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Deficient postural adaptation and freezing lead to gait initiation abnormalities in Parkinson's disease. Gait initiation is characterized by longer motor preparation, which is a marker of increased risk of falling, and by abnormal postural adjustments. Better understanding the nature of these motor preparation disturbances will enable us to adapt rehabilitation and reduce falls. Our objective was to describe the different components (in the motor, cognitive and limbic domains) of gait initiation parameters in Parkinson's disease. Forty-four patients with Parkinson's disease performed repeated step initiations under high attentional load with decision-making. The proportions of multiple anticipatory postural adjustments and anticipatory postural adjustment errors, markers of abnormal motor preparation, were measured. A logistic regression analysis studied the relationships between step initiation perturbations and the demographic, motor, cognitive, and neuropsychiatric characteristics of the patients. Multiple anticipatory postural adjustments and anticipatory postural adjustments errors lengthened step execution time. Motor severity explained the multiple anticipatory postural adjustments, suggesting a pathological role. Attentional performance explained anticipatory postural adjustments errors. Demographic and neuropsychiatric characteristics didn't contribute significantly to the abnormal anticipatory postural adjustments. Motor disability contributes to the delay in step execution in Parkinson's disease through multiple anticipatory postural adjustments, highlighting the need to target motor preparation improvement in rehabilitation. • Deficient postural adaptation and freezing lead to gait initiation abnormalities in Parkinson's disease • Motor severity explained the multiple anticipatory postural adjustments. • Worse attentional performance explained anticipatory postural adjustments errors [ABSTRACT FROM AUTHOR]

The utilization of nonlinear differential equations has resulted in remarkable progress across various scientific domains, including physics, biology, ecology, and quantum mechanics. Nonetheless, obtaining multiple solutions for nonlinear differential equations can pose considerable challenges, particularly when it is difficult to find suitable initial guesses. To address this issue, we propose a pioneering approach known as the Companion-Based Multilevel Finite Element Method (CBMFEM). This novel technique efficiently and accurately generates multiple initial guesses for solving nonlinear elliptic semi-linear equations containing polynomial nonlinear terms through the use of finite element methods with conforming elements. As a theoretical foundation of CBMFEM, we present an appropriate and new concept of the isolated solution to the nonlinear elliptic equations with multiple solutions. The newly introduced concept is used to establish the inf-sup condition for the linearized equation around the isolated solution. Furthermore, it is crucially used to derive a theoretical error analysis of finite element methods for nonlinear elliptic equations with multiple solutions. A number of numerical results obtained using CBMFEM are then presented and compared with a traditional method. These not only show the CBMFEM's superiority, but also support our theoretical analysis. Additionally, these results showcase the effectiveness and potential of our proposed method in tackling the challenges associated with multiple solutions in nonlinear differential equations with different types of boundary conditions. [ABSTRACT FROM AUTHOR]

We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and provide a theoretical estimate of the error. We conclude with some numerical experiments to further support the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, we derive a geometrically nonlinear plate model based on the Kirchhoff hypothesis and the large deflection hypothesis, and provide an error analysis of the corresponding element-free Galerkin method. The penalty method is employed to enforce boundary conditions. The error estimate explicitly depends on nodal spacing, number of monomial basis functions, continuity of weight functions, and penalty factors, which provides some practical choices among these key parameters in engineering applications. In addition, we offer guidance on selecting appropriate penalty factors to improve numerical accuracy. Numerical experiments, involving clamped square and circle plates with uniform and nonuniform nodes, as well as a plate model with a corner singularity, are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Our aim is to study a posteriori error estimates for the finite element method of the parabolic boundary control problems on a bounded convex polygonal domain. For discretization, piecewise linear and continuous finite elements are used to approximate the state and the adjoint-state variables, while piecewise constant functions are employed to approximate the control variable. The backward Euler implicit scheme is applied to discretize the time derivative. An adaptation of a novel elliptic reconstruction technique plays a key role in deriving the error estimates. The residual type a posteriori error estimates for the state and adjoint-state variables are derived in the L ∞ (0 , T ; H 1 (Ω)) -norm. Furthermore, an error bound for the control variable is established in the L ∞ (0 , T ; L 2 (Γ)) -norm. The numerical experiments illustrate the performance of the derived estimators. The adaptive mesh generated via the error indicators is very less in comparison to the uniform mesh, which shows the effectiveness of our derived estimators. [ABSTRACT FROM AUTHOR]

In this paper, we present a new error analysis of a class of charge-conservative finite element methods for stationary inductionless magnetohydrodynamics (MHD) equations. The methods use the standard inf-sup stable Mini/Taylor–Hood pairs to discretize the velocity and pressure, and the Raviart–Thomas face element for solving the current density. Due to the strong coupling of the system and the pollution of the lower-order Raviart–Thomas face approximation in analysis, the existing analysis is not optimal. In terms of a mixed Poisson projection and the corresponding estimate in negative norms, we establish new and optimal error estimates. In particular, we prove that the method with the lowest-order Raviart–Thomas face element and Mini element provides the optimal accuracy for the velocity in L 2 -norm, and the method with the lowest-order Raviart–Thomas face element and P 2 − P 1 Taylor-Hood element supplies the optimal accuracy for the velocity in H 1 -norm and the pressure in L 2 -norm. Furthermore, we propose a simple recovery technique to obtain a new numerical current density of one order higher accuracy by re-solving a mixed Poisson equation. Numerical results are provided to verify the theoretical analysis. • New and optimal error analysis of charge-conservative finite element methods are established. • A simple recovery technique is proposed to obtain a new current density with higher accuracy. • Numerical examples are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

