Thermosolutal LTNE Porous Mixed Convection Under the Influence of the Soret Effect

The effects of horizontal pressure gradient and Soret coefficient on the onset of double-diffusive convection in a fluid-saturated porous layer under the influence of local thermal nonequilibrium (LTNE) temperatures are analyzed. Darcy's law with local acceleration term, which involves the two-field temperature model describing the fluid and solid phases separately and the approximation of Oberbeck-Boussinesq, is used. The dynamics of small-amplitude perturbations on the basic mixed convection flow is studied numerically. Using the Galerkin method along with the QZ-algorithm, the eighth order eigenvalue differential equation obtained by employing linear stability analysis is solved. The solution provides the neutral stability curves and determines the threshold of linear instability, and the critical values of thermal Darcy-Rayleigh number, wave number, and the frequency at the onset of instability are determined for various values of control parameters. It is found that, rather than the stationary motion, the instability is found to be via oscillatory motion. Besides, the contribution to each parameter on stability characteristics is explored in detail, and some relevant findings have been described that have not been reported hitherto in the literature.

On the efficiency of high-order difference schemes for the Schro¨dinger equation

Исследуется ряд двух- и трехслойных разностных схем, построенных на расширенных шаблонах, до восьмого порядка точности для уравнения Шрёдингера. Наряду с многоточечными схемами рассматривается метод коррекции Ричардсона в приложении к схеме четвертого порядка аппроксимации, повышающий порядок точности путем построения линейных комбинаций приближенных решений, полученных на различных вложенных сетках. Проведено сравнение методов по устойчивости, сложности реализации алгоритмов и объему вычислений, необходимых для достижения заданной точности. На основе теоретического анализа и численных экспериментов выявлены методы, наиболее эффективные для практического применения The efficiency of difference methods for solving problems of nonlinear wave optics is largely determined by the order of accuracy. Schemes up to the fourth order of accuracy have the traditional architecture of three-point stencils and standard conditions for the application of algorithms. However, a further increase in the order in the general case is associated with the need to expand the stencils using multipoint difference approximations of the derivatives. The use of such schemes forces formulating additional boundary conditions, which are not present in the differential problem, and leads to the need to invert the matrices of the strip structure, which are different from the traditional tridiagonal ones. An exception is the Richardson correction method, which is aimed at increasing the order of accuracy by constructing special linear combinations of approximate solutions obtained on various nested grids according to traditional structure schemes. This method does not require the formulation of additional boundary conditions and inversion of strip matrices. In this paper, we consider several explicit and implicit multipoint difference schemes up to the eighth order of accuracy for the Schr¨odinger equation. In addition, a simple and double Richardson correction method is also investigated in relation to the classical fourth-order scheme. A simple correction raises the order to sixth and a double correction to eighth. This large collection of schemes is theoretically compared in terms of their properties such as the order of approximation, stability, the complexity of the implementation of a numerical algorithm, and the amount of arithmetic operations required to achieve a given accuracy. The theoretical analysis is supplemented by numerical experiments on the selected test problem. The main conclusion drawn from the research results is that of all the considered schemes, the Richardson-corrected scheme is the most preferable in terms of the investigated properties

Extended local convergence for Newton-type solver under weak conditions

We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence was shown earlier in the special case of the k-dimensional Euclidean space, using hypotheses up to the eighth derivative although these derivatives do not appear in the method. We show convergence using only the rst derivative. This way we extend the applicability of the methods. Numerical examples are used to show the convergence conditions. Finally, the basins of attraction of the method, on some test problems are presented.

Exploiting the S-Iteration Process for Solving Power Flow Problems: Novel Algorithms and Comprehensive Analysis

In recent studies, the competitiveness of the Newton-S-Iteration-Process (Newton-SIP) techniques to efficiently solve the Power Flow (PF) problems in both well and ill-conditioned systems has been highlighted, concluding that these methods may be suitable for industrial applications. This paper aims to tackle some of the open topics brought for this kind of techniques. Different PF techniques are proposed based on the most recently developed Newton-SIP methods. In addition, convergence analysis and a comparative study of four different Newton-SIP methods PF techniques are presented. To check the features of considered PF techniques, several numerical experiments are carried out. Results show that the considered Newton-SIP techniques can achieve up to an eighth order of convergence and typically are more efficient and robust than the Newton–Raphson (NR) technique. Finally, it is shown that the overall performance of the considered PF techniques is strongly influenced by the values of parameters involved in the iterative procedure.

Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits

The family of Numerov-type methods that effectively uses seven stages per step is considered. All the coefficients of the methods belonging to this family can be expressed analytically with respect to four free parameters. These coefficients are trained through a differential evolution technique in order to perform best in a wide range of Keplerian-type orbits. Then it is observed with extended numerical tests that a certain method behaves extremely well in a variety of orbits (e.g., Kepler, perturbed Kepler, Arenstorf, Pleiades) for various steplengths used by the methods and for various intervals of integration.

Generation and Evolution Conditions of Polygonal Wear of High-Speed Wheel

Wheel polygonal wear has long been a problem that confused the safety of railway operation which has important theoretical value and research significance. In this paper, the conditions of polygonal wear of high-speed wheel are analyzed based on the wear model and verified by the field measured data. Considering the wheel track interaction caused by rotation, a finite element model of wheelset rotor dynamics is established. The effects of rotor speed, mass eccentricity, wheelset, and track flexibility on the vibration characteristics of wheelset rotor system and wheel polygonal wear characteristics are analyzed by beam element and solid element, respectively. The results show that the wheel longitudinal vibration is the main reason of wheel polygonal wear, and the wheel polygonal wear follows the law of “constant frequency and divisible.” Its “constant frequency” comes from the wheel track contact vibration, which stimulates the third-order vertical bending vibration of wheelset and the eighth-order coupled bending vibration of track, and the order is equal to the ratio of “constant frequency” to the wheelset rotation frequency.

Research on Deterministic Measurement Matrix of Power Line Carrier Compressed Sensing

To verify the advantages of deterministic matrix applied to power line carrier communication (PLCC) based on compressed sensing (CS). This article analyzed the research status of commonly used deterministic measurement matrices, and made simulation comparison. It is found that different types of deterministic measurement matrices generated based on chaotic mapping had higher reconstruction accuracy and higher reconstruction efficiency than Gaussian random matrix. Then, according to simulation results and the characteristics of PLCC signal, the Chebyshev sparse circulant (CSC) measurement matrix was designed by combining eighth-order Chebyshev chaotic and the idea of sparse and circulant. Actual circuit measurement shows that when compression rate was 40% and 60%, the reconstruction loss of CSC is 0.72dB and 0.49dB higher than that of Chebyshev chaotic measurement matrix and Chebyshev circulate measurement matrix, respectively. Obviously, the CSC measurement matrix designed in this paper can effectively improve the reconstruction accuracy.

Fixed-Time Synergetic Control-Based Chaos Suppression for Eighth-Order IFOCIM Drive System

This paper investigates chaos suppression in widely used indirect field oriented controlled induction machine (IFOCIM) drive system using fixed-time synergetic control method. The complex eighth-order IFOCIM drive system shows chaotic oscillations during a specific range of the integral gain of the PI speed controller. The conventional synergetic control method is improved by employing the fixed-time theory, the characteristics of the designed controller are chattering free and the convergence time is limited within a fixed-time upper bound depending on the controller parameters. The fixed-time synergetic control method is used to converge a selected macro variable to the origin within the fixed time upper bound. The controller can stabilize the chaotic system dynamics in a good way within a short time.