Search

Accurate prediction of snow water equivalent (SWE) can be valuable for water resource managers. Re-cently, deep learning methods such as long short-term memory (LSTM) have exhibited high accuracy in simulating hydrologic variables and can integrate lagged observations to improve prediction, but their benefits were not clear for SWE simulations. Here we tested an LSTM network with data integration (DI) for SWE in the western United States to integrate 30-day-lagged or 7-day-lagged observations of either SWE or satellite-observed snow cover fraction (SCF) to improve future predictions. SCF proved beneficial only for shallow-snow sites during snowmelt, while lagged SWE integration significantly improved prediction accuracy for both shallow-and deep-snow sites. The median Nash–Sutcliffe model efficiency coefficient (NSE) in temporal testing improved from 0.92 to 0.97 with 30-day-lagged SWE integration, and root-mean-square error (RMSE) and the difference between estimated and observed peak SWE values dmax were reduced by 41% and 57%, respectively. DI effectively mitigated accumulated model and forcing errors that would otherwise be persistent. Moreover, by applying DI to different observations (30-day-lagged, 7-day-lagged), we revealed the spatial distribution of errors with different persistent lengths. For example, integrating 30-day-lagged SWE was ineffective for ephemeral snow sites in the southwestern United States, but significantly reduced monthly-scale biases for regions with sta-ble seasonal snowpack such as high-elevation sites in California. These biases are likely attributable to large interannual variability in snowfall or site-specific snow redistribution patterns that can accumulate to impactful levels over time for nonephemeral sites. These results set up benchmark levels and provide guidance for future model improvement strategies.

Compared to traditional partial differential equation modeling methods, Markov switching models can accurately capture the abrupt changes or jumps that complex systems often experience in the real world. In this paper, we propose a novel wave equation model with Markovian switching to represent complex systems with state‐jumping phenomena better, and the well‐posedness of the model is proved. In addition, a numerical method with non‐uniform grids is also proposed for the proposed model to simulate the data in realistic situations, which is based on the use of finite element discretization in space and central difference discretization in time. Finally, we conduct several experiments to analyze the errors and stability of the proposed model and the traditional model. The results show that the Markov switching model proposed in this paper has a smaller error than the traditional models while ensuring stability and can more accurately simulate the state jump phenomena of real‐world systems. [ABSTRACT FROM AUTHOR]

Domain adaptation is an important subfield of transfer learning, it has been successfully applied in many applications of machine learning. Recently, significant theoretical and algorithmic advances have been achieved in domain adaptation. The theoretical analyses for domain adaptation are based on VC dimension and Rademacher complexity. There are also some covering number-based results, but most of these bounds are based on the results of Rademacher complexity, indirectly given by the relationship between covering number and Rademacher complexity. In this paper, we propose a theoretical analysis framework for domain adaptation, thus the error bound can be derived directly by covering number, which is an effective method for analyzing the generalization error in statistical learning theory. We derive generalization error bound for domain adaptation with a class of loss functions satisfying the assumptions. We also propose a mixup contrastive adversarial network for domain adaptation by introducing a mixup module for enhancing the alignment of the source and target domains during domain transfer, and a contrastive learning module for solving class-level alignment after domain transfer. Experimental results demonstrate the effectiveness of the proposed algorithm and the property of the theoretical results. [ABSTRACT FROM AUTHOR]

The least squares vorticity stabilization (LSVS), proposed in N. Ahmed, G. R. Barrenechea, E. Burman, J. Guzmán, A. Linke, and C. Merdon (“A pressure-robust discretization of Oseen’s equation using stabilization in the vorticity equation,” SIAM J. Numer. Anal., vol. 59, no. 5, pp. 2746–2774, 2021) for the Scott–Vogelius finite element discretization of the Oseen equations, is studied as an augmentation of the popular grad-div stabilized Taylor–Hood pair of spaces. An error analysis is presented which exploits the situation that the velocity spaces of Scott–Vogelius and Taylor–Hood are identical. Convection-robust error bounds are derived under the assumption that the Scott–Vogelius discretization is well posed on the considered grid. Numerical studies support the analytic results and they show that the LSVS-grad-div method might lead to notable error reductions compared with the standard grad-div method. [ABSTRACT FROM AUTHOR]

We study the stability and convergence properties of a semi-implicit time stepping scheme for the incompressible Navier–Stokes equations with variable density and viscosity. The density is assumed to be approximated in a way that conserves the minimum-maximum principle. The scheme uses a fractional time-stepping method and the momentum, which is equal to the product of the density and velocity, as a primary unknown. The semi-implicit algorithm for the coupled momentum-pressure is shown to be conditionally stable and the velocity is shown to converge in L 2 norm with order one in time. Numerical illustrations confirm that the algorithm is stable and convergent under classic CFL condition even for sharp density profiles. [ABSTRACT FROM AUTHOR]

In this paper, we propose an explicit two-grid spectral deferred correction method for solving the nonlinear fractional pantograph differential equations. We design a partition including the global and local grids, which reduces the interaction between the subintervals caused by the delay term. We also analyze the numerical errors of the suggested approach for the prediction step and the correction step, respectively. Numerical experiments confirm the theoretical expectations. [ABSTRACT FROM AUTHOR]