The dual five-axis machining machine is state-of-the-art equipment designed for producing thin-walled aerospace parts like skins and panels. It comprises two five-axis machine tools with mirrored synchronous motions: one bi-rotary machine for milling and the other machine for follow-up support. The high absolute accuracy of the five-axis machine tools themselves and the high synchronous motion accuracy between the two machines are both crucial to ensure machining accuracy. This paper proposes an efficient method to measure and identify geometric and dynamic errors of dual five-axis machine tools. Using the R-test combined with three measurement trajectories to measure the absolute motion error of two five-axis machine tools and the synchronous motion error between the two machines. The designed trajectories include the main rotary axis linkage conditions and can fully reflect the primary motion forms of the dual five-axis machine tool. The main position-independent geometric errors and rotational axis linkage dynamic errors are identified by converting quasi-static and dynamic measurement data from three different trajectories into a unified reference coordinate system. The entire process requires only one instrument installation, effectively avoiding time-consuming repetitive installations and calibration processes while reducing the impact of installation errors on results. The effectiveness of the proposed method for measuring and identifying the geometric and dynamic errors is analyzed combined with Monte Carlo simulation. Experiments were carried out on a dual five-axis mirror milling system (MMS) with a 5000 mm X-stroke. Both simulations and experiments confirmed that the proposed method is efficient in quickly identifying key error sources of the MMS. [Display omitted] • An efficient method to measure and identify geometric and dynamic errors during synchronous motion of the MMS is proposed. • A geometric and dynamic error model is introduced for identifying key errors using error sensitivity theory. • A 3-step measurement strategy that enables rapid separation of linkage errors of the MMS is introduced. • Both simulation and experiment show the proposed method could obtain key error sources of the MMS with high efficiency. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to investigate the error analysis for the damped Boussinesq equation with the Ciarlet-Raviart mixed finite element method, focusing on achieving superconvergence. By employing a skillful mean technique and a high precision estimate of the bilinear element, as well as combining with projection and interpolation technique, we first obtain a superclose error estimate between interpolation of the exact solution and numerical solution. Subsequently, by applying an interpolation post-processing approach, we efficiently derive a global superconvergence result. Finally, several numerical results are presented to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we derive error estimates for two second-order numerical schemes for solving the viscous Cahn-Hilliard equation with hyperbolic relaxation, one based on the second-order Crank-Nicolson time marching method and the other on the backward differentiation formula. In both schemes, the nonlinear potential is discretized by the Invariant Energy Quadratization (IEQ) method, which employs an auxiliary variable to produce a linear and unconditional energy-stable structure. After assuming some reasonable boundedness and continuity conditions for the nonlinear function, the optimal error estimate is rigorously derived using mathematical induction. Finally, several numerical experiments are carried out to verify the theoretical predictions of the convergence rate and energy stability of the algorithms. [ABSTRACT FROM AUTHOR]

In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results. • A new locally mass conservative finite element method with interior over-penalized enriched Galerkin methods (IOP-EG). • A priori error analysis of IOP-EG independent of over-penalization. • A robust preconditioner construction and analysis by operator preconditioning approach. [ABSTRACT FROM AUTHOR]

We present a new analysis of finite element methods for partial differential equations over curved domains. In many applications, a change of variables translates a physical Poisson problem over a curved physical domain into a parametric Poisson problem over a polytopal parametric domain. Whilst this change of variables greatly simplifies the geometry and numerical implementations, the coordinate transformation typically features only low regularity. In the parametric Poisson problem, this manifests as rough coefficients and data, which diminish the elliptic regularity, and as roughness of the parametric solution. Our main result addresses how to nevertheless recover high-order finite element convergence rates, the key component being a recently developed broken Bramble-Hilbert lemma. This analysis has numerous applications, where the geometric transformation is either computable or merely a theoretical tool. We propose a simplified technique as easier, more broadly applicable, yet just as powerful as previous isoparametric methods. In particular, we reassess the error analysis of isoparametric finite element methods and prove high-order error estimates for isoparametric FEM even when the physical solution is not continuous. Numerical examples confirm our theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, we present an immersed finite element (IFE) method for solving the elastodynamics interface problems on interface-unfitted meshes. For spatial discretization, we use vector-valued P 1 and Q 1 IFE spaces. We establish some important properties of these IFE spaces, such as inverse inequalities, which will be crucial in the error analysis. For temporal discretization, both the semi-discrete and the fully discrete schemes are derived. The proposed schemes are proved to be unconditionally stable and enjoy optimal rates of convergence in the energy, L 2 and semi- H 1 norms. Numerical examples are designed to verify our theoretical analysis and to demonstrate the stability and robustness of our schemes. [ABSTRACT FROM AUTHOR]

Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide device with isotropic material. According to the existing conformal coordinate transformation, we deduce the perfect parameters required by the conformal device. And the finite element method and error analysis of the model equation and the basic process of adaptive algorithm are given. We first simulated a carpet cloak and bending waveguide device with perfect parameters; then we used the idea of parameter segmentation to design a carpet cloak that requires 35 isotropic materials and use the idea of layering to design the conformal bending waveguide device, and relevant numerical results are presented; finally, we designed the adaptive finite element algorithm to realize the numerical simulation of Maxwell's equations in isotropic material. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel discontinuous Galerkin (DG) finite element method for solving the Poisson's equation u x x + u y y = f (x , y) on Cartesian grids. The proposed method consists of first applying the standard DG method in the x -spatial variable leading to a system of ordinary differential equations (ODEs) in the y -variable. Then, using the method of line, the DG method is directly applied to discretize the resulting system of ODEs. In fact, we propose a fully DG scheme that uses p -th and q -th degree DG methods in the x and y variables, respectively. We show that, under proper choices of numerical fluxes, the method achieves optimal convergence rate in the L 2 -norm of O (h p + 1) + O (k q + 1) for the DG solution, where h and k denote, respectively, the mesh step sizes for the x and y variables. Our theoretical results are validated through several numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, based on the Wachspress generalized barycentric coordinates, we propose and analyze a polygonal finite volume element method (PFVEM) for solving the anisotropic diffusion equation on convex polygonal meshes. In particular, the PFVEM reduces to the classical P 1 -FVEM on triangular meshes and it is not identical to the classical Q 1 -FVEM on quadrilateral meshes. A new proof is given to Proposition 8 in [19] , a result that is crucial to the derivation of the interpolation error estimates in both H 1 and H 2 norms. The original proof is based on a certain geometric assumption, which is shown not always true by a counterexample given in this paper. Moreover, for the error analysis of the PFVEM, we prove the H 2 error estimate of the Wachspress interpolation. Under the coercivity assumption, the optimal H 1 error estimate for the finite volume element solution is obtained. Several numerical examples are presented to show the efficiency and robustness of the proposed method for the heterogeneous and anisotropic diffusion problems on polygonal meshes. [ABSTRACT FROM AUTHOR]

In this paper, the regularity of the solution for a multi-term time-fractional fourth-order equation is analyzed, and the derived result shows that the solution behaves a weak singularity at initial time t = 0. By introducing an intermediate variable p = − Δ u , we obtain a system of two second-order differential equations, which is discretised by using the L1 scheme on graded meshes in time and the mixed finite element method (MFEM) in space. It is shown that the optimal pointwise-in-time error estimate is derived for the proposed scheme. Moreover, the fast L1-MFEM is constructed to improve the computational efficiency. Finally, numerical experiments are provided to further verify our theoretical convergent result and the computational efficiency of the proposed two schemes. [ABSTRACT FROM AUTHOR]

We consider error estimates and post-processing technique of the lowest order Raviart–Thomas mixed finite element method for parabolic problems. A super-convergence of the original unknown and flux is established, which is based on negative norm error estimates. At given time step, we introduce an auxiliary elliptic problem and propose a recovery strategy to obtain one-order higher finite element solutions. Corresponding results are well-known for Lagrange finite element methods for parabolic equations. By using discrete functional analysis tools developed for Discontinuous Galerkin finite element methods, we extend the analyses to the lowest order Raviart–Thomas mixed method and prove second order accuracy of the recovered numerical solutions rigorously. The proposed post-processing technique is suitable on general meshes for both two and three dimensional problems. Numerical results are provided to verify our theoretical analysis and demonstrate the efficiency of the proposed recovery methods. [ABSTRACT FROM AUTHOR]

Commentary on an article by David M. G. Lewis, Laith Al-Shawaf, Ayten Yesim Semchenko, and Kortnee C. Evans (2022). Lewis et al. tested two cognitive algorithms for how individuals perceive attractiveness of potential mates under uncertainty. The authors hypothesized that male participants would overperceive attractiveness (MOAB) and that female participants would underperceive attractiveness (FUAB), based in an Error Management Theory analysis of choice outcomes. The authors concluded that a sex- and attractiveness-differentiated bias existed, such that men overperceived attractiveness when shown stimuli of unattractive women and that women underperceived attractiveness when shown stimuli of attractive men. A reanalysis of this data using continuous ratings of attractiveness rather than dichotomized ratings of attractiveness revealed a crossover interaction that is inconsistent with the hypothesized algorithms and no statistically significant effects of sex. Instead, these results are more consistent with an evolutionary optimality hypothesis based on Signal Detection Theory (Brandner et al., 2021). Additional methodological concerns are discussed. [ABSTRACT FROM AUTHOR]

This paper points at four common misconceptions in quantitative studies of the built environment and travel, all of which rooted in a lack of theoretical reflection on the causal mechanisms by which built environment characteristics could plausibly influence travel behavior. Based on a review of 62 published articles over the period 2017–2022, the following misconceptions are discussed: Omission of metropolitan and city-level built environment characteristics; ignoring internal causal relationships between different built environment characteristics; inclusion of control variables that are themselves heavily influenced by built environment characteristics; and misconception of the phenomenon of residential self-selection. The paper ends by pointing at remedies for avoiding these misconceptions. [ABSTRACT FROM AUTHOR]

