Coefficient Functions Research Articles

T-wave inversion through inhomogeneous voltage diffusion within the FK3V cardiac model.

The heart beats are due to the synchronized contraction of cardiomyocytes triggered by a periodic sequence of electrical signals called action potentials, which originate in the sinoatrial node and spread through the heart's electrical system. A large body of work is devoted to modeling the propagation of the action potential and to reproducing reliably its shape and duration. Connection of computational modeling of cells to macroscopic phenomenological curves such as the electrocardiogram has been also intense, due to its clinical importance in analyzing cardiovascular diseases. In this work, we simulate the dynamics of action potential propagation using the three-variable Fenton-Karma model that can account for both normal and damaged cells through a the spatially inhomogeneous voltage diffusion coefficient. We monitor the action potential propagation in the cardiac tissue and calculate the pseudo-electrocardiogram that reproduces the R and T waves. The R-wave amplitude varies according to a double exponential law as a function of the (spatially homogeneous, for an isotropic tissue) diffusion coefficient. The addition of spatial inhomogeneity in the diffusion coefficient by means of a defected region representing damaged cardiac cells may result in T-wave inversion in the calculated pseudo-electrocardiogram. The transition from positive to negative polarity of the T-wave is analyzed as a function of the length and the depth of the defected region.

Tuning the physical properties of inorganic novel perovskite materials Ca3PX3 (X=I, Br and Cl): Density function theory

In photovoltaic technology, inorganic perovskite solar cells formed from halide have developed into a noteworthy prospect, primarily attributable to their exceptional efficiency, cost-effectiveness, and straightforward manufacturing techniques. Lead-free A3BX3 inorganic perovskites have generated significant attention within the environmentally friendly solar industry thanks to their extraordinary characteristics encompassing thermoelectricity, optoelectronics, and elasticity. This research focuses on the attributes of the structural, electrical, and optical inorganic halide perovskites Ca3PX3 (X = I, Br, and Cl) using the first-principles density-functional theory (FP-DFT). According to the electronic band structures, Ca3PI3, Ca3PBr3, and Ca3PCl3 show semiconductor characteristics with a straight bandgap of 1.4909 eV, 1.9502 eV, and 2.2058 eV, respectively, at the Γ(gamma)-point. Whenever one takes consideration into account the spin-orbital coupling (SOC) effect, the bandgap of the Ca3PI3, Ca3PBr3, and Ca3PCl3 perovskites is minimized to 1.2382 eV, 1.6456 eV, and 1.9056 eV. All these structures' bandgaps are compressed under compressive strain while they expand with tensile strain. The optical properties indicate that these materials have outstanding visible light consumption capabilities due to their distinct band features, comprising functions of dielectric, consumption coefficient, and function of electron collapse. Observations indicate that the dielectric constant peaks of Ca3PX3 (where X represents I, Br, or Cl) exhibit a redshift, moving towards lower photon energy levels as compressive strain increases. Conversely, they show a blueshift behavior, shifting to a greater amount of photon energy levels by applying tensile strain. Therefore, these characteristics render Ca3PX3 perovskites highly suitable for optimizing light guidance for solar power and energy retention tools.

SA-Based QoS Aware Workflow Scheduling of Collaborative Tasks in Grid Computing

Scheduling workflow tasks in grid computing is a complex process, especially if it is associated with satisfying the user's requirements to complete tasks within a specified time, with lowest possible cost. This paper presents a proposed Simulated Annealing (SA) based Grid Workflow Tasks Scheduling Approach (SA-GWTSA) that takes into account users’ QoS (quality of service) constraints in terms of cost and time. For a given set of inter-dependent workflow tasks, it generates an optimal schedule, which minimizes the execution time and cost, such that the optimized time is within the time constraints (deadline) imposed by the user. In SA-GWTSA, the workflow tasks, which are modeled as a DAG, are divided into task divisions, each of which consists of a set of sequential tasks. Then, the optimal sub-schedules of all task divisions are computed applying SA algorithm, and used to obtain the execution schedule of the entire workflow. In the proposed algorithm, the sub-schedule of each branch division is represented by a vector, in which each element holds the ID of the service provider chosen from a list of service providers capable of executing the corresponding task in the branch. The algorithm uses a fitness function that is formulated as a multi-objective function of time and cost, which gives users the ability to determine their requirements of time against cost, by changing the weighting coefficients in the objective function. The paper also exhibits the experimental results of assessing the performance of SA-GWTSA with workflows samples of different sizes, compared to different scheduling algorithms: Greedy-Time, Greedy-Cost, and Modified Greedy-Cost.