In this paper, we extend the utilization of pseudostress-based formulation, recently employed for solving diverse linear and nonlinear problems in continuum mechanics via mixed finite element methods, to the weak Galerkin method (WG) framework and its respective applications. More precisely, we propose and analyze a mixed weak Galerkin method for a pseudostress formulation of the two-dimensional Brinkman equations with Dirichlet boundary conditions, then compute the velocity and pressure via postprocessing formulae. We begin by recalling the corresponding continuous variational formulation and a summary of the main WG method, including the weak divergence operator and the discrete space, which are needed for our approach. In particular, in order to define the weak discrete bilinear form, whose continuous version involves the classical divergence operator, we propose the weak divergence operator as a well-known alternative for the classical divergence operator in a suitable discrete subspace. Next, we show that the discrete bilinear form satisfies the hypotheses required by the Lax–Milgram lemma. In this way, we prove the well-posedness of the weak Galerkin scheme and derive a priori error estimates for the numerical pseudostress, velocity, and pressure. Finally, several numerical results confirming the theoretical rates of convergence and illustrating the good performance of the method are presented. The results in this work are fundamental and can be extended into more relevant models. [ABSTRACT FROM AUTHOR]

We discuss the identification of a time‐dependent potential in a time‐fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by leveraging the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we present a flux‐based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady‐state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming an inf‐sup condition, we prove its well‐posedness and error estimates of optimal order. We show that the inf‐sup condition is satisfied by some triangular elements. Numerical results are also provided to support our theoretical results. [ABSTRACT FROM AUTHOR]

Accurately predicting errors incurred in a cross-section model for two-step reactor analysis enables the development of optimal case matrices and more efficient cross-section models. In a companion paper, we developed a systematic methodology for the partial derivatives cross-section model through rigorous analytic error analysis. In this paper, we verify our methodology against the conventional "brute force" numerical approach using a typical pressurized water reactor (PWR) lattice. By successfully reproducing known results, we gain confidence in our methodology's application to advanced reactor environments, where optimal case matrices are generally not known. Our error methodology relies on accurately estimating bounds on the derivatives of the cross-section functions, a task we achieve through an order of convergence study. We use these derivative bounds in derived error expressions to obtain pointwise and setwise cross-section error bounds and verify these results with reference solutions of various two-group cross sections. We then propagate the cross-section error bounds to reactivity error using first-order perturbation theory and analyze their combined effect. Application of this approach to our test problem corroborates our prior qualitative findings with quantitative evidence and reveals the relative magnitudes of interpolation and model form error sources across diverse PWR cross-section functionalizations. Our results suggest systematic pathways for improving case matrix construction to minimize the overall error. These findings also confirm what is well known to the light water reactor design community, which is that interpolation error of cross sections for standard interpolation procedures and case matrix structures is on the order of 10 pcm or less. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multi-lattice problems, and investigating historical effects within the macroscopic depletion model. [ABSTRACT FROM AUTHOR]

Accurate assessment of uncertainties in cross-section data is crucial for reliable nuclear reactor simulations and safety analyses. In this study, we focus on the interpolation procedure of the partial derivatives (PD) cross-section model used to evaluate nodal parameters from pregenerated multigroup libraries. Our primary objective is to develop a systematic methodology that enables prediction of the incurred errors in the cross-section model, leading to the development of optimal case matrices, more efficient cross-section models, and informed case matrix construction for reactor types lacking substantial data and experience. We make progress toward this objective through a rigorous analytic error analysis enabled by the derivation of error expressions and bounds for the PD model based on the discovery that the method is a form of Lagrange interpolation. Our investigations reveal distinct outcomes depending on the chosen cross-section functionalizations, achieved by identifying the sources of error. These error sources are found to include interpolation error, which is always present, and model form error, which is a property of the supplied case matrix. We show that simply increasing grid refinement through the addition of branches may not always lead to decreased cross-section errors, particularly in cases where the model form error predominantly contributes to the total error. We present numerical results and verification in a companion paper, showing these different error characteristics for various cross-section functionalizations. Although applied to current light water reactor environments, our methodology offers a means for advanced reactor analysts to develop case matrices with quantified error levels, advancing the goal of a general methodology for robust two-step reactor analysis. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multilattice problems, and investigating historical effects within the macroscopic depletion model. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the full discretization of linear wave equations, where the space discretization is carried out with a discontinuous Galerkin method on spatial meshes which are locally refined or have a large wave speed on only a small part of the mesh. Such small local structures lead to a strong Courant–Friedrichs–Lewy (CFL) condition in explicit time integration schemes causing a severe loss in efficiency. For these problems, various local time-stepping schemes have been proposed in the literature in the last years and have been shown to be very efficient. Here, we construct a quite general class of local time integration methods preserving a perturbed energy and containing local time-stepping and locally implicit methods as special cases. For these two variants we prove stability and optimal convergence rates in space and time. Numerical results confirm the stability behavior and show the proved convergence rates. [ABSTRACT FROM AUTHOR]

