Hermite Method Research Articles

Dynamic Analysis of Intermittent-Motion Conveyor Actuator

Conveyors are one of the important components of transport systems and are used in almost all branches of mechanical engineering. This paper investigates the dynamics of the intermittent motion conveyor mechanical system. The mechanical transmission is a planetary mechanism with elliptical gears, in which the intermittent motion of the output shaft is provided by a variable gear ratio of non-circular gears. A single-mass dynamic model is built by reducing the masses, forces and moments to the initial link, which is the input shaft of the mechanism. The solutions of the equations of initial link motion were obtained using two methods, the energy-mass method and the third-order Hermite method. Dynamic studies by the energy-mass method made it possible to determine flywheel moment of inertia to reduce the coefficient of initial link rotation irregularity. The convergence of the functions of the initial link angular velocity obtained by both methods was confirmed. The results can be used for further force analysis, strength calculations, design and manufacture of the conveyor.

Comparative analysis of the accuracy requirements of the equipment for determining the mean integral refractive index of air using different realizations of the gradient method

The speed of propagation of electromagnetic waves in the Earth’s atmosphere differs from the speed of their propagation in a vacuum, which is one of the main factors that have a significant impact on the accuracy of long distance measurement. This influence is taken into account in long distance measurement with the correction for the mean integral group refractive index of air, which depends on such meteorological parameters as temperature, atmospheric pressure and relative air humidity. The purpose of this work is to compare the accuracy requirements for equipment designed to measure temperature, pressure, and relative humidity required to determine the above correction by the gradient method using the Euler-Maclaurin quadrature formula (hereafter, the Euler-Maclaurin method) and the formula based on Hermite interpolation polynomials (hereafter, the Hermite method). The requirements for the uncertainty of measurements carried out with the sensors of meteorological parameters, allowing to find the mean integral group refractive index of air, providing length measurements of the baselines of up to 5 km with an expanded uncertainty of not more than 1 mm, are established. Keywords: atmosphere; mean integral group refractive index of air; laser long distance measurement

A Hermite collocation method for approximating a class of highly oscillatory integral equations using new Gaussian radial basis functions

In this paper, we investigate the oscillation properties of solutions of a class of highly oscillatory Volterra integral equations and develop a Hermite collocation method to approximate the solution of these equations. We begin our analysis by obtaining an asymptotic expansion for the solution of these equations using their resolvent representation. We then introduce a new Gaussian radial basis function interpolation to provide a numerical solution for these equations. The convergence analysis of the proposed method is also studied, which shows that increasing the number of collocation points or the number of mesh points controls the impact of the oscillation parameter in the whole error. Some numerical examples are presented to show the accuracy of the proposed scheme.

A generalized Fourier\u2013Hermite method for the Vlasov\u2013Poisson system

A generalized Fourier–Hermite semi-discretization for the Vlasov–Poisson equation is introduced. The formulation of the method includes as special cases the symmetrically-weighted and asymmetrically-weighted Fourier–Hermite methods from the literature. The numerical scheme is formulated as a weighted Galerkin method with two separate scaling parameters for the Hermite polynomial and the exponential part of the new basis functions. Exact formulas for the error in mass, momentum, and energy conservation of the method depending on the parameters are devised and L^2 stability is discussed. The numerical experiments show that an optimal choice of the additional parameter in the generalized method can yield improved accuracy compared to the existing methods, but also reveal the distinct stability properties of the symmetrically-weighted method.

A novel Markov chain method for predicting granular mixing process in rotary drums under different rotation speeds

The granular mixing in rotary drums has been intensively studied using discrete element method (DEM). However, DEM is computationally intensive. When the operating condition (such as rotation speed) of the drum is changed, a new round of time-consuming DEM simulation must be performed, whereas the data generated in previous rounds are not utilized. In order to solve this problem, we propose a Hermite interpolation-based Markov chain method (HI-MCM) to replace DEM simulation, so that granular mixing process under new drum speeds can be quickly predicted. HI-MCM utilizes the data generated by only several DEM simulations to establish Markov chain models, with which the granular mixing process at new rotation speeds can be then quickly predicted by Hermite interpolated Markov chain models. Tests demonstrate that the particle spatial distribution and mixing degree predicted by HI-MCM agrees well with DEM simulation results, while the computing time is less than 1% of that needed by DEM and current Markov chain methods. Moreover, the proposed HI-MCM shows good robustness to the change of Markov chain parameter (learning time step). The proposed method has potential usages in online prediction of granular mixing in rotary drums.