Aerodynamic and Flow Characteristics of a Rough Airfoil: A Numerical Study

A computational study explores the aerodynamic and flow properties of rough-surfaced NACA-0018 airfoils using turbulent K-omega SST methodology and the control volume method. Ansys Fluent 2022 R2 was used to do the simulations, and Reynolds numbers between 5000 and 10000 were used. The analysis of how the rough surface affects the performance of the airfoil was the main goal of the study. The skin friction coefficient, drag force, lift force, pressure contours, and stream functions were among the many variables assessed. To have a thorough understanding of the flow behavior, these parameters were studied at various Reynolds numbers. The findings revealed a clear pattern: along the wall of the airfoil, the average drag force, lift force, and skin friction coefficient all increased linearly as the Reynolds number rose from 5000 to 10000. This discovery sheds important light on how the rough surface affects the overall aerodynamic performance of the airfoil. This study advances knowledge of the aerodynamic behavior of rough airfoils by illuminating the flow characteristics and their relationship to surface roughness. Significant results impact aeronautics, wind turbine design, and other airfoil applications.

Phosphorus adsorbed by HCl desorption–activated red mud adsorbents: a molecular dynamics studys

In this study, modified red mud after phosphorus adsorption was used as the adsorbent, and HCl and deionized water were used as desorbents to desorb phosphorus. The components in the adsorbent were optimized based on density functional theory, and adsorbent and desorbent models were established. Molecular dynamics simulation was performed to determine the phosphorus concentration before and after desorption, interaction energies, radial distribution function(RDF), mean-square displacement(MSD), and diffusion coefficient. The Monte Carlo method was used to simulate the desorption isotherm, desorption site, heat of desorption, and desorption energy. Simulation results showed that deionized water could only desorb phosphorus on the adsorbent surface, and the stability of the system deteriorated upon adding HCl. HCl destroyed the ionic and hydrogen bonding between the O atoms in H2PO4 − and reactive metal and oxygen atoms in the activated red mud particles. Moreover, the van der Waals force decreased considerably. The ionic and hydrogen bonds between H2PO4 − and the surface of activated red mud particles were broken by HCl, which accelerated the desorption of phosphorus from the adsorbent surface. The interaction between HCl and phosphorus accelerated the diffusion, which decreased the adsorption capacity. Moreover, the desorption capacity increased with increasing temperature.

What if the Covid-19 Pandemic Never Happened Estimation of the Tourist Arrivals for 2020 Via Levenberg-Marquardt Optimization and K-Star (K ) Machine Learning Algorithms

Based on the probability theory, which is used to model uncertainty and randomness in real-world situations, the study aims to understand the impact of uncertain conditions, such as the Covid-19 pandemic, on the accuracy of the algorithms and the resulting losses to a country's tourism industry. The contribution of this paper to the international body of knowledge is twofold: firstly, it advances theoretical understanding of the use of probability theory in modelling real-world problems; and secondly, it offers a methodological approach for estimating tourist arrivals that accounts for the impact of extreme events. To achieve these aims, the Levenberg-Marquardt optimization was first applied to determine the optimal coefficients of the exponential function for estimating tourist arrivals from 1950 to 2020. Next, the K-Star machine learning algorithm was applied to the dataset with and without Covid-19 cases to estimate tourist arrivals.

Learning the flux and diffusion function for degenerate convection-diffusion equations using different types of observations

In recent years, there has been an increasing interest in utilizing deep learning-based techniques to predict solutions to various partial differential equations. In this study, we investigate the identification of an unknown flux function and diffusion coefficient in a one-dimensional convection-diffusion equation. The diffusion function is allowed to vanish on intervals implying that solutions generally possess low regularity, i.e., are discontinuous. Therefore, solutions must be interpreted in the sense of entropy solutions which combine a weak formulation with an additional constraint (entropy condition). We explore a methodology that utilizes symbolic neural networks (S-Nets) in combination with an entropy-consistent discrete numerical scheme (ECDNS). Different types of observation data are explored. Extensive experiments in this paper demonstrate that the proposed method is a robust tool to identify the unknown flux and diffusion function. The flux and diffusion functions are restricted to be rational functions.