This experimental study aims to evaluate the quality of post-edited texts, originally translated using computer-assisted translation (CAT) tools, in comparison with traditional human translation. This study investigates the quality of post-editing (PE) compared to traditional translation from scratch (TFS) in the context of Arabic-English translation, utilizing the Phrase CAT tool. The main hypothesis posits that PE yields a final product whose quality is similar or equivalent to that of TFS. The participants' scores and error frequencies were evaluated using the American Translators Association framework for standardized error marking, and terminology, word choice, mistranslation, addition/omission, spelling, punctuation, case, inconsistency, style, and grammar in both approaches were compared. Data from nine professional Saudi translators showed that PE generally outperformed TFS in terminology, spelling, punctuation, and case, whereas TFS exhibited strengths in consistency, style, grammar, and literal translation. Statistical analysis confirmed the similarity in overall error rates between PE and TFS. The difference in mean error numbers between TFS and PE was not statistically significant. Thus, the disparity in means likely resulted from random chance and might not indicate substantive differences between the two groups. These results imply that PE yields quality that is comparable or equivalent to that of TFS, proving the aforementioned hypothesis. The implications highlight the need for CAT tool training and PE skills among translators to meet the demands of evolving translation technologies. Furthermore, this study underscores the importance of integrating PE training into translation curricula and organizing workshops to improve CAT tool usage. [ABSTRACT FROM AUTHOR]

We propose to use a hybridizable discontinuous Galerkin (HDG) method combined with the continuous Galerkin (CG) method to approximate Maxwell's equations. We make two contributions in this paper. First, even though there are many papers using HDG methods to approximate Maxwell's equations, to our knowledge they all assume that the coefficients are smooth (or constant). Here, we derive optimal convergence estimates for our HDG-CG approximation when the electromagnetic coefficients are piecewise W 1 , ∞ . This requires new techniques of analysis. Second, we use CG elements to approximate the Lagrange multiplier used to enforce the divergence condition and we obtain a discrete system in which we can decouple the discrete Lagrange multiplier. Because we are using a continuous Lagrange multiplier space, the number of degrees of freedom devoted to this are less than for other HDG methods. We present numerical experiments to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

Accurate estimation of wind power is essential for predicting and maintaining the power balance in the power system. This paper proposes a novel approach to enhance the accuracy of wind power estimation through a hybrid model integrating neural networks and error discrimination‐correction techniques. In order to improve the accuracy of estimation, a bidirectional gating recurrent unit is developed, forming an initial wind power estimation curve through training. Additionally, a sequential model‐based algorithmic configuration optimizes bidirectional gating recurrent unit's network hyperparameters. To tackle estimation errors, a multi‐layer perceptron combined with sequential model‐based algorithmic configuration is employed to create a classification model that automatically discerns the quality of estimates. Subsequently, an innovative correction model, based on grey relevancy degree and relevancy errors, is devised to rectify erroneous estimates. The final estimates result from a summation of the initial estimates and the values derived from error corrections. By analysing the real data from a wind farm in northwest China, a simulation test validates the proposed hybrid model. Experimental results demonstrate a substantial improvement in modelling accuracy when compared to the initial model. [ABSTRACT FROM AUTHOR]

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme. [ABSTRACT FROM AUTHOR]

This research presents an efficient and highly accurate cubic B-spline method (CBSM) for solving second-order linear boundary value problems (BVPs). The method achieves sixth-order convergence, supported by rigorous error analysis, ensuring rapid error reduction with mesh refinement. The effectiveness of the CBSM is validated through four numerical examples, showcasing its accuracy, reliability, and computational efficiency, making it well-suited for large-scale problems. A comparative analysis with existing methods confirms the superior performance of the CBSM, positioning it as a practical and powerful tool for solving second-order BVPs. [ABSTRACT FROM AUTHOR]

In this paper, a generalized finite difference method (GFDM) is proposed and analyzed for meshless numerical solution of the time-fractional diffusion-wave equation. Two (3 − α) -order accurate temporal discretization schemes are presented by using the L1 formula and the original H2N2 or fast H2N2 formulas to discretize the time-fractional derivative of order α ∈ (1 , 2). The stability of the temporal discretization schemes is analyzed. Then, the time-fractional diffusion-wave initial-boundary value problem is transformed into a series of time-independent integer-order boundary value problems, and discrete linear algebraic systems are built by the application of the GFDM. Accuracy analysis of the GFDM with both original H2N2 and fast H2N2 formulas is presented in theory, and numerical experimental results are provided to verify the theoretical results and the effectiveness of the proposed meshless method. [ABSTRACT FROM AUTHOR]

In this paper, we develop the Hermite-type virtual element method to solve the second order problem. A Hermite-type virtual element of degree ≥3 is constructed, which can be taken as an extension of classical Hermite finite element to polygonal meshes. For this virtual element, we rigorously prove some inverse inequalities and the boundedness of basis functions. Further, we prove the interpolation error estimates. Based on a computable H 1 -projection, we give the discrete formulation and prove the optimal convergence for the Hermite-type virtual element method. Finally, we show some numerical results to verify the convergence of Hermite-type virtual element. Additionally, compared with other virtual elements, both theoretical analysis and numerical experiments demonstrate that the Hermite-type virtual element has fewer global degrees of freedom and results in significant computational savings. [ABSTRACT FROM AUTHOR]