This work presents a general framework regarding the recovery of matrices equipped with hybrid low-rank and local-smooth properties from just a few measurements consisting of linear combinations of the matrix entries. Concretely, we consider the problem of robust low-rank matrix recovery using Weighted Nuclear Norm plus Weight Total Variation (WNNWTV) minimization. First of all, based on a new restricted isometry property, we prove that the WNNWTV method possesses an error bound consisting of a low-rank approximation term, a total variation approximation term, and an observation error term. It should be noted that although there are many models considering both properties, there are very few recoverable error theories about such models. Specifically, the theoretical error bound provides an automatic mechanism to reducing regularization parameters with no need for cross-validation while keeping almost the same selection result with commonly used cross-validation technique. Subsequently, the proposed method is reformulated into a regularized unconstrained problem, and we study its optimization aspects in detail based on the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on synthetic data and two applications, i.e. hyperspectral image recovery and dynamic magnetic resonance imaging recovery verified our theories and proposed algorithms. • A general theoretical recovery guarantee for the WNNWTV method is studied. • An effective regularization parameter selection mechanism is theoretically given. • An optimization framework for the unconstrained problem of WNNWTV is given. • Applications to HSI and dMRI recovery verified the superior performance of WNNWTV. [ABSTRACT FROM AUTHOR]

Fringe Projection Profilometry (Fringe Projection Profilometry ， FPP), renowned for its speed, precision, and automation advantages, has found extensive applications in industries such as mechanical processing and quality inspection. A critical challenge within fringe projection techniques involves ensuring robust unwrapping while minimizing the necessary fringe images. While various unwrapping methods exist to reduce the number of projected images, there is a deficiency in efficient unwrapping methods developed under the guidance of error analysis theory. In this study, we derive a robustness function from FPP's error theory to assess the unwrapping robustness of different encoded images. Using this robustness function, we select highly robust single-color encoded fringe images and achieve unwrapping robustness with minimal training cost based on a single fringe pattern. Furthermore, this unwrapping process does not necessitate the establishment of complex training databases, as the K-nearest neighbor (K-Nearest Neighbor ， KNN) algorithm learns the correspondence between image tricolor grayscale values and fringe orders from multi-frequency unwrapping method. Finally, experimental validation through a checkerboard measurement confirms that the proposed method can achieve robust unwrapping with low training costs using only one encoded fringe, thereby affirming the effectiveness of the introduced robustness function and the feasibility of the designed color encoded single fringe pattern unwrapping method. • Firstly, the concept of robustness function for encoded unwrapping method in FPP is proposed. • Secondly, the robustness function is summarized as a general formula, and an application case for it is provided. • Thirdly, the colorful 3-ary gray code encoding unwrapping method is proposed. [ABSTRACT FROM AUTHOR]

Glass substrate (GS) heating is a fundamental but significant technology for organic light emitting diode (OLED), which is critical to OLED displaying quality and efficiency. A rapid and reliable theoretical model is intensely demanded to guide practical system design, simulation analysis and experimental research for GS heating, but present radiative models are improper or inconvenient. Therefore, this paper establishes a new and direct calculation model with the addition of correctional coefficient 0.5 to blackbody radiation power of electric heating tube (EHT) and the proposal of comprehensive angle coefficient X , which can solve single and multi-source radiation problems theoretically. The simulation and experiment are both conducted for comparison analysis. The temperature errors of theory and simulation for multi EHTs are all within 1 % when compared with experimental results, which well validates the reliability and accuracy of theoretical and simulation models. Large EHT radius r , small distance L between EHT and GS, and suitable EHT number n are suggested, which benefits to the improvement of radiation heating and temperature uniformity of GS. It is hoped that this study can provide a useful tool on thermal radiation analysis and also a valuable promotion for practical OLED heating technology. [ABSTRACT FROM AUTHOR]

Spectral leakage is a frequency domain error caused by truncation of time domain data. In structural vibration tests, truncating the response data while retaining high signal-to-noise data can significantly diminish the impact of ambient noise. However, this approach introduces spectral leakage error, which significantly impact the identification methods for frequency domain damping ratios. The reason is that spectral leakage error alters the spectral value, and accurate spectral data is crucial for the damping ratio identification in these frequency domain methods. In this paper, a spectral leakage error compensation theory is proposed to identify damping ratio without such error. Firstly, the expression of spectral leakage error is derived from frequency response function and free decay data. Then, the frequency domain decomposition method is integrated with the spectral leakage error expression to formulate compensating equations. The damping ratios without spectral leakage error are obtained by iterating through these equations. Finally, a numerical example and benchmark model are employed to validate the effectiveness of the spectral leakage error compensation theory. The results show that the theory can effectively compensate the spectral leakage error and accurately identify damping ratios. • Analyzed and confirmed the cause of spectral leakage is the truncation of time-domain data. • The expression of spectral leakage error is derived from frequency response function. • Proposed a spectral leakage error compensation theory on damping ratio identification. • A modal separation algorithm is proposed to avoid different order mode affecting each other. [ABSTRACT FROM AUTHOR]