Estimation of Tire Side-Slip Angles Based on the Frequency Domain Lateral Acceleration Characteristics Inside Tires

The identification and control of tire side slip angle is the key to vehicle stability control. Intelligent tire technology based on the sensing of side-slip acceleration inside the tire provides a novel method for estimating the tire side-slip angle. This study proposed a method to estimate the tire side-slip angle by using the frequency domain lateral acceleration of the tire. First, an intelligent tire testing system was constructed by independently developing a special rim assembly and data collector. A three-axis accelerometer was placed on the right side of the tire, and the acceleration value was acquired by using a wired method with a sampling frequency of 50 kHz. Second, based on the constructed test system, a tire side deflection test was carried out on the Flat Trac bench. Through data analysis, it was found that the lateral acceleration was in the frequency domain of 400 Hz. As the side-slip angle increased from −4° to 4°, the vibration amplitude gradually decreased. Moreover, the vibration amplitude within 0.5~2 kHz was highly correlated with the side-slip angle. Subsequently, the vibration amplitude of the lateral acceleration within 2 kHz was extracted at an interval of 20 Hz as the feature point, and a frequency domain data set FDAy3 was established together with the vertical load and tire pressure. Finally, the support vector machine (SVM) algorithm was employed to make predictions on the data set. The grid search method was utilized to find the optimal parameter values of the model penalty factor c and radial basis kernel function coefficient g, which were 1.4142 and 0.0884, respectively. The results suggested that the root mean square error of the model prediction was 0.0806°, and the maximum estimated angle deviation of the prediction was 0.4587°. Meanwhile, the optimal prediction accuracy and real-time performance were achieved when the number of feature points and the feature frequency band were 25 and within 500 Hz, respectively. The findings of this study confirm that it is feasible to estimate the tire side-slip angle based on the frequency domain lateral acceleration of the tire, which provides a new method for tire side-slip angle estimation.

A MCMC method based on surrogate model and Gaussian process parameterization for infinite Bayesian PDE inversion

This work focuses on an inversion problem derived from parametric partial differential equations (PDEs) with an infinite-dimensional parameter, represented as a coefficient function. The objective is to estimate this coefficient function accurately despite having only noisy measurements of the PDE solution at sparse input points. Conventional methods for inversion require numerous calls to a refined PDE solver, resulting in significant computational complexity, especially for challenging PDE problems, making the inference of the coefficient function practically infeasible. To address this issue, we propose a MCMC method that combines an deep learning-based surrogate and Gaussian process parameterization to efficiently infer the posterior of the coefficient function. The surrogate model is a combination of a cost-effective coarse PDE solver and a neural network-based transformation which provides an approximate solution derived from the refined PDE solver but based on the coarse PDE solution. The coefficient function is represented by Gaussian process with finite number of spatially dependent parameters and this parametric representation will be beneficial for the preconditioned Crank-Nicolson (pCN) Markov chain Monte Carlo method to sample efficiently from the posterior distribution. Approximate Bayesian computation method is used for constructing an informative dataset for the transformation learning. Our numerical examples demonstrate the effectiveness of this approach in accurately estimating the coefficient function while significantly reducing the computational burden associated with traditional inversion techniques.

MIXED PROBLEM FOR A NONLINEAR IMPULSIVE DIFFERENTIAL EQUATION OF PARABOLIC TYPE

In this paper, we consider a nonlinear impulsive parabolic type partial differential equation with nonlinear impulsive conditions. Dirichlet type boundary value conditions with respect to spatial variable is used, and eigenvalues and eigenfunctions of the spectral problem are founded. The Fourier method of the separation of variables is applied. A countable system of nonlinear functional equations is obtained with respect to the Fourier coefficients of the unknown function. A theorem on a unique solvability of the countable system of nonlinear functional equations is proved by the method of successive approximations. A criteria of uniqueness and existence of a solution for the nonlinear impulsive mixed problem is obtained. A solution of the mixed problem is derived in the form of the Fourier series. The absolute and uniform convergence of the Fourier series is proved.

A Symmetric Kernel Smoothing Estimation of the Time-Varying Coefficient for Medical Costs

In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT).

The modularity of Siegel’s zeta functions

Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and functional equations. Coefficients of these zeta functions are called measures of representations, and play an important role in the arithmetic theory of quadratic forms. In a 1938 paper, Siegel made a comment to the effect that the modularity of his zeta functions would be proved with the help of a suitable converse theorem. In the present paper, we accomplish Siegel’s original plan by using a Weil-type converse theorem for Maass forms, which has appeared recently. It is also shown that “half” of Siegel’s zeta functions correspond to holomorphic modular forms.