Hermite wavelet method for solving oscillatory electrical circuit equations

In this research, numerical solutions based on Hermite wavelets have been presented for solving oscillatory electrical circuit equations. The proposed numerical technique is based on Hermite wavelet basis functions, operational matrices of integration and collocation points. Numerical experiments have been performed to illustrate the accuracy and efficiency of the proposed scheme.

Model and Simulation of Artillery Kill Probability to Sea Targets

It is an important military problem for artillery to fire at sea targets. To determine the damage probability of artillery is the premise for commanders to organize operations. In this paper, we distinguish single target and multi-target and establish the shooting model of island and reef Garrison Artillery at sea. For single target, the hit probability is used to evaluate the firing effectiveness of cluster target, and the average number of damaged targets is used as the evaluation index, This paper analyzes the first, second and third groups of errors that affect the hit probability, and calculates the hit probability by using Gauss Hermite method; it uses multi scale area shooting method for cluster targets, and gives the expression of determining scale number and firepower coverage area. The simulation results of single target and multi-target are respectively simulated and calculated by Matlab tool. The simulation results have promotion and reference value, It can provide a strong theoretical support for the commander to command the troops to fire at sea single target and cluster target.

A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods

AbstractThe Lotka‐Volterra model is a very famous model and frequently used to describe the dynamics of ecological systems in which two species interact, one a predator and one its prey. In this present work, a comparative study is presented for solving Lotka‐Volterra model which has an important role in Biological sciences. The Lotka‐Volterra equations are solved by spectral collocation method (SCM) by using shifted Chebyshev polynomials of first kind. Then, a numerical example with two different cases is presented to demonstrate the accuracy and effectiveness of the numerical schemes. Using spectral method, we get a system of nonlinear algebraic equations which are solved by Newton's iteration method. Also the achieved solutions are compared with another solutions obtained by the Hermite wavelets method (HWM). Further, this work reflects that the integer order Lotka‐Volterra model and the fractional order one have close relationship where integer order model is a special case of fractional order. The behaviors study of predator and prey populations due to presence of fractional derivative are the key features of the present work. Our numerical and graphical results indicate that the proposed methods are simple, powerful and fully compatible for treatment of the Lotka‐Volterra model of fractional order.

AN APPROXIMATE SOLUTION FOR LORENTZIAN SPHERICAL TIMELIKE CURVES

In this article, the differential equation of lorentzian spherical timelike curves is obtained in E14. It is seen that the differential equation characterizing Lorentzian spherical timelike curves is equivalent to a linear, third order, differential equation with variable coefficients. It is impossible to solve these equations analytically. In this article, a new numerical technique based on hermite polynomials is presented using the initial conditions for the approximate solution. This method is called the modified hermite matrix-collocation method. With this technique, the solution of the problem is reduced to the solution of an algebraic equation system and the approximate solution is obtained. In addition, the validity and applicability of the technique is explained by a sample application.

Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation

We present high order accurate numerical methods for the wave equation that combines efficient Hermite methods with geometrically flexible discontinuous Galerkin methods by using overset grids. Near boundaries we use thin boundary fitted curvilinear grids and in the volume we use Cartesian grids so that the computational complexity of the solvers approaches a structured Cartesian Hermite method. Unlike many other overset methods we do not need to add artificial dissipation but we find that the built-in dissipation of the Hermite and discontinuous Galerkin methods is sufficient to maintain the stability. By numerical experiments we demonstrate the stability, accuracy, efficiency, and the applicability of the methods to forward and inverse problems.

