Accurate Solutions Research Articles

Liquid Sloshing in Soil-Supported Multiple Cylindrical Tanks Equipped with Baffle under Horizontal Excitation

The dynamic behavior of liquid storage tanks is one of the research issues about fluid–structure interaction problems. The analysis errors of the dynamics of multiple adjacent tanks can exist if neglecting soil–tank interaction since tanks are typically supported on flexible soil. In the present paper, the dynamics of a group of baffled cylindrical storage tanks supported on a circular surface foundation and undergoing horizontal excitation are analytically examined. For upper multiple tank–liquid–baffle subsystems, accurate solutions to the velocity potential for liquid sloshing are acquired according to the subdomain partition technique. A theoretical model is utilized to portray the continuous sloshing of each tank. For the soil–foundation subsystem, a lumped-parameter model is used to characterize the impacts of soil on upper-tank structures using Chebyshev complex polynomials that present the fitting results of horizontal, rocking, and coupling impedance functions. Then, a model of the soil–foundation–tank–liquid–baffle system is constructed on the basis of the substructure approach. The present sloshing frequencies, sloshing height, and hydrodynamic shear as well as the moment under rigid/soft soil foundations are compared to the available exact results and the numerical results to prove the validity of the present model. The error of the maximum sloshing height between the present and the numerical solutions is within 5.27%; the solution efficiency of system dynamics from the present model is 40–50 times faster than that from the ADINA model. A detailed parameter analysis of the dynamic characteristics and earthquake responses of the coupling system is presented. The research novelty is that an equivalent analytical model is presented, and it allows for investigating the dynamics of soil-supported multiple cylindrical tanks with a baffle, providing acceptable accuracy and high calculation efficiency.

An improved Mickens’ solution for nonlinear vibrations

The Duffing equation and other nonlinear equations of motion of nonlinear vibrations are widely applied in the fields of engineering and science, especially mechanical and electrical engineering. The modified Mickens extended iteration method has been utilized in this article to investigate for further accurate solutions to the Duffing equation and an equation of motion of nonlinear vibrations. The third approximate frequency shows good agreement with the exact result for both oscillators. For simplicity in algebraic calculations, the increasing harmonic terms have been taken to the fifth order. In order to establish the reliability and effectiveness of the proposed approach, the results obtained through this method are compared with those available in the literature. The comparison of the obtained solutions with numerical solutions shows a remarkable accuracy. Also, it becomes evident that the modified Mickens extended iteration method is significantly simpler, more accurate, efficient, and straightforward than other existing methods. The highest percentage error in the third approximate frequency of an equation of motion of nonlinear vibrations is less than 0.0488, and the maximal percentage error in the third approximate frequency of the Duffing oscillator is less than 0.0065. The proposed technique is principally exhibited in nonlinear models where the nonlinear terms are strong, but it can also be broadly applicable to other problems arising in engineering. Mathematics Subject Codes34A34, 34C25, 37N15 (AMS Mathematics Subject Classification 2010)

Correct Use of Oscillating-Cup Viscometers for High-Temperature Absolute Measurements of Newtonian Melts

Oscillating-body viscometers have been used in the past to measure, in an absolute way, the viscosity of molten materials at high temperatures, from salts, metals, alloys, and semiconductors. However, the simultaneous use of basic or incomplete mathematical models, to mimic the experiment, and less careful engineering solutions for the design and operation of the instruments, led in the past to high discrepancies between the data obtained in several laboratories. This was caused by the incorrect use of the method’s theory, less accurate solutions of the complex solutions, that involve solid state and fluid mechanics, and unreal instrument design. From these types of viscometers, oscillating-cup instruments have had the most success in measuring viscosity at high temperatures, and they will be the object of this paper. It was written as a resource for workers interested in transport properties of materials when considering its use for the absolute measurement of fluids viscosity in their work, or in judging the results of others' work when comparing data with their own. The paper starts with the most accurate theory of the method’s description, followed by a discussion of its validity, application to instrument design, and consequent operation. Several constraints were identified and recommendations were made to minimize the effects of failing to satisfy them. Finally, a discussion about the uncertainty budget calculations for a real experiment is made. If all these points are followed in the design and operation of the instrument, results in global uncertainties Ur(η) between 0.02 and 0.04 are possible to obtain, up to high temperatures. If these constraints are not satisfied, erroneous measurements can be made, making comparisons and quality assessment difficult.