This paper introduces a numerical approach by generalizing Legendre wavelets for solving nonlinear Caputo–Hadamard fractional differential equations. The methodology involves the extension of classical Legendre wavelets, namely the generalized Legendre wavelets (gLWs), along with the development of operational matrices for Hadamard fractional integration and Caputo–Hadamard fractional differentiation. The proposed method combines the gLWs with the Adomian decomposition method to address the nonlinearities inherent in fractional equations through Adomian polynomials. A detailed methodology is presented for applying the proposed method to nonlinear Caputo–Hadamard fractional differential equations, accompanied by error analysis and numerical simulations to demonstrate its reliability and accuracy. [ABSTRACT FROM AUTHOR]

Sequence-to-sequence models have been applied to many challenging problems, including those in text and speech technologies. Normalization is one of them. It refers to transforming non-standard language forms into their standard counterparts. Non-standard language forms come from different written and spoken sources. This paper deals with one such source, namely speech from the less-resourced highly inflected Slovenian language. The paper explores speech corpora recently collected in public and private environments. We analyze the efficiencies of three sequence-to-sequence models for automatic normalization from literal transcriptions to standard forms. Experiments were performed using words, subwords, and characters as basic units for normalization. In the article, we demonstrate that the superiority of the approach is linked to the choice of the basic modeling unit. Statistical models prefer words, while neural network-based models prefer characters. The experimental results show that the best results are obtained with neural architectures based on characters. Long short-term memory and transformer architectures gave comparable results. We also present a novel analysis tool, which we use for in-depth error analysis of results obtained by character-based models. This analysis showed that systems with similar overall results can differ in the performance for different types of errors. Errors obtained with the transformer architecture are easier to correct in the post-editing process. This is an important insight, as creating speech corpora is a time-consuming and costly process. The analysis tool also incorporates two statistical significance tests: approximate randomization and bootstrap resampling. Both statistical tests confirm the improved results of neural network-based models compared to statistical ones. [ABSTRACT FROM AUTHOR]

The main goal of this study is to solve a class of linear and nonlinear Volterra integral equations (VIEs) of the third kind. The proposed technique estimates the solution of these equations using a technique based on MLS approximation and shifted Chebyshev polynomials. The approach is independent of the geometry of the domain and does not require any background meshes; therefore, it can be considered a meshless approach. The new method is effective and more flexible for many types of VIEs of the third kind, and its algorithm can be simply implemented on computers. The construction of a new technique for the proposed equations has been introduced. The convergence analysis is also studied. The convergence precision of the new approach is checked on classes of VIEs of the third kind, and the results validate the theoretical error estimates. Finally, numerical tests are provided to illustrate the accuracy and reliability of this approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was available. Our goal was to identify these unknown quantities under the environment of uncertain measurement output data. A distributionally robust parameter estimation problem (i.e., a bi-level parameter estimation (BLPE) problem) subject to the NCTSTD system was presented, where the expectation of the discrepancy between the output of the NCTSTD system and the uncertain measured output data with respect to its probability distributions was included in the cost functional. By applying the duality theory, the BLPE problem was transformed into a single-level parameter estimation (SLPE) problem with non-smooth term approximated by a smoothing technique and its error analysis was given. Then, the gradients of the cost function of the SLPE problem were derived. A hybrid optimization algorithm was proposed for solving the SLPE problem. The paper concluded by presenting the simulation results. [ABSTRACT FROM AUTHOR]

Digitized counter-diabatic (CD) optimization algorithms have been proposed and extensively studied to enhance performance in quantum computing by accelerating adiabatic processes while minimizing energy transitions. While adding approximate counter-diabatic terms can initially introduce adiabatic errors that decrease over time, Trotter errors from decomposition approximation persist. On the other hand, increasing the high-order nested commutators for CD terms may improve adiabatic errors but could also introduce additional Trotter errors. In this article, we examine the two-qubit model to explore the interplay between approximate CD, adiabatic errors, Trotter errors, coefficients, and commutators. Through these analyses, we aim to gain insights into optimizing these factors for better fidelity, a shallower circuit depth, and a reduced gate number in near-term gate-based quantum computing. [ABSTRACT FROM AUTHOR]

