective method for predicting reservoir physical parameters. At the same time, azimuth seismic data is a reliable source of information for predicting underground reservoir elastic parameters, fracture parameters, and interface parameters and has rich underground information. However, it is difficult to determine whether the anisotropy of the reservoir is caused by stress or the original fractures. Therefore, distinguishing the influence of fractures and initial stress in the reservoir from azimuth seismic data is the key to predicting reservoir parameters. Because of the problem of insufficient consideration of the influence of stress and fracture weakness in OA media, based on Born's first-order scattering theory and Bayesian inversion framework, an approximate equation for the reflection coefficient decoupling fracture anisotropy and stress-induced anisotropy was constructed, and a linear inversion method based on the approximate equation was developed, realizing the exploration of methods for predicting fracture weakness and stress action parameters. Model testing and actual work area application have verified the feasibility and practicability of predicting underground medium parameters from seismic response characteristics.

Ground response during of EPB shield shutdown in gravel ground based on coupled CEL-FEM analysis

The shutdown of earth pressure balance (EPB) shield tunneling in gravel stratum can easily lead to significant unexpected ground deformation. In order to study the response of gravel strata during shield shutdown and the characteristic change of soil state in the chamber, this paper establishes a coupled Eulerian-Lagrangian finite element method (CEL-FEM) coupling analysis model that reflects the interaction between the spoiled soil and gravel strata. The plastic flow parameters of CEL spoiled soil are calibrated using the slump method, and a quantitative relationship between the slump value, plastic flow parameters, equivalent coefficient of loosening, and excavation face support pressure is established. The reliability and applicability of CEL method in the simulation of shield shutdown are verified by the field measurements. Results show that: (1) The chamber’s soil equivalent loose coefficient is inversely proportional to the soil slump value which is related to soil’s plastic flow parameters. (2) The shield shutdown in gravel strata has a more significant impact on the deep strata displacement than on the surface. (3) During the shield shutdown stage, the chamber pressure should be dynamically adjusted based on the soil deformation characteristics, and an increase of 16% could result in a stable rebalance.