Joint Data and Model-Driven Simultaneous Inversion of Velocity and Density

Summary Density is an important parameter for both geological research and geophysical exploration. However, for model-driven seismic inversion methods, high-fidelity density inversion is challenging due to seismic wave travel-time insensitivity to density, and crosstalk that density has with velocity. To circumvent the challenge of density inversion, some inversion methods treat density as a constant value or derive density from velocity through empirical equation. On the other hand, deep learning approaches are completely driven by data and have strong target-oriented characteristics, offering a new way to solve multi-parameter coupling problems. Nevertheless, the accuracy of the inversion results of data-driven algorithms is directly related to the amount and diversity of the training data, and thus, they lack the universality of model-driven algorithms. To achieve accurate density inversion, we propose a simultaneous inversion algorithm for velocity and density that combines the advantages of data- and model- driven approaches: A neural network model (U-T), combining the U-net and Transformer architectures, is proposed to construct nonlinear mappings between seismic data as inputs and the velocity and density as predictions. Next, the model-driven inversion algorithm uses the U-T prediction as the initial model to obtain the final accurate solution. In the model-driven module, envelope-based sparse constrained deconvolution is used to obtain full-band seismic data, while a variable dominant frequency full waveform inversion algorithm is employed to perform multi-scale inversion, ultimately leading to accurate inversion results of velocity and density. The performance of the algorithm on the Sigsbee2A and Marmousi models demonstrates its effectiveness.

The application prospects of robot pose estimation technology: exploring new directions based on YOLOv8-ApexNet.

Service robot technology is increasingly gaining prominence in the field of artificial intelligence. However, persistent limitations continue to impede its widespread implementation. In this regard, human motion pose estimation emerges as a crucial challenge necessary for enhancing the perceptual and decision-making capacities of service robots. This paper introduces a groundbreaking model, YOLOv8-ApexNet, which integrates advanced technologies, including Bidirectional Routing Attention (BRA) and Generalized Feature Pyramid Network (GFPN). BRA facilitates the capture of inter-keypoint correlations within dynamic environments by introducing a bidirectional information propagation mechanism. Furthermore, GFPN adeptly extracts and integrates feature information across different scales, enabling the model to make more precise predictions for targets of various sizes and shapes. Empirical research findings reveal significant performance enhancements of the YOLOv8-ApexNet model across the COCO and MPII datasets. Compared to existing methodologies, the model demonstrates pronounced advantages in keypoint localization accuracy and robustness. The significance of this research lies in providing an efficient and accurate solution tailored for the realm of service robotics, effectively mitigating the deficiencies inherent in current approaches. By bolstering the accuracy of perception and decision-making, our endeavors unequivocally endorse the widespread integration of service robots within practical applications.

An ensemble-based stage-prediction machine learning approach for classifying fetal disease

Fetal diseases often lead to the death of many babies during pregnancies. Machine learning and deep learning are promising technologies providing efficient and effective detection and treatment of various fetal diseases. We contribute to the medical field by addressing the critical challenge of fetal disease classification, a concern affecting females and infants. This study utilizes 22 features associated with fetal heart rate extracted from 2126 patient records within the Cardiotocography(CTG) datasets. Our classification system offers a cost-effective, efficient, and accurate solution. It classifies fetal diseases into three categories: Normal, Suspect, and Pathological, based on preprocessed data that underwent MinMax Scaling and employed dimensionality reduction techniques, including Principal Component Analysis(PCA) and Autoencoders. By incorporating dimensionality reduction techniques, the computation time has been reduced from 9 to 26 s to just 4 and 15 s, which is less than half of the original computation time. We assessed the performance of 11 standard machine learning algorithms and various performance metrics to identify the best classification model. We have applied the K-fold Cross-Validation technique to validate our model to improve machine learning models and identify the most effective algorithm. When the results are compared, it is observed that Extreme Gradient Boosting (XGBoost) gained the highest accuracy of 0.99% also highest precision 0.93% and outperformed all the other machine learning algorithms.

Improved differential evolution algorithm based on cooperative multi-population

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness.

Taqman PACMAN: a simple molecular approach for positive rapid antigen test confirmation during periods of low prevalence.