Observational data inherently contain noise which manifests as uncertainties in the measured parameters and creates positive biases or noise floors in second‐order products like variances, fluxes, and spectra. Historical methods estimate and subsequently subtract noise floors, but struggle with accuracy. Gardner and Chu (2020, doi.org/10.1364/AO.400375) proposed an interleaved data processing method, which inherently eliminates biases from variances and fluxes, and suggested that the method could also eliminate noise floors of power spectra. We investigate the interleaved method for spectral analysis of atmospheric waves through theoretical studies, forward modeling, and demonstration with lidar data. Our work shows that calculating the cross‐power spectral density (CPSD) from two interleaved subsamples does reduce the spectral noise floor significantly. However, only the Co‐PSD (the real part of CPSD) eliminates the noise floor completely, while taking the absolute magnitude of CPSD adds a reduced noise floor back to the spectrum when the sample number is finite. This reduced noise floor can be further minimized through averaging over more observations, completely different from traditional spectrum calculations whose noise floor cannot be reduced by incorporating more samples. We demonstrate the first application of the interleaved method to spectral data, successfully eliminating the noise floor using the Co‐PSD in a forward model and in lidar observations of the vertical wavenumber of gravity waves at McMurdo, Antarctica. This high accuracy is gained by sacrificing precision due to photon‐count splitting, requiring additional observations to counter this effect. We provide quantitative assessment of accuracy and precision as well as application recommendations. Plain Language Summary: Atmospheric waves serve a vital role in global energy and momentum transportation between the lower and upper atmosphere, driving major atmospheric circulations. These waves exist across many scales, from large planetary waves to medium‐ and small‐scale gravity waves (GW). GW are a key factor driving many atmospheric phenomena, but due to their relatively smaller scales, they are difficult to study. The spectra of GW are important to understanding wave dynamics and informing the development of atmospheric models, as these spectra contain critical information about how wave‐transported energy is distributed amongst different temporal and spatial frequencies. A major tool in improving our knowledge and modeling of GW is their direct observations. Although being powerful wave observation tools, lidar and radar data contain noise in their measurements which manifests as noise floors, obscuring derived wave power spectra. These floors cannot be removed by averaging more samples, as is done for other parameters, making it difficult to accurately interpret the spectra. Pre‐existing techniques can remove this floor, but they struggle with accuracy, especially in high‐noise conditions. This study introduces and demonstrates the use of an interleaved method of spectral processing, which eliminates the noise floors altogether, enabling high‐accuracy calculation of wave spectra. Key Points: We develop an interleaved data processing technique to compute cross‐power spectral density (CPSD) for deriving unbiased wave spectraAccuracy and precision analyses of coincident‐power spectral density (Co‐PSD) and CPSD magnitude show Co‐PSD eliminating noise floor entirelyThe spectral interleaved method is shown to eliminate noise floor, demonstrated using a forward model and Antarctic lidar observations [ABSTRACT FROM AUTHOR]

In this paper, for quickly solving one‐ and two‐dimensional space‐fractional sine‐Gordon equations with distributed delay, we suggest several accelerated schemes of direct compact difference (DCD) methods. For one‐dimensional (1D) problems, with a function transformation, we construct an indirect compact difference (ICD) method, which requires less calculation cost than the corresponding DCD method, and prove under the appropriate conditions that ICD method has second‐order (resp. forth‐order) calculation accuracy in time (resp. space). By extending the argument for 1D case, we further obtain an ICD method for solving two‐dimensional (2D) problems and derive the similar convergence result. For ICD and DCD methods of 2D problems, we also give their alternative direction implicit (ADI) schemes. Moreover, for the fast implementations of ICD method of 1D problems and indirect ADI method of 2D problems, we further present their acceleration strategies. Finally, with a series of numerical experiments, the findings in this paper are further confirmed. [ABSTRACT FROM AUTHOR]

In recent years, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome the mentioned challenge. This paper presents two new diffusive representations to approximate the Caputo fractional derivative of order 0 < α < 1. An error analysis of the newly presented methods together with some numerical examples is provided at the end. [ABSTRACT FROM AUTHOR]

An enriched hybrid high-order method is designed for the Stokes equations of fluid flow and is fully applicable to generic curved meshes. Minimal regularity requirements of the enrichment spaces are given, and an abstract error analysis of the scheme is provided. The method achieves consistency in the enrichment space and is proven to converge optimally in energy error. The scheme is applied to 2D flow around circular cylinders, for which the local behaviour of the velocity and pressure fields is known. By enriching the local spaces with these solutions, superior numerical results near the submerged cylinders are achieved. [ABSTRACT FROM AUTHOR]

In this work, two numerical techniques are compared for solving one and two-dimensional convection-diffusion equations. First technique is referred as "MCUAT tension B-spline," and the second technique is labeled as "MCUAH tension B-spline." Various aspects are examined to validate the compatibility of results, including comparisons between numerical and exact solutions and evaluation of different error norms. Present errors are compared with existing literature, presenting a remarkable improvisation. Statistical validation of work is tested via a correlation matrix heatmap generated in Python. The order of convergence of the proposed work is also included. Via an observation of comparison of results, it is claimed that UAT results are slightly better than UAH results. Different aspects of correlation, such as strongly negative correlation and perfect positive correlation, are notified. The present work will introduce new dimensions to the field of numerical techniques. [ABSTRACT FROM AUTHOR]

This study investigates the cognitive impacts of video game immersion and task interference on immediate and delayed recall as well as recognition tasks. We enrolled 160 subjects aged 18 to 29, who were regular players of "shoot-em-up" video games for at least 3 years. Participants were assigned to one of three experimental groups or a control group. The experimental conditions varied in the timing and type of tasks: the first group performed a video game session between recall tasks, the second group multitasked with video games and recall tasks simultaneously, and the third group engaged in task switching from video games to recall tasks. Using the Rey Auditory Verbal Learning Test, we measured the effects of these conditions on cognitive performance, focusing on error types and recall accuracy. Results indicated that multitasking and task switching significantly affected the subjects' performance, with notable decrements in recall and recognition accuracy in conditions of high task interference. The study highlights the cognitive costs associated with multitasking in immersive digital games and provides insights into how task similarity and interference might increase error rates and affect memory performance. [ABSTRACT FROM AUTHOR]