• Propose a sensor location model to identity sensor locations and determine all link flows. • Identify two types of uncertainty in NSLP that can produce important alterations of all link flows. • Use the knowledge of linear algebra to illustrate error propagation theory. • Prove theoretically the superiority of locating traffic sensors on all incoming links in uncertainty control. • Serve for traffic sensor installation under uncertainty. The full link flow observability problem is to identify the minimum set of links to be installed with sensors in a traffic network that allows the unique determination of all link flow volumes. In our previous work (Shao et al., 2016), we proposed a flow conservation system using turning ratios as prior information, and suggested that installing sensors on all exclusive incoming road links in the traffic network (called "incoming layout") can uniquely determine the flow information of all network links. However, the link flow observed by the sensor is inevitably subject to measurement errors, and there is also a risk that some deviation in prior information (i.e., turning ratios) will be propagated while extending flows over the whole network. Considering these two types of uncertainty, the "incoming layout" is not only a feasible solution, but in this study, has been proved to minimize the cumulative uncertainty in the process of inferring all link flows caused by the sensor measurement error and the deviation of prior information. Specifically, the superiority of the "incoming layout" is proved theoretically, including two cases. (i) Considering only the sensor measurement error, the error propagation theory is analytically expressed using the knowledge of linear algebra. The related error propagation matrix is found to be the key to help demonstrate that the cumulative uncertainty of the "incoming layout" is always smaller than that of the "general layout". (ii) Considering the sensor measurement error and the deviation of prior information, vectorization operator is introduced to quantify the effect of the prior information deviation on the accuracy of link flow inference, which is beneficial to prove the superiority of the "incoming layout" in minimizing the cumulative uncertainty of all link flows. [ABSTRACT FROM AUTHOR]

Superconvergence error analysis is investigated of a mixed finite element method (MFEM) for the time-dependent natural convection problem. The backward Euler scheme is adopted for the discrete in time, while the Bernadi-Rangel element is used to approximate the velocity u and the pressure p , and the bilinear element to the temperature T in space, respectively. Combined with the characters of the chosen elements and skillful techniques, the superclose results of order O (h 2 + τ) for u , T in the H 1 -norm and p in L 2 -norm are deduced rigorously, where h is the subdivision scale and τ , the time step. Further, the global superconvergence results are obtained through the interpolation postprocessing technique. We mention that in the high accuracy results obtained in this paper, the restriction between the h and τ is removed by the space-time splitting skill. Finally, numerical tests are also established to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

A discontinuous Galerkin finite element approximation for the Kelvin-Voight viscoelastic fluid flow equations, is proposed and analyzed here when the force function is time independent or in L ∞ (L 2) -space. Based on the new a priori and regularity results for the semi-discrete solutions, well-posedness and consistency of the discontinuous Galerkin scheme are discussed. A priori error estimates of the semidiscrete velocity and pressure approximations in L ∞ (L 2) and L ∞ (L 2) -norms, respectively, using the discontinuous Galerkin method are then derived. Our proof relies on the standard elliptic duality argument and a modified Sobolev-Stokes operator defined on appropriate broken Sobolev spaces. For sufficiently small data, uniform in time error estimates are proved. Furthermore, backward Euler scheme is considered for a full discretization and optimal fully discrete error estimates are derived. Finally we work out numerical experiments to substantiate our theoretical findings. It is worth mentioning that the analysis here is the first of its kind for the Kelvin-Voight model. [ABSTRACT FROM AUTHOR]

Effective control of pipeline systems requires adequate mathematical models. To match an object with the model it is necessary to analyze data on physical system structure and parameters and on operating processes (or the fluid flow regimes). Operating parameter measurements serve as data source for operational control. Incorrect SCADA readings bring about erroneous simulation results and unfounded dispatch decisions. Sometimes it is rather easy to identify information system failures and tell the cause. But sometimes as in the case of stage-by-stage failure such as sensor drift failure identification becomes really difficult. To detect and eliminate a progressive defect it is advisable to use maximum of available data, that is all measurements of the operating parameters (pressure, flow rate and, possibly, temperature) transmitted during the last few SCADA sessions. This approach takes into account the interdependence of operating parameters within the same session as well as specific parameter measurements during a number of sessions. The suggested model of identifying the failed device and the failure moment is built on a stochastic basis. The measurement results are considered random variables, which distribution obeys error theory standard assumptions. • Information processing on a set of the operating parameters measurements of the pipeline system. • Models for failures recognizing of pressure gauges and flow meters. • Determination of the failure moment and place at the metrological complex. • Potential applicability of the methodology to unaccounted for gas. [ABSTRACT FROM AUTHOR]

This paper concerns a stochastic partial differential equation driven by Poisson jump for Cerenkov radiation. Firstly, we utilize the backward Euler method and the finite element method to obtain the numerical solution and the error analysis of numerical solution. Secondly, we discuss the inverse source problem, which is ill-posed. Tikhonov regularization method is used to get the regularization solution, and the proof of error analysis is given for the exact solution and regularization solution of the source term. Finally, the error comparison between the two is realized by MATLAB. The experiment shows that when the number of terms is more and the regularization parameter is smaller, the error of the exact solution and regularization solution of the source term is smaller. [ABSTRACT FROM AUTHOR]

In this work, we present first- and second-order energy-stable linear schemes for the Swift-Hohenberg equation based on first-order backward Euler and Crank-Nicolson schemes, respectively. We prove rigorously that the schemes satisfy the energy dissipation property. We also derive the error analysis for our schemes. Moreover, we adopt a spectral-Galerkin approximation for the spatial variables and establish error estimates for the fully discrete second-order Crank-Nicolson scheme. Numerical results are presented to validate our theoretical analysis. [ABSTRACT FROM AUTHOR]