Rapid antigen testing for SARS-CoV-2 was widely deployed during the COVID-19 pandemic. In settings of low prevalence, national guidance recommends that positive antigen test results be confirmed with molecular testing. Given the high testing burden on clinical laboratories during the COVID-19 pandemic, the high volume of positive antigen tests submitted for confirmatory testing posed challenges for laboratory workflow. This study demonstrated that a simple PCR method without prior nucleic acid purification is an accurate and cost-effective solution for positive rapid antigen test confirmation. Implementing this method allowed molecular confirmatory testing for positive antigen tests to be sustained as antigen testing was expanded into large populations such as workplaces, schools, and households.

A comprehensive study of subdivision collocation method for Burgers’ equation

This study explores the use of subdivision schemes to efficiently solve Burgers’ equation. Burgers’ equation is a fundamental fluid dynamics equation that describes the nonlinear behavior of fluid flow. This type of nonlinear equation is difficult to solve analytically, which makes the numerical solution an important tool. The subdivision collocation method (SCM) converts Burgers’ equation into a system of algebraic linear equations using the quasilinearization technique. The results of this study demonstrate that the proposed approach yields accurate numerical solutions for Burgers’ equation. Additionally, the subdivision approach is computationally efficient and requires fewer computational resources than existing numerical methods, making it a promising tool for solving Burgers’ equation in practical applications. Overall, this study provides valuable insights into the approximate solution of Burgers’ equation by implementing subdivision schemes.

Multi-objective hydrothermal performance optimization of a microchannel heat sink equipped with delta winglet vortex generators using NSGA-II genetic algorithm

Microchannel heat sinks provide the solution to the ever-increasing heat flux generated from micro-electric components. In this study, performance optimization of a microchannel heat sink with delta winglet vortex generators was carried out based on the data obtained from numerical CFD simulations. A total of 192 design points were generated by altering the fluid velocity in terms of Reynolds number (Re), winglet width (Wd), length (Ld), and the angle of attachment (β) of the winglet. The Artificial Neural Network (ANN) model coupled with Non-dominated Sorting Genetic Algorithm NSGA-II was used simultaneously to minimize the friction factor and increase the Nusselt number. The ANN model predicted the output values within the error limit of 10%. The Pareto optimal front generated by the algorithm contains the input parameters in the range 982 < Re < 988, 177 μm <Ld < 233 μm, 10 μm <Wd < 25 μm, 57° <β < 64°. Decision-making methods TOPSIS, LINMAP, and Shannon entropy were employed to calculate the optimal solution from the data set and the obtained points showcased 70%, 120% and 158% surge in Nusselt number while an increase of friction factor by 35%, 109%, and 140% respectively is reported. The Performance Evaluation Criteria (PEC) values obtained from the best solutions were 1.52, 1.72, and 1.92, respectively. Furthermore, the accuracy of the optimal solutions was verified numerically. The flow and thermal field of the microchannel are also analyzed, and results showed that the angle of attachment and width of the winglet played a crucial role in the overall performance.

Predicting the Remaining Useful Life of Lithium-Ion Batteries Using 10 Random Data Points and a Flexible Parallel Neural Network

Accurate Remaining Useful Life (RUL) prediction of lithium batteries is crucial for enhancing their performance and extending their lifespan. Existing studies focus on continuous or relatively sparse datasets; however, continuous and complete datasets are rarely available in practical applications due to missing or inaccessible data. This study attempts to achieve the prediction of lithium battery RUL using random sparse data from only 10 data points, aligning more closely with practical industrial scenarios. Furthermore, we introduce the application of a Flexible Parallel Neural Network (FPNN) for the first time in predicting the RUL of lithium batteries. By combining these two approaches, our tests on the MIT dataset show that by randomly downsampling 10 points per cycle from 10 cycles, we can reconstruct new meaningful features and achieve a Mean Absolute Percentage Error (MAPE) of 2.36% in predicting the RUL. When the input data are limited to the first 10 cycles using the dataset constructed from random downsampling and the FPNN, the predicted RUL MAPE is 0.75%. The method proposed in this study offers an accurate, adaptable, and comprehensible new solution for predicting the RUL of lithium batteries, paving a new research path in the field of battery health monitoring.