A multi-target predictive model for predicting tool wear and surface roughness

To simultaneously predict tool wear and surface roughness accurately during machining, this paper develops a multi-target predictive model that leverages a novel two-step feature-integration approach and Multi-kernel Gaussian process autoregressive regression (MK-GPAR). Compared with the traditional Gaussian process autoregressive regression (GPAR) models, the MK-GPAR demonstrates an enhanced capability in capturing detailed structures within heterogeneous data originating from various sources or disparate data forms. The weight coefficients of the kernel functions in MK-GPAR are typically assigned a value of 1 to minimize their influence on the predictive model. Furthermore, when compared to conventional multi-target predictive models like Gradient Boosting, Support Vector Regression (SVR), and K-Nearest Neighbors (KNN), the GPAR not only delivers higher-accuracy predictions for tool wear and surface roughness but also provides corresponding confidence intervals (CI). However, the CI of predictions for tool wear and surface roughness provided by MK-GPAR are inconsistent, which will seriously affect the reliability of the evaluation of the prediction results. The proposed two-step feature-integration approach is employed to enhance signal features effectively, reduce noise, and mitigate its adverse impact, thus enhancing the consistency and smoothness of the CI. The two-step feature-integration approach integrates principal component analysis (PCA) and orthogonal neighborhood preserving projections (ONPP) to merge force and vibration signal features obtained from the fixture's monitoring signals. Following the two-step feature-integration (first PCA, then ONPP) process, the MK-GPAR is utilized to build a multi-target predictive model for tool wear and surface roughness prediction. The impact of the proposed two-step feature-integration method on the prediction performance of the MK-GPAR is demonstrated revealed milling experiments. The experimental findings indicate that the proposed two-step feature-integration method significantly enhances the accuracy of predictions and the consistency of CI of the MK-GPAR. This research lays the foundation for implementing the multi-target predictive model in real industrial environments to predict tool wear and surface roughness.

Interaction solutions of (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation via bilinear method

Using the bilinear neural network method (BNNM) and the symbolic computation system Mathematica, this paper explains how to find an exact solution for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation. In terms of activation function and weight coefficient, BNNM is a more appealing option for users than traditional symbolic computation methods. It is possible to develop a wide range of solutions and expand the classes of exact solutions by modifying the activation function. The activation function’s versatility allows it to generate a wide range of solutions with several theoretical and practical uses. The analytical solution is obtained by using a double layer type, while the rogue wave solution and mixed solutions are obtained by using a single layer type. The evolution of these waves is then illustrated using various 3D graphs, 2D graphs, and density plots.

Viscosity of imidazolium ionic liquids and mixtures of ILs from entropy scaling using the PC-SAFT and ePC-SAFT equations of state

Entropy scaling is a promising method for the development of engineering models for transport properties of ionic liquids (ILs). Here we present two entropy scaling models for the viscosity of ionic liquids and their mixtures at various temperatures and pressures: 1) a molecular-based approach treating each IL as one pure species and using the PC-SAFT equation of state (EoS); and 2) treating each ion as a separate species and using the ePC-SAFT EoS. Both approaches were correlated to viscosity data of 12 ionic liquids from the imidazolium cation class and three different anions comprising 4233 data points with overall average absolute deviations (%AARDs) of less than 8 % over a wide range of temperature and pressures. The ion-based approach was better able to correlate IL viscosity at low temperatures and/or high pressure (to 4011 bar) than the molecular approach. The functional entropy-scaling coefficients for both models were regressed as linear functions of molecular weight, which allowed good prediction of another nine ionic liquids not in the training set. Interestingly, both approaches well predict the viscosity of binary mixtures of imidazolium ionic liquids. In addition, the effect of various reference viscosities and comparison with the Peng-Robinson EoS was performed.

Wave reflection and transmission in seawater-unconsolidated-consolidated sediment models based on VGS([formula omitted]) and Biot theories

It proves challenging to accurately describe wave propagation within layers of sediment with significant variations in physical properties and states, using a single sediment acoustic theory. In this paper, we construct a sedimentary wave field model applicable to sedimentary layers containing different physical properties, by combining Biot theory and viscous-grain-shearing theory, and give an analytical solution for the coefficients of the wavefield potential function. The acoustic reflection coefficients of the seafloor surface are obtained accordingly. The comparison against the in-situ test of the Seabed Characterization Experiment shows that our model is better capable to describing wave propagation in structures with multiple sediment types. We give the most suitable model for the New England Mud Patch sediment structure by establishing different assignments of sedimentary acoustic theories, and discuss the effect of porosity and thickness of different layers on the reflection coefficients of waves of different frequencies.