This study delves into the potential polynomial and rational wave solutions of the Kudryashov–Sinelshchikov equation. This equation has multiple applications including the modeling of propagation for nonlinear waves in various physical systems. Through detailed numerical simulations using the finite element approach, we present a set of accurate solitary and soliton solutions for this equation. To validate the effectiveness of our proposed method, we utilize a collocation finite element approach based on quintic B-spline functions. Error norms, including L2 and L∞, are employed to assess the precision of our numerical solutions, ensuring their reliability and accuracy. Visual representations, such as graphs derived from tabulated data, offer valuable insights into the dynamic changes of the equation over time or in response to varying parameters. Furthermore, we compute conservation quantities of motion and investigate the stability of our numerical scheme using Von Neumann theory, providing a comprehensive analysis of the Kudryashov–Sinelshchikov equation and the robustness of our computational approach. The strong alignment between our analytical and numerical results underscores the efficacy of our methodology, which can be extended to tackle more complex nonlinear models with direct relevance to various fields of science and enineering. [ABSTRACT FROM AUTHOR]

The present article introduces, mathematically analyzes, and numerically validates a new weak Galerkin mixed finite element method based on Banach spaces for the stationary Navier–Stokes equation in pseudostress–velocity formulation. Specifically, a modified pseudostress tensor, which depends on the pressure as well as the diffusive and convective terms, is introduced as an auxiliary unknown, and the incompressibility condition is then used to eliminate the pressure, which is subsequently computed using a postprocessing formula. Consequently, to discretize the resulting mixed formulation, it is sufficient to provide a tensorial weak Galerkin space for the pseudostress and a space of piecewise polynomial vectors of total degree at most ’k’ for the velocity. Moreover, the weak gradient/divergence operator is utilized to propose the weak discrete bilinear forms, whose continuous version involves the classical gradient/divergence operators. The well-posedness of the numerical solution is proven using a fixed-point approach and the discrete versions of the Babuška–Brezzi theory and the Banach–Nečas–Babuška theorem. Additionally, an a priori error estimate is derived for the proposed method. Finally, several numerical results illustrating the method’s good performance and confirming the theoretical rates of convergence are presented. [ABSTRACT FROM AUTHOR]

We prove the optimal convergence in space and time for the linear acoustic wave equation in its second-order formulation in time, using the hybrid high-order method for space discretization and the leapfrog (central finite difference) scheme for time discretization. The proof hinges on energy arguments similar to those classically deployed in the context of continuous finite elements or discontinuous Galerkin methods, but some novel ideas need to be introduced to handle the static coupling between cell and face unknowns. Because of the close ties between the methods, the present proof can be readily extended to cover space semi-disretization using the hybridizable discontinuous Galerkin method and the weak Galerkin method. [ABSTRACT FROM AUTHOR]

This paper examines the variable-order fractional Lorenz system with distinct types of delays. The application of the Arzela–Ascoli theorem is made to prove the existence of solutions for the given problem, while the Banach fixed point theorem is employed to derive the uniqueness results. The utilization of the Adams–Bashforth–Moulton technique facilitates the exploration and resolution of the approximation solution, complemented by a thorough error analysis of particular approaches. The computational simulations showing chaotic behaviors in various delayed systems with different variable orders demonstrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In long‐range missions based on angle‐of‐arrival positioning, the angle measurement error of unmanned aerial vehicles is a major source of error. Therefore, reducing the unmanned aerial vehicle angle measurement error is crucial to achieve accurate remote positioning. In this paper, we propose a space vector–based method to correct the space vector of the target for the unmanned aerial vehicles when there are fewer than three available reference points, which in turn corrects the angular value of the target relative to the unmanned aerial vehicles. Simulation results show that when the distance between the reference point and the unmanned aerial vehicles is smaller than the distance between the target and the unmanned aerial vehicles, the azimuth measurement error can be reduced to 55% of the original error for the case of a single reference point, while the pitch angle measurement error remains almost unchanged. In the case of more than two reference points, the azimuth measurement error can be reduced to 1e5 and the pitch angle measurement error can be reduced to 30% of the original error. This method can be adapted to the rapid positioning task for high‐speed and high‐mobility targets without iteration, low computation, good correction effect, and the need of prior known data set reference. [ABSTRACT FROM AUTHOR]

Since the non-time-synchronized lightning positioning method does not rely on the time synchronization of the stations in the positioning system, it eliminates the errors arising from the pursuit of time synchronization and potentially achieves higher positioning accuracy. This paper provides a comprehensive overview of the errors present in the three-dimensional lightning positioning system. It compares the results of traditional positioning methods with those of non-time-synchronized lightning positioning algorithms. Subsequently, a simulation analysis of the positioning errors is conducted specifically for the non-time-synchronized lightning positioning method. The results show that (1) the non-time-synchronized lightning positioning method exhibits greater errors when utilizing two randomly positioned radiation sources for location determination. Consequently, the resulting positioning outcomes only provide a general overview of the lightning discharge. (2) The positioning outcomes resemble those of the traditional method when employing a fixed-coordinate beacon point. However, the errors in the three-dimensional positional coordinates of these fixed-coordinate beacon points significantly impact the deviations in the positioning results. This impact is positively correlated with the positional error of the beacon point, considering both the orientation and magnitude. (3) Similarly to the traditional method, the farther away from the center of the positioning network, the larger the radial error. (4) The spatial position of the selected fixed-coordinate beacon point has little influence on the error. [ABSTRACT FROM AUTHOR]