Stability of a realistic astrophysical pulsar and its mass–radius relation in higher-order curvature gravity

The objective of this research is to explore compact celestial objects while considering the framework of an extended gravitational theory known as R+f(G) gravity. The notations R and G denote the Ricci scalar and the Gauss–Bonnet invariant, respectively. Radio pulsars, which are neutron stars with masses greater than 1.8 times that of the Sun (M⊙), provide exceptional opportunities for delving into fundamental physics in extraordinary environments unparalleled in the observable universe and surpassing the capabilities of experiments conducted on Earth. Through the utilization of both the linear and quadratic expressions of the function f(G)=α1G2, where α1 (with dimensional units of [length6]) are incorporated, we have achieved an accurate analytical solution for anisotropic perfect-fluid spheres in a state of hydrostatic equilibrium. By integrating the dimensional parameters α1 and the compactness factor, defined as C=2GMRc2, we showcase our capacity to encompass and depict all physical characteristics within the stellar structure. We illustrate that the model is capable of producing a stable arrangement for the pulsar PSR J0740+6620, encompassing its geometric and physical properties. We illustrate that by utilizing the quadratic form of G in the R+f(G) framework, the Krori-Barua ansatz establishes semi-analytical relationships between radial pressure (pr), tangential pressure (pt), and density (ρ). Remarkably, in the context of the positive/negative α1 quadratic R+f(G) gravity framework, the maximum compactness is inherently restricted to values fail below the Buchdahl limit when the surface density exceeds 4×1014 g/cm3. This differs from General Relativity (GR) in which the compactness is unlikely to approach the black hole limit. The model predicts a core density that is multiple times greater than the saturation nuclear density, represented as ρnuc=4×1014 g/cm3, and a surface density ρs that surpasses the nuclear saturation density. We offer the mass–radius diagram associated with the boundary density we have determined, and this diagram has been shown to be consistent with other observational discoveries.

A new 3D plastoelastohydrodynamic lubrication model for rough surfaces

Plastoelastohydrodynamic lubrication of rough surfaces (R-PEHL) is a cutting-edge area of research in interface fluid-structure coupling analysis. The existing R-PEHL model calculates the elastic-plastic deformation of rough surface by the Love equation in a semi-infinite space smooth surface, which deviates from the actual surface. Therefore, it is an innovative work to study the exact solution of elastic-plastic deformation of rough surface and its influence on the solution results of R-PEHL model. In this paper, a new contact calculation model of plastoelastohydrodynamic lubrication (PEHL) with three-dimensional (3D) rough surface is proposed by integrating numerical method of EHL and finite element method. The new model eliminates an original error introduced by the assumption of semi-infinite space in contact calculation, providing wide applicability and high accuracy. Under the given rough surfaces and working conditions, the study reveals that: (1) the oil film pressure calculated by the new model is lower than that of the smooth surface in semi-infinite space by 200–800 MPa; (2) the Mises stress of the new model is 2.5%–26.6% higher than that of the smooth surface in semi-infinite space; (3) compared with the semi-infinite space assumption, the rough surface plastic deformation of the new model is increased by 71%–173%, and the local plastic deformation singularity may appear under the semi-infinite space assumption; (4) the plastic deformation caused by the first contact cycle on the rough surface of the new model accounts for 66.7%–92.9% of the total plastic deformation, and the plastic deformation of the semi-infinite space accounts for 50%–83.3%. This study resolves the contradiction between the smooth surface assumption and the rough surface in the existing R-PEHL model, establishing a solid logic foundation for the accurate solution of R-PEHL model.

A New Efficient Hybrid Method Based on FEM and FDM for Solving Burgers’ Equation with Forcing Term

This paper presents a study on the numerical solutions of the Burgers’ equation with forcing effects. The article proposes three hybrid methods that combine two-point, three-point, and four-point discretization in time with the Galerkin finite element method in space (TDFEM2, TDFEM3, and TDFEM4). These methods use backward finite difference in time and the finite element method in space to solve the Burgers’ equation. The resulting system of the nonlinear ordinary differential equations is then solved using MATLAB computer codes at each time step. To check the efficiency and accuracy, a comparison between the three methods is carried out by considering the three Burgers’ problems. The accuracy of the methods is expressed in terms of the error norms. The combined methods are advantageous for small viscosity and can produce highly accurate solutions in a shorter time compared to existing numerical schemes in the literature. In contrast to many existing numerical schemes in the literature developed to solve Burgers’ equation, the methods can exhibit the correct physical behavior for very small values of viscosity. It has been demonstrated that the TDFEM2, TDFEM3, and TDFEM4 can be competitive numerical methods for addressing Burgers-type parabolic partial differential equations arising in various fields of science and engineering.