Electrical connectors are crucial electro-mechanical components, with insertion, withdrawal, and electrical contact characteristics serving as key indicators of their reliability. Studying the electro-mechanical characteristics and regression models of electrical connectors is vital to enhance their reliability. This work focuses on the M2-type electrical connector, investigating its electro-mechanical characteristics and developing a regression model. A withdrawal force calculation model is established using cantilever beam theory. Simulation and analysis provide data on insertion force, contact pressure, and contact resistance. Experiments on insertion, withdrawal, and electrical contact are conducted using an insertion force tester and a DC low-resistance instrument, comparing experimental results with simulations. The study reveals the fitting relationship between contact pressure and contact resistance for the M2-type connector. Key findings include a stable fluctuation in contact pressure with a relative error of 1.72% between simulated and tested values, an average discrepancy of 3.81% for insertion force, and 2.38% for withdrawal force, with insertion force slightly higher than withdrawal force. Contact resistance shows a U-shaped trend with pin displacement, with an average experimental error 3.70% and 1.16% lower than theoretical values (4.86%). The new regression model (quadratic polynomial fitting) demonstrates mean absolute percentage errors of 0.1458% for simulation values and 0.2219% for experimental values, significantly lower than those obtained using theoretical formulas (0.7046% and 0.3451%). These results provide theoretical guidance for studying electro-mechanical characteristics and designing experiments for electrical connectors, offering valuable insights for designing and ensuring the reliability of new types of electrical connectors. • A novel slanted groove electrical connector is designed. • A research framework for electro-mechanical characteristics is proposed. • The criterion excluding experimental abnormal data is built. • The relative error of theory, simulation, and experimental results is very small. • A novel regression model for contact pressure and contact resistance is put forward. [ABSTRACT FROM AUTHOR]

The aim of this article is to present a penalty finite element method (PFEM) in fully discrete form for the unsteady incompressible magnetohydrodynamic (MHD) equations. The proposed method is applied to address the incompressible constraint "div v =0". The backward Euler scheme is used for temporal discretization, and the (P 1 b , P 1 , P 1) finite element pair is used for spatial discretization, which satisfies the discrete LBB condition. Moreover, rigorous analysis of the optimal error estimate for the fully discrete PFEM is provided, which depends on penalty parameter ϵ , the mesh size h and the time step size Δ t. Finally, some benchmark numerical experiments which include the hydromagnetic Kelvin-Helmholtz instability, flow around a cylinder and lid driven cavity flow, are carried out to illustrate the theoretical results and the effectiveness of the our proposed method. • We propose a first order penalty decoupled method. • The saddle point problem is transformed into two small problems to solve. • The optimal error estimate for the fully discrete penalty finite element method is derived. • The results of theoretical analysis are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

For the nonlinear Klein-Gordon (NKG) equation with weak nonlinearity characterized by a small parameter ε ∈ (0 , 1 ] , the numerical methods for long-time dynamics have received more and more attention. For the NKG equation up to the time at O (1 / ε 2) , the error bounds of classical numerical methods depend significantly on the small parameters ε which creates serious numerical burdens as ε → 0 +. Recently, an exponential wave integrator Fourier pseudo-spectral (EWIFP) method for the NKG equation has been proposed (Feng et al., 2021) which is uniformly accurate about ε and of course performs well over the classical methods. However, the EWIFP method can not preserve the discrete energy, which is an important structural feature of the true solution in the long-time dynamics from the perspective of geometric numerical integration. In addition, the EWIFP method only is conditionally stable under specific stability condition and the authors did not give a convergence analysis for the method without any CFL condition restrictions on the grid ratio. In this work, we propose an energy-preserving EWIFP (EPEWIFP) method. The proposed method is proved to be time symmetric, unconditionally stable and preserves the discrete energy. We carry out a rigorously error analysis and give uniform error bounds of the method at O (h m 0 + ε 2 − β τ 2) up to the time at O (1 / ε β) with β ∈ [ 0 , 2 ] , mesh size h , time step τ and an integer m 0 determined by the regularity conditions. In general, the NKG equation with weak nonlinearity can be converted to an oscillatory NKG equation with wavelength at O (ε 2) in time. It is easy to extend the error bounds and energy-preservation properties to the oscillatory NKG equation. Numerical results confirm our error bounds and energy-preservation properties. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial-boundary value problem for the three-dimensional incompressible magnetohydrodynamic coupled heat equation through the Boussinesq approximation. A finite element fully discrete scheme is proposed for approximating and solving this coupled system numerically, where the second-order extrapolation scheme is used for the discretization of time derivative terms and the mixed finite element method is used for the spatial discretization. Furthermore, we use the mini finite element to approximate the velocity and pressure, and use piecewise linear finite elements to approximate the magnetic field and temperature. We prove the unconditional stability of fully discrete scheme and derive the optimal second-order convergent accuracy in both time and spatial directions. Finally, numerical results are presented to illustrate the second-order convergence rates by taking the CFL condition of order 1. [ABSTRACT FROM AUTHOR]