In this paper, the streamline diffusion weak Galerkin finite element method is proposed and analyzed for solving unsteady time convection diffusion problem in two dimension. The v-elliptic property and the stability of this scheme are proved in terms of some conditions. We derive an error estimate in L² (μ) and H¹ (μ) norm. Numerical experiments have demonstrated the effectiveness of the method in solving convection propagation problems, and the theoretical analysis has been validated. [ABSTRACT FROM AUTHOR]

Weddle transformed rule is mixed up with Birkhoff-Young rule to form the mixed quadrature rule of exactness seven. The above rule is numerically verified and the bound for the error is resolved with suitable examples to obtain the efficiency and applicability of the proposed scheme. The numerical results are found to close to analytical solutionn. [ABSTRACT FROM AUTHOR]

The swing torque and rotational torque after the spherical bearing is installed directly affect the performance of the spherical bearing. At this stage, the friction torque detection equipment of the spherical bearing is mainly used to detect uninstalled bearings. A set of rotation and swing after the bearing is installed is designed. Torque detection system. The detection principles of rotational torque and swing torque required for flexibility detection were analyzed, the functional design requirements and main technical indicators of the detection system were clarified, and the overall design plan of the detection system was established; the host structure of the detection system was designed, including rotational torque detection system, swing torque detection system, clamping system and calibration system; completed the scheme design of the detection control system, selected the torque sensor and servo motor, designed the main electrical control circuit of the detector; conducted error analysis of the detector. [ABSTRACT FROM AUTHOR]

In this paper, the numerical method for solving a class of generalized fractional advection-diffusion equation (GFADE) is considered. The fractional derivative involving scale and weight factors is imposed for the temporal derivative and is analogous to the Caputo fractional derivative following an integration-after-differentiation composition. It covers many popular fractional derivatives by fixing different weights $ w(t) $ w (t) and scale functions $ z(t) $ z (t) inside. The numerical solution of such GFADE is derived via a collocation method, where conventional Legendre polynomials are implemented. Convergence and error analysis of polynomial expansions are studied theoretically. Numerical examples are considered with different boundary conditions to confirm the theoretical findings. By comparing the above examples with those from existing literature, we find that our proposed numerical method is simple, stable and easy to implement. [ABSTRACT FROM AUTHOR]

To solve the temperature/strain cross-sensitivity problem, simultaneous measurement of temperature and strain can be achieved by using the two spectra of LP01 mode and LP11 mode in few-mode fiber Bragg grating (FM-FBG). However, in the same fiber the temperature/strain sensitivity difference is small, so the sensing accuracy is limited greatly. In this paper, we calculate the relation between sensing accuracy and sensitivity-difference and obtain that the enlarged sensitivity difference could improve the sensing accuracy. FBGs are engraved on two kinds fibers single-mode (SM) and few-mode (FM) with different geometrical dimensions; the sensing coefficients of LP01 mode in SM-FBG and LP11 mode/LP01 mode in FM-FBG are calibrated firstly and then are used to sense the temperature/strain. The experimental results show that parallelly using LP01 mode in SM-FBG and LP11 mode in FM-FBG achieves simultaneous measurement of temperature and strain, and error is reduced greatly compared with the sensing results using LP11 mode and LP01 mode in FM-FBG or using LP01 mode in SM-FBG and LP01 mode in FM-FBG, where the wavelength-temperature/strain coefficient difference is maximum. The temperature measurement error is 1.64°C, and the strain measurement error is 20.04 με, which is consistent with the theoretical analysis. The sensing results provide technical reference for FBG multi-parameter sensing measurement and the practical engineering application. [ABSTRACT FROM AUTHOR]

In this manuscript, we aim to study the semi-analytical and the numerical solution of a semilinear time-fractional diffusion equation where the time-fractional term includes the combination of tempered fractional derivative and k-Caputo fractional derivative with a parameter . The application of the new integral transform, namely Elzaki transform of the tempered k-Caputo fractional derivative is shown here and thereafter the semi-analytical solution is obtained by using the Elzaki decomposition method. The model problem is linearized using Newton's quasilinearization method, and then the quasilinearized problem is discretized by the difference scheme namely tempered - method. Stability and convergence analysis of the proposed scheme have been discussed in the -norm using the energy method. In support of the theoretical results, numerical example has been incorporated. [ABSTRACT FROM AUTHOR]

In this paper, we use weight function approach to construct a new King-like family of methods to solve nonlinear equations with multiple roots. Here the weight functions are chosen appropriately to reach the maximum convergence order eight and the family is optimal in the sense of Kung–Traub conjecture. Moreover, local convergence of a fourth order modified King's family for multiple roots is also studied. Radii of convergence balls of fourth order schemes are computed and compared with an existing method. Numerical examples have been presented based on applications of some real life problems and the results obtained show the superiority of our eighth order schemes over the existing ones. To study the dynamical behaviour of the proposed schemes, basins of attraction have also been presented which verifies that proposed eighth order schemes have more convergent points and requires less number of iterations in comparison to the existing methods. [ABSTRACT FROM AUTHOR]