REFINEMENT AND ACCURACY CONTROL OF THE SOLUTION METHOD FOR THE DURABILITY PROBLEM OF A CORRODING STRUCTURE USING NEURAL NETWORK

Context. The prediction of the time until failure of corroding hinge-rod structures is a crucial component in risk management across various industrial sectors. An accurate solution to the durability problem of corroding structures allows for the prevention of undesired consequences that may arise in the event of an emergency situation. Alongside this, the question of the effectiveness of existing methods for solving this problem and ways to enhance them arises.&#x0D; Objective. The objective is to refine the method of solving the durability problem of a corroding structure using an artificial neural network and establish accuracy control.&#x0D; Method. To refine the original method, alternative sets of input data for the artificial neural network which increase information about the change in axial forces over time are considered. For each set of input data a set of models is trained. Based on target metric values distribution among the obtained sets, a set is selected where the minimum value of the mathematical expectation of the target metric is achieved. For the set of models corresponding to the identified best set, accuracy control of the method is determined by establishing the relationship between the mathematical expectation of the target metric and the parameters of the numerical solution.&#x0D; Results. The conditions under which a lower value of the mathematical expectation of the target metric is obtained compared to the original method are determined. The results of numerical experiments, depending on the considered case, show, in average, an improvement on 43.54% and 9.67% in the refined method compared to the original. Additionally, the proposed refinement reduces the computational costs required to find a solution by omitting certain steps of the original method. An accuracy control rule of the method is established, which allows to obtain on average a given error value without performing extra computations.&#x0D; Conclusions. The obtained results indicate the feasibility of applying the proposed refinement. A higher accuracy in predicting the time until failure of corroding hinge-rod structures allows to reduce the risks of an emergency situation. Additionally, accuracy control enables finding a balance between computational costs and the accuracy of solving the problem. KEYWORDS

Design of fruit fly optimization algorithm based on Gaussian distribution and its application to image processing

The Fruit Fly Optimization Algorithm (FOA) has strong applicability, which can be optimized directly after the objective is determined not by building a complex model. Due to the problems of the algorithm such as easy prematureness, low solution accuracy, and easy to fall into local optimality. Therefore, the Gaussian Distribution Fruit Fly Optimization Algorithm (GaussFOA) based on Gaussian distribution was first proposed to solve the shortcomings of FOA. Then GaussFOA was applied to image segmentation processing. Finally, the experimental results were compared with FOA, the improved Fruit Fly Optimization Algorithm with Changing Step and Strategy (CSSFOA), and the Linear Generation Mechanism of Candidate Solution of Fruit Fly Optimization Algorithm (LGMSFOA). The results showed that GaussFOA had 100 % success rate compared with FOA, CSSFOA, and LGMSFOA under the same function. This algorithm also had the best finding mean and standard deviation. The low and high threshold division was compared in terms of the number of segmentation thresholds. The GaussFOA had the best value of both the average and the standard deviation of the search for merit. The segmentation results under high threshold were more obvious when compared with the segmentation results of low threshold GaussFOA. The image immunity of GaussFOA was 8.57 %, 10 %, and 29.97 % higher than that of FOA, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). This indicated that the model constructed based on GaussFOA had improved the image segmentation effect and stability compared with other algorithms. The findings of the research can offer a new path for the processing techniques of images.

Fast computation of the observer motion effects induced on monopole frequency spectra for tabulated functions