Oxysulfide perovskites: reduction of the electronic band gap of RbTaO3 by sulfur substitution

In this study, the effects of sulfur substitution on the structural, mechanical, electronic, optical, and thermodynamic properties of RbTaO3−x S x have been investigated using the WIEN2k code in the framework of density functional theory (DFT). The cubic phase of RbTaO3 transforms to tetragonal for RbTaO2S and RbTaOS2; the latter transforms again to a cubic phase with added sulfur for RbTaS3. The results show that substituting S for O anions in RbTaO3 effectively decreased the band gap [calculated using TB-mBJ functional] from 2.717 eV to 1.438 eV, 0.286 eV, and 0.103 eV for the RbTaO3, RbTaO2S, RbTaOS2, and RbTaS3 compounds, respectively. The optical constants such as dielectric constant, refractive index, absorption coefficient, photoconductivity, reflectivity, and loss function have been calculated and analyzed. The elastic constants and moduli and their anisotropic nature were also investigated. Finally, the Debye temperature, thermal conductivity, melting temperature, specific capacities, and thermal expansion coefficients were computed and analyzed using established formalisms. The reduced band gap (1.438 eV) and high absorption coefficient (∼106 cm−1) of RbTaO2S, make it suitable for solar cell applications and for other visible light devices. Both ordered structure and super-cell have been used to cross-check results for RbTaO2S and RbTaOS2 compositions.

Functional Linear Regression: A Case Study from the Food Industry

A problem of analyzing functions in statistics is a very recent phenomenon that has been extensively investigated. The functionality in observed data, that is, when data are generated through a process naturally described as functional, occurs in many areas of sciences. For example, time series in financial engineering, imagining records in medicine, or spectrometric wavelengths in chemometrics can be considered as a discrete approximation of a continuous set of mathematical objects. In the initial step, observed real-valued data are transposed into functional data by smoothing or interpolation technique. These functional objects can then be directly used in the framework of statistical regressions. The aim of this paper is to show an estimation of the functional linear regression, where the observed covariate is functional, and its corresponding response is scalar. In the empirical study, we utilize spectrometric data with an objective to predict the fat content in a meat sample given the spectrum of absorbances, which are recorded through the infrared analyzer, by using the estimated functional linear regression. The functional regression coefficient is estimated through the basis spline expansion, for which we evaluate a different number of basis splines and propose the best predictor estimator.

The prediction of deformation in the process of erecting ship blocks based on inherent strain approach

Ship structures are referred to as plated and/or welded structures. Plates are sequentially welded using a high-temperature heat source to assemble the overall ship. The heat source used in the sequential welding inevitably generates imperfections in the ship structure, e.g., welding-induced deformation. Predicting welding-induced deformation is a critical task in design and control management at a shipyard, and much research has focused on the inherent strain method among possible efficient numerical methods. However, determining the inherent strain requires the synchronisation of all strain terms as a function of time and welding uncertainty because the welding position depends on the human worker. The present study thus derives time-dependent terms for inherent strain of the overall welding process and includes the welding position and cooling method in the function of the heat transfer coefficient. The inherent strain is derived through the detailed analysis of the overall welding process in terms of the application and utilisation, and it is simulated and reviewed for the erection of the hull block of a container ship and an LNG carrier. The inherent strain is expected to be used as a simple form of strain in the further study of various large welded structures and materials and in research on welding parameters.

DFT and Monte Carlo simulations of Optical, Structural, electronic and Electrocaloric properties of Ca3Ti2O7 compound

Using the DFT we investigated the optical, structural and electronic properties of Ca3Ti2O7 with the full-potential linearized augmented plane-wave (FP-LAPW) approach with the code “Wien2k”. The lattice constants of Ca3Ti2O7 have been derived by the GGA-PBE approximation. We obtained an indirect energy band gap value of Eg = 1.774 eV between N and Γ points. The thermodynamic properties have also been calculated and debated. In addition, the absorption coefficient, reflectivity, optical conductivity, dielectric function, refractive index and extinction coefficient are achieved. In some cases, the electro-caloric properties of the Ca3Ti2O7 compound have been examined by Monte Carlo simulations. The polarization with different electric field values is also demonstrated. This polarization shows a phase transition from a ferroelectric to a para-electric state close to the Curie temperature TC equal to 1104.001 K. At last, the electric entropy changes of the temperatures have been inferred. To complete this study, we have calculated the relative cooling power (RCP) parameter for the corresponding Ca3Ti2O7 and the electrical hysteresis loops.