We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods, i.e. discontinuous Galerkin methods on general polygonal and polyhedral (polytopic, for short) grids, featuring elements with edges/faces that may be in arbitrary number (potentially unlimited) and whose measure may be arbitrarily small. Our approach is then very well suited to tame the geometrical complexity featured by most of applications in the computational geoscience field. From the modelling point of view, we adopt a reduction strategy that treats fractures as manifolds of codimension one and we employ the primal version of Darcy's law to describe the flow in both the bulk and in the fracture network. In addition, some physically consistent conditions couple the two problems, allowing for jump of pressure at their interface, and they as well prescribe the behaviour of the fluid along the intersections, imposing pressure continuity and flux conservation. Both the bulk and fracture discretizations are obtained employing the Symmetric Interior Penalty DG method extended to the polytopic setting. The key instrument to obtain a polyDG approximation of the problem in the fracture network is the generalization of the concepts of jump and average at the intersection, so that the contribution from all the fractures is taken into account. We prove the well-posedness of the discrete formulation and perform an error analysis obtaining a priori hp -error estimates. All our theoretical results are validated performing preliminary numerical tests with known analytical solution. [ABSTRACT FROM AUTHOR]

In their commentary on our paper, Brandner et al. commit an elementary statistical mistake that leads to entirely erroneous conclusions. When this statistical error is corrected, the effects described in our original paper appear exactly as reported. In principle, we could end our reply there. However, ending our reply there would be a lost opportunity for promoting best practices in Error Management Theory (EMT) research. The commentators make several other missteps that present the opportunity to draw attention to important principles in EMT research and offer clarifications that we hope assist in the operationalization, design, and interpretation of EMT-inspired studies in the future. We discuss these points and provide several EMT research scenarios to help to illustrate a key principle. We hope this reply highlights some of the key elements of best practices in EMT research and sheds light on pitfalls that researchers must make sure to avoid. [ABSTRACT FROM AUTHOR]

In this work, a time-fractional biharmonic equation with a Caputo derivative of fractional order α ∈ (0 , 1) is considered, whose solutions exhibit a weak singularity at initial time t = 0. For this problem, a system of two second-order differential equations is derived by introducing a intermediate variable p = − Δ u , then discretised the system using the standard finite element method in space together with the L1 discretisation of Caputo derivative on graded mesh in time. The H 1 -norm stability result of the method is established, and then a sharp H 1 -norm local convergent result is presented. Finally, numerical experiments are provided to further verify our theoretical analysis for each fixed value of α. [ABSTRACT FROM AUTHOR]

In incompressible flow problems, the finite element discretization of pressure and velocity can be done through either stable spaces or stabilized pairs. For equal-order stabilized methods with piecewise linear discretization, the classical theory guarantees only linear convergence for the pressure approximation. However, a higher order is often observed, yet seldom discussed, in numerical practice. Such experimental observations may, in the absence of a sound a priori error analysis, mislead the selection of finite element spaces in practical applications. Therefore, we present here a numerical analysis demonstrating that an initial higher-order pressure convergence may in fact occur under certain conditions, for equal-order elements of any degree. Moreover, our numerical experiments clearly indicate that whether and for how long this behavior holds is a problem-dependent matter. These findings confirm that an optimal pressure convergence can in general not be expected when using unbalanced velocity-pressure pairs. [ABSTRACT FROM AUTHOR]

People must make inferences about a potential mate's desirability based on incomplete information. Under such uncertainty, there are two possible errors: people could overperceive a mate's desirability, which might lead to regrettable mating behavior, or they could underperceive the mate's desirability, which might lead to missing a valuable opportunity. How do people balance the risks of these errors, and do men and women respond differently? Based on an analysis of the relative costs of these two types of error, we generated two new hypotheses about biases in initial person perception: the Male Overperception of Attractiveness Bias (MOAB) and the Female Underperception of Attractive Bias (FUAB). Participants (N = 398), who were recruited via social media, an email distribution list, and snowball sampling, rated the attractiveness of unfamiliar opposite-sex targets twice: once from a blurred image, and once from a clear image. By randomizing order of presentation (blurred first vs. clear first), we isolated the unique effects of uncertainty —which was only present when the participant saw the blurred image first. As predicted, men over perceived women's attractiveness, on average. By contrast, as predicted, women under perceived men's attractiveness, on average. Because multiple possible decision rules could produce these effects, the effects do not reveal the algorithm responsible for them. We explicitly addressed this level of analysis by identifying multiple candidate algorithms and testing the divergent predictions they yield. This suggested the existence of more nuanced biases: men overperceived the attractiveness of unattractive (but not attractive) women, whereas women underperceived the attractiveness of attractive (but not unattractive) men. These findings highlight the importance of incorporating algorithm in analyses of cognitive biases. [ABSTRACT FROM AUTHOR]

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are L L ⁎ methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h -refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. We show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we construct, analyze, and numerically validate a class of H (div) -mixed virtual element method for the semilinear parabolic problem in mixed form, in which the parabolic problem is reformulated in terms of the velocity and the pressure of the time-dependent Darcy flow. The Newton linearized method for the nonlinear term is designed to cooperate with the second-order backward differentiation formula of the temporal discretization scheme. This allows each time step to only require the solution of a small and well-structured linear system rather than the solution of a nonlinear system. The linearization improves computational efficiency without decreasing convergence rates. Moreover, the "Fortin" operator and its approximation properties are applied to derive an optimal error estimates O (h k + 1 + τ 2) for the virtual element solution of the velocity and the pressure. Finally, its remarkable performance is illustrated by several numerical examples that also validate the theoretical rates of convergence. [ABSTRACT FROM AUTHOR]