Context. Various methods have been studied to compute the boosting effects produced by the observer peculiar motion, which modifies and transfers the isotropic monopole frequency spectrum of the cosmic background radiation to higher multipoles. Explicit analytical solutions for the spherical harmonic expansion coefficients were already presented and applied to different types of background spectrum, strongly alleviating the computational effort needed for accurate theoretical predictions. The frequency spectra at higher multipoles are inherently led by higher-order derivatives of the monopole spectrum. Provided that it can be well described by analytic or semi-analytic functions, the computation of its transfer is not affected by numerical instabilities when evaluated at the required level of numerical accuracy. Instead, monopole frequency spectra described by tabulated functions are computed with a relatively poor frequency resolution in comparison with the Doppler shift, which necessitates interpolation of the tabular representation. The spectra are also affected by uncertainties related to intrinsic inaccuracies in the modelling or in the related observational data as well as to limited accuracy in their numerical computation. These uncertainties propagate and increase with the derivative order, possibly preventing the trustworthy computation of the transfer to higher multipoles and of the observed monopole. Aims. We study methods to filter the original function or its derivatives and the multipole spectra, to mitigate numerical instabilities, and to derive reliable predictions of the harmonic coefficients for different cosmic background models. Methods. From the analytical solutions, and assuming that the monopole spectrum can be expanded in Taylor’s series, we derive explicit expressions for the harmonic coefficients up to the multipole ℓmax = 6 in terms of monopole spectrum derivatives. We then consider different low-pass filters: prefiltering in Fourier space of the tabular representation; filtering in both real and Fourier space of the numerical derivatives; interpolation approaches; and a dedicated method based on amplification and deamplification of the boosted signal. We study the quality of these methods when applied to suitable analytical approximations of the tabulated functions, possibly polluted with simulated noise. These methods are then applied to the tabulations. Results. We consider two very different types of monopole spectra superimposed to the cosmic microwave background: the (smooth) extragalactic source microwave background signal from radio-loud active galactic nuclei and the (feature-rich) redshifted 21 cm line, and present our results in terms of spherical harmonic coefficients. The direct prediction of these coefficients can be noisy at ℓ &gt; 1 or, depending on the uncertainty level, even at ℓ ≤ 1. Without assuming a functional form for the extragalactic background spectrum, the Gaussian prefiltering coupled to the sequential real-space filtering of derivatives allows us to derive accurate predictions up to ℓ ∼ 6, while a log–log polynomial representation, which is appropriate over several decades, gives accurate solutions at any ℓ. Instead, it is difficult to characterise the 21 cm line model variety, and so it is relevant to work without assumptions about the underlying function. Typically, the prefiltering provides accurate predictions up to ℓ ≃ 3 or 4, while the further sequential filtering of the derivatives or the boosting amplification and deamplification method improves the results up to ℓ = 4, while also allowing reasonable estimations of the spectrum at higher ℓ. Conclusions. The proposed methods can significantly extend the range of realistic cosmic background models manageable with a fast computation, beyond the cases characterised a priori by analytical or semi-analytical functions. These methods require only an affordable increase in computation time compared to the direct calculation via simple interpolation.

A shock-stable rotated-hybrid Riemann solver on rectangular and triangular grids

The rotated Riemann solver is robust against the carbuncle phenomenon, especially for multidimensional computation. Moreover, hybrid techniques are usually used to enhance the stability of an accurate scheme by combining an accurate scheme with a diffusive scheme. This paper proposes a rotated-hybrid Riemann solver named the rotated-HLLC+ scheme. The scheme is developed by hybridizing the Harten–Lax–van Leer contact (HLLC) scheme with the advection upstream splitting method based on a flux vector splitting (AUSMV+) scheme by following the rotated Riemann solver approach. The unit vector n1 is calculated from the velocity-difference vector, and the unit vector n2 is the orthogonal vector. The linearized analysis suggests that the HLLC scheme should be used in the direction of n1 and the AUSMV+ scheme in the direction n2. In this way, the hybrid scheme becomes shock-stable with less numerical dissipation. Moreover, the pressure-based method is used to detect the shock wave. Several numerical experiments suggest that the pressure cutoff parameter εp=0.01 may be generally suitable and provide a stable solution with little additional numerical dissipation. The last two numerical examples show that the computational performance of the rotated-HLLC+ scheme is comparable to the HLLC scheme for the weak shock reflection over convex double wedges. However, the scheme is approximately 9% faster than the HLLC scheme for the double Mach reflection of a strong shock wave. The proposed scheme gives fast, stable, and accurate solutions on rectangular and triangular grids.

FasTrack - A Speedy Geo Based Attendance Tracker

To ease the process of doing 10 min tasks i.e, taking attendance in under 40 seconds.This Location- Based Attendance Web Application is a boon for Educational Institutions utilizing Django, HTML, CSS, and JavaScript to streamline attendance. Faculty members generate unique codes for students, who input them along with their roll numbers. The system validates attendance using location data, comparing student and faculty coordinates within a 10-meter threshold.This innovative system significantly reduces attendance tracking time from 5- 10 minutes to 30 seconds, optimizing overall academic workflow. Faculty efficiency is enhanced, allowing for better utilization of class time. The application offers a swift and accurate attendance management solution for educational institutions.

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.