Optimal-rate finite-element solution of Dirichlet problems in curved domains with straight-edged tetrahedra

Abstract In a series of papers published since 2017 the author introduced a simple alternative of the $n$-simplex type, to enhance the accuracy of approximations of second-order boundary value problems subject to Dirichlet boundary conditions, posed on smooth curved domains. This technique is based upon trial functions consisting of piecewise polynomials defined on straight-edged triangular or tetrahedral meshes, interpolating the Dirichlet boundary conditions at points of the true boundary. In contrast, the test functions are defined by the standard degrees of freedom associated with the underlying method for polytopic domains. While the mathematical analysis of the method for Lagrange and Hermite methods for two-dimensional second- and fourth-order problems was carried out in earlier paper by the author this paper is devoted to the study of the three-dimensional case. Well-posedness, uniform stability and optimal a priori error estimates in the energy norm are proved for a tetrahedron-based Lagrange family of finite elements. Novel error estimates in the $L^2$-norm, for the class of problems considered in this work, are also proved. A series of numerical examples illustrates the potential of the new technique. In particular, its superior accuracy at equivalent cost, as compared to the isoparametric technique, is highlighted.

Hermite collocation method for obtaining the chaotic behavior of a nonlinear coupled system of FDEs

This paper is devoted to introduce an efficient solver using the Hermite collocation technique (HCT), of the coupled system of fractional differential equations (FDEs). The given systems are of basic importance in modeling various phenomena like Cascades and Compartment Analysis, Pond Pollution, Home Heating, Chemostats, and Microorganism Culturing, Nutrient Flow in an Aquarium, Biomass Transfer, Forecasting Prices, Electrical Network, Earthquake Effects on Buildings. The proposed method reduces the system of FDEs to a system of algebraic equations in the coefficients of the expansion using the Hermite polynomials. The introduced method is computer oriented and provides highly accurate solution. To demonstrate the efficiency of the method, two examples are solved and the results are displayed graphically. Finally, we convert the presented coupled systems from the case of its standard form to a first-order ordinary differential equations to compare the obtained numerical solutions with those solutions using the fourth-order Runge–Kutta method (RK4).

Hermite wavelet method for the numerical solution of nonlinear singular initial value problems

Hermite wavelet method for the numerical solution of nonlinear singular initial value problems

Heat Transfer Enhancement by Coupling of Carbon Nanotubes and SiO2 Nanofluids: A Numerical Approach

This article comprises the study of three-dimensional squeezing flow of (CNT-SiO2/H2O) hybrid nanofluid. The flow is confined inside a rotating channel whose lower wall is stretchable as well as permeable. Heat transfer with viscous dissipation is a main subject of interest. We have analyzed mathematically the benefits of hybridizing SiO 2 -based nanofluid with carbon nanotubes ( CNTs ) nanoparticles. To describe the effective thermal conductivity of the CNTs -based nanofluid, a renovated Hamilton–Crosser model (RHCM) has been employed. This model is an extension of Hamilton and Crosser’s model because it also incorporates the effect of the interfacial layer. For the present flow scenario, the governing equations (after the implementation of similarity transformations) results in a set of ordinary differential equations (ODEs). We have solved that system of ODEs, coupled with suitable boundary conditions (BCs), by implementing a newly proposed modified Hermite wavelet method (MHWM). The credibility of the proposed algorithm has been ensured by comparing the procured results with the result obtained by the Runge-Kutta-Fehlberg solution. Moreover, graphical assistance has also been provided to inspect the significance of various embedded parameters on the temperature and velocity profile. The expression for the local Nusselt number and the skin friction coefficient were also derived, and their influential behavior has been briefly discussed.

RETRACTED ARTICLE: Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

Abstract A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Zero-Coupon, Forward, and Par Yield Curves for the Nigerian Bond Market