This paper presents a second-order finite element scheme for the approximations of the three-dimensional (3D) incompressible magnetohydrodynamics system with variable density (VD-MHD), where two-step backward differentiation formula (BDF2) is used to discrete the time derivative and the (P 2 , P 1 b , P 1 , P 1) finite elements are used to approximate the density, velocity, pressure and magnetic. Based on an equivalent VD-MHD system, the proposed finite element algorithm is unconditionally stable in the sense that the discrete energy inequalities hold without small condition of the time step size. After a rigorous analysis, the optimal L 2 error estimates (τ 2 + h 2) of the density, velocity field and magnetic field are established, where τ and h are the time step size and mesh size. Finally, numerical results are given to support these convergence rates. [ABSTRACT FROM AUTHOR]

Our study focuses on the interplay of two secondary school mathematics teachers' emotions and decision-making in pivotal teaching moments. We highlight the interaction between teacher emotions and in-the-moment decision-making, and resources that coordinate this interplay, suggesting a theoretical and methodological way of addressing it. Our analyzed data comes from three teachers' lessons and four semi-structured interviews. When analyzing pivotal moments where the teacher handles students' errors, it appeared that teacher emotions and resources are interrelated elements of the decision-making. Findings show that: (1) teachers' emotions, while handling students' errors, are mostly negative, but differ in their kind and source; (2) the formation of teacher emotions and actions often seems to draw on the same resources (social-spatial, anticipatory-temporal, moral-ideological dimensions, and teacher's responsibility about mathematics; (3)teachers' actions, while handling students' errors, differ in relation to the resources and the emotions that coordinate their formation. • Teachers' emotions interplay with their decision-making process during teaching. • This interplay can be captured by studying emotions' action tendency and appraisal components in relation to teachers' decision-making resources. • Emotions' appraisal component is directly related to the dimensions of the in-the-moment decision-making's resources. • Teachers' in-the-moment decisions are shaped both by their emotions and by other resources (or combination of resources). [ABSTRACT FROM AUTHOR]

Although Error Management Theory (EMT) can explain male sexual overperception, more advanced Signal Detection Theory (SDT) analyses can identify sensitivity and bias separately. An SDT analysis of perceptions of relatively clear interest/disinterest signals (Study 1) found that sensitivity to sexual interest/disinterest signals drove participants' perceptions, rather than an overall bias to perceive sexual interest. Cues of interest were generally underperceived, while sensitivity and accuracy were uniformly high. EMT analysis also found overall sexual interest underperception, but with men slightly overperceiving interest relative to women. These discrepant results were due to EMT using difference scores, which obscure baseline perceptions for men and women. Individual differences in life history strategy, mating strategy, and mate value did not affect sensitivity or bias. Study 2 largely replicated these results using more ambivalent scenarios, except EMT analyses found men's misperception to be significantly larger than women's, despite being closer to pre-rated communication levels. These results show that sexual communication may be more nuanced than previously thought, and that an SDT analysis is more appropriate for such data. [ABSTRACT FROM AUTHOR]

In this paper we study both the fast computation and the related error analysis of many different finite and infinite oscillatory Bessel transforms. By transforming the Bessel function into Confluent hypergeometric function and using its asymptotic expansion, we develop an efficient approach by the contours in the complex plane, corresponding to the paths of steepest descent. Furthermore, we conduct their error analyses in inverse powers of the frequency ω. The related error analyses show that the precision can be improved by either adding more Gauss-Laguerre nodes or increasing the frequency ω. In particular, the method exhibits the high error order. Meanwhile, we apply the proposed method to some other kinds of oscillatory integrals through some simple changes of variables. Numerical experiments can verify our theoretical analysis. It is also shown that the new algorithms are more efficient than the existing Filon-type method and can achieve the same level of accuracy with the method (the XMX method) proposed in Xu, Milovanović and Xiang [46] by some numerical experiments under the given conditions. A combination of the n 1 -point Gauss-Laguerre quadrature rule and the n 2 -point generalized Gauss-Laguerre quadrature rule are used in the XMX method. However, we only use the Gauss-Laguerre quadrature rule for one time in the established method, which makes the theoretical and error analysis simpler than the XMX method. [ABSTRACT FROM AUTHOR]

Stability and error estimates for a projection based variational multiscale finite element scheme for Oseen problem in a time-dependent domain are derived in this paper. The use of Geometric Conservation Law (GCL) provides an unconditional stable scheme, whereas a restriction on the time-step needs to be imposed to obtain stability estimates independent of the mesh velocity when GCL is violated. Further, a priori error estimate is derived for the semi-discrete problem obtained with the backward Euler time discretization. [ABSTRACT FROM AUTHOR]

A high-order compact alternating direction implicit scheme is considered to solve the two-dimensional time-fractional integro-differential equation with weak singularity near the initial time in this paper. The L 1 formula and trapezoidal PI rule on nonuniform meshes, which greatly improve the temporal accuracy compared to the method on uniform grids, are adopted to approximate the Caputo derivative and the Riemann-Liouville integral, respectively. With the help of a modified discrete fractional Grönwall inequality and some crucial skills, the stability and convergence of the proposed scheme are analyzed. Numerical results confirm the sharpness of the error analysis. [ABSTRACT FROM AUTHOR]