In this article, we analyse the fractional Cattaneo heat equation for studying the conduction of heat in porous medium. This equation is also used in studying extended irreversible thermodynamics, material, plasma, cosmological model, computational biology, and diffusion theory in crystalline solids. The Sumudu adomian decomposition technique, which is combination of Sumudu transform and a numerical technique, is applied for getting numerical solution. The existence and uniqueness is analysed by using the fixed point theorem and the highest error of the designed technique is also analysed. Finally, the accuracy of the designed numerical method is presented by solving two examples and the findings are compared with the existing method. [ABSTRACT FROM AUTHOR]

This research work aims to theoretically examine the influence of various factors on the three-dimensional nanofluid flow. The study includes parameters such as temperature ratio coefficient, Prandtl numbers, Schmidt, Soret, Dufour, Biot, expansion ratio coefficient, Power index, and nanoparticle volume fraction parameter, as well as the effect of non-linear thermal radiation and magnetic parameter on the behavior of the nanofluid. These characteristics significantly impact the flow of the three-dimensional boundary layer in the presence of an expansion plate. To facilitate the investigation, we have selected nanofluids that contain water-based copper and aluminum oxide for this study. We have developed a model of a system of partial differential equations (SYS-PDEs) with non-linear terms. Based on selected similarity equations, the SYS-PDEs with non-linear terms has been transformed into a system of ordinary differential equations (SYS-ODEs) whose terms are non-linear. To approximate and solve the obtained SYS-ODEs, we utilized a modified spectral Chebyshev polynomials' first derivative pseudo-Galerkin spectral method. Additionally, we conducted an error analysis discussion to ensure the credibility of our results. We presented our analysis in graphical form and provided comments on each figure along with the effects of the various parameters studied. Consequently, we concluded that the power low is an essential factor affecting the flow's behavior, such as the nanofluid's velocity, temperature, and concentration. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Dalian Polytechnic University is the property of Journal of Dalian Polytechnic University Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Aiming at the interpolation and prediction problems in pit monitoring data processing, this paper introduced the interpolation model and extrapolation model of the generalised extended approximation method. Firstly, the formula of the generalised extended approximation method was derived, and then the 10-month monitoring data of the vertical displacement monitoring point of the pile top of a foundation pit was used for denoising pre-processing before calculation and analysis. The interpolation analysis was carried out based on the generalised extended approximation method, and the sliding algorithm was adopted to study the relationship between the combination of different unit domain nodes r, extended domain nodes s and approximation function terms t and the interpolation accuracy. The results of the data calculations show that the accuracy is relatively stable when s is larger, r and t are relatively small and closer, and the interpolation accuracy of the combination r = 2, t = 3 and s = 4 reaches the highest. The extrapolation accuracy of the generalised extended approximation method is investigated, and the data analysis shows that there is a positive relationship between the number of known nodes and the interpolation accuracy. The study concludes that the interpolation model and extrapolation model of the generalised extended approximation method have high computational accuracy, which can reach the sub-millimetre level, and are suitable for pit monitoring data processing, with good engineering value and application prospects. [ABSTRACT FROM AUTHOR]

This work presents a numerical method based on the Genocchi polynomials to solve linear Fredholm Integro-Differential Equations (LFIDEs). The process of the method is to transform the (LFIDE) into a matrix equation. This is done by approximating the unknown function, its derivatives, and integral kernel using Genocchi polynomials. After using the equidistant collocation points we solve the corresponding linear system with unknown Genocchi coefficients. To prove the accuracy and efficiency of the current method we mentioned some numerical examples. Comparing the obtained results with the exact solutions and some existing methods, it turns out that the current method gives a better approximation. [ABSTRACT FROM AUTHOR]

The bridge influence line can effectively reflect its overall structural stiffness, and it has been used in the studies of safety assessment, model updating, and the dynamic weighing of bridges. To accurately obtain the influence line of a bridge, an Empirical and Variational Mixed Modal Decomposition (E-VMD) method is used to remove the dynamic component from the vehicle-induced deflection response of a bridge, which requires the preset fundamental frequency of the structure to be used as the cutoff frequency for the intrinsic modal decomposition operation. However, the true fundamental frequency is often obtained from the picker, and the testing process requires the interruption of traffic to carry out the mode decomposition. To realize the rapid testing of the influence lines of bridges, a new method of indirectly identifying the operational modal frequency and deflection influence lines of bridge structures from the axle dynamic response is proposed as an example of cable-stayed bridge structures. Based on the energy method, an analytical solution of the first-order frequency of vertical bending is obtained for a short-tower cable-stayed bridge, which can be used as the initial base frequency to roughly measure the deflection influence line of the cable-stayed bridge. The residual difference between the deflection response and the roughly measured influence line under the excitation of the vehicle is operated by Fast Fourier Transform, from which the operational fundamental frequency identification of the bridge is realized. Using the operational fundamental frequency as the cutoff frequency and comparing the influence-line identification equations, the empirical variational mixed modal decomposition, and the Tikhonov regularization to establish a more accurate identification of the deflection influence line, the deflection influence line is finally identified. The accuracy and practicality of the proposed method are verified by real cable-stayed bridge engineering cases. The results show that the relative error between the recognized bridge fundamental frequency and the measured fundamental frequency is 0.32%, and the relative error of the recognized deflection influence line is 0.83%. The identification value of the deflection influence line has a certain precision. [ABSTRACT FROM AUTHOR]