The Nigerian bond market is currently one of the most liquid in sub-Saharan Africa. Many African countries regard it as a model from which to learn and based on which to develop their respective bond markets. The developments achieved in the Nigerian bond market are of particular interest to both investors and fixed income analysts—both domestic and international. One of the important tools required for fixed income analysis, pricing, and trading is the yield curve. To the best of our knowledge, even though the Nigerian bond market has a secondary market yield curve, the yield curve is a yield-to-maturity curve, and not zero-coupon yield curve. The purpose of this study is to model the zero-coupon, par, and forward yield curves for the Nigerian bond market. We use various methods such as the piecewise cubic Hermite method, the piecewise cubic spline method (with not-a-knot end condition), the Nelson–Siegel–Svensson method, and the variable roughness penalty method. Data are obtained from the FMDQ OTC website. The results show that the piecewise cubic Hermite method is very suitable for producing the Nigerian par and zero-coupon yield curves. Our best recommended method for producing the Nigerian zero-coupon yield curve is therefore the piecewise cubic Hermite method, followed by the Nelson–Siegel–Svensson method. For the forward yield curve, the results show that the best method is the Nelson–Siegel–Svensson method, followed by the variable roughness penalty method.

Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

Abstract A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Leapfrog Time-Stepping for Hermite Methods

We introduce Hermite-leapfrog methods for first order linear wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors et al. (Math Comput 75(254):595–630, 2006). The new schemes stagger field variables in both time and space and are high-order accurate for equations with smooth solutions and coefficients. We provide a detailed description of the method and demonstrate that the method conserves variable quantities. Higher dimensional versions of the method are constructed via tensor products. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.

Extreme and spectrum characteristics of wind loads on super-large cooling tower under different four-tower combinations

The wind loads distribution on the super-large cooling tower under the interference effect of tower group is very complicated. Particularly, energy distribution of fluctuation wind loads and extreme model is difficult to be predicted. However, accurate calculations of these two factors are the most direct ways for analysis of wind resistance dynamics of super-large cooling tower. The wind tunnel tests of the highest super-large cooling tower under five typical tower combinations (serial, rectangular, rhombus, L-shaped, and inclined L-shaped) with 320 working conditions were performed. On this basis, non-Gaussian and non-stationary properties of local wind pressure and overall force coefficient of super-large cooling tower were analyzed. Distribution laws of local wind pressure extremes and overall force coefficient extremes were discussed based on Hermite method and peak factor method. Key attention was paid to the mapping relationships of characteristic angles with local and overall aerodynamic force extremes. The effects of four-tower combination modes on fluctuation wind loads energy of super-large cooling tower were studied based on the power spectral density function, intrinsic mode function, and evolution power spectral density function. Besides, the estimation formulas of local wind pressure spectrum and overall pressure coefficient spectrum of super-large cooling tower under four-tower combination were proposed. It can be found that the extremes of local wind pressure and overall aerodynamic force could be predicted based on the linear relationship between characteristic angles and fluctuation wind loads. In addition, it is suggested to choose serial combination first, followed by inclined L-shaped, L-shaped, rhombus, and rectangular modes successively.

Local Hermite (LH) Method: An accurate and robust smooth technique for high-gradient strain reconstruction in digital image correlation

High-gradient strain field (HSF) measurement is attracting more and more attention from engineering and scientific fields, where digital image correlation (DIC) is widely adopted to calculate the dramatically changing displacement fields on stressed samples. Accurate reconstruction of reliable strain field from noisy displacement field is one of the key issues, since strain calculation is highly sensitive to displacement noise. The formally proposed improved Hermite finite element smoothing method (IHFESM) and fast Hermite element method (FHEM) are effective global smoothing techniques based on Tikhonov regularization. However, they involve complex meshing and global regularization matrix assembly processes. In this work, we present a local version of FHEM, called local Hermite (LH) method, in which one Hermite element is taken as a smoothing window centered on one displacement data, and the whole field is handled point-wisely. Two types of LH method are obtained by employing Hermite element with two types of continuities, i.e. C1 and C2. The smoothed displacement and strain are consequently computed from the regularized local surface as done in FHEM. Two kinds of simulated noisy displacement fields and one high-gradient displacement field obtained from shape memory alloy (SMA) tensile test are used to compare the performance of the proposed LH methods with the widely used point-wise least-squares (PLS) method. Experiments show that LH method with C2 element is nearly insensitive to window size, which is a quite useful property for practical engineering test without much prior knowledge. More importantly, it generally produces lower error than PLS in resolving local HSF. Thus, LH is a robust and accurate method which is highly recommended for practical HSF measurement.