Search results for: Newton%20interpolation

Authors: M. O. Oke, T. S. Workneh

Abstract:

Drying behaviour of blanched sweet potato in a cabinet dryer using different five air temperatures (40-80oC) and ten sweet potato varieties sliced to 5 mm thickness were investigated. The drying data were fitted to eight models. The Modified Henderson and Pabis model gave the best fit to the experimental moisture ratio data obtained during the drying of all the varieties while Newton (Lewis) and Wang and Singh models gave the least fit. The values of Deff obtained for Bophelo variety (1.27 x 10-9 to 1.77 x 10-9 m2/s) was the least while that of S191 (1.93 x 10-9 to 2.47 x 10-9 m2/s) was the highest which indicates that moisture diffusivity in sweet potato is affected by the genetic factor. Activation energy values ranged from 0.27-6.54 kJ/mol. The lower activation energy indicates that drying of sweet potato slices requires less energy and is hence a cost and energy saving method. The drying behavior of blanched sweet potato was investigated in a cabinet dryer. Drying time decreased considerably with increase in hot air temperature. Out of the eight models fitted, the Modified Henderson and Pabis model gave the best fit to the experimental moisture ratio data on all the varieties while Newton, Wang and Singh models gave the least. The lower activation energy (0.27-6.54 kJ/mol) obtained indicates that drying of sweet potato slices requires less energy and is hence a cost and energy saving method.

Keywords: sweet potato slice, drying models, moisture ratio, moisture diffusivity, activation energy

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Authors: Young Hee Geum

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In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding, order of convergent

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Authors: Suwarsono, Ario S. Baskoro, Gandjar Kiswanto, Budiono

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Friction Stir Welding (FSW) is a relatively new technique for joining metal. In some cases on aluminum joining, FSW gives better results compared with the arc welding processes, including the quality of welds and produces less distortion.FSW welding process for a light structure and thin materials requires small forces as possible, to avoid structure deflection. The joining process on FSW occurs because of melting temperature and compressive forces, the temperature generation of caused by material deformation and friction between the cutting tool and material. In this research, High speed rotation of spindle was expected to reduce the force required for deformation. The welding material was Aluminum A1100, with thickness of 0.4 mm. The tool was made of HSS material which was shaped by micro grinding process. Tool shoulder diameter is 4 mm, and the length of pin was 0.6 mm (with pin diameter= 1.5 mm). The parameters that varied were the plunge speed (2 mm/min, 3 mm/min, 4 mm/min). The tool speed is fixed at 33,000 rpm. Responses of FSSW parameters to analyze were Axial Force (Z-Force), Temperature and the Shear Strength of welds. Research found the optimum µFSSW parameters, it can be concluded that the most important parameters in the μFSSW process was plunge speed. lowest plunge speed (2 mm / min) causing the lowest axial force (110.40 Newton). The increases of plunge speed will increase the axial force (maximum Z-Farce= 236.03 Newton), and decrease the shear strength of welds.

Keywords: friction stir spot welding, aluminum A1100, plunge speed, axial force, shear strength

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Authors: Rakesh Kumar, A. K. Ghosh

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The paper presents the modeling of linear and nonlinear longitudinal aerodynamics using real flight data of Hansa-3 aircraft gathered at low and high angles of attack. The Neural-Gauss-Newton (NGN) method has been applied to model the linear and nonlinear longitudinal dynamics and estimate parameters from flight data. Unsteady aerodynamics due to flow separation at high angles of attack near stall has been included in the aerodynamic model using Kirchhoff’s quasi-steady stall model. NGN method is an algorithm that utilizes Feed Forward Neural Network (FFNN) and Gauss-Newton optimization to estimate the parameters and it does not require any a priori postulation of mathematical model or solving of equations of motion. NGN method was validated on real flight data generated at moderate angles of attack before application to the data at high angles of attack. The estimates obtained from compatible flight data using NGN method were validated by comparing with wind tunnel values and the maximum likelihood estimates. Validation was also carried out by comparing the response of measured motion variables with the response generated by using estimates a different control input. Next, NGN method was applied to real flight data generated by executing a well-designed quasi-steady stall maneuver. The results obtained in terms of stall characteristics and aerodynamic parameters were encouraging and reasonably accurate to establish NGN as a method for modeling nonlinear aerodynamics from real flight data at high angles of attack.

Keywords: parameter estimation, NGN method, linear and nonlinear, aerodynamic modeling

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Authors: Dimitris Varsamis, Nicholas Karampetakis

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It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: bivariate interpolation polynomial, polynomial basis, transformations, interpolating polynomial

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Authors: Krima M. Rohela, Raja Sabarinath Sundaralingam

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Humans have been launching rockets since the beginning of the space age in the late 1950s. We have come a long way since then, and the success rate for the launch of rockets has increased considerably. With every successful launch, there is a large amount of junk or debris which is released into the upper layers of the atmosphere. Space debris has been a huge concern for a very long time now. This includes the rocket shells released from the launch and the parts of defunct satellites. Some of this junk will come to fall towards the Earth and burn in the atmosphere. But most of the junk goes into orbit around the Earth, and they remain in orbits for at least 100 years. This can cause a lot of problems to other functioning satellites and may affect the future manned missions to space. The main concern of the space-debris is the increase in space activities, which leads to risks of collisions if not taken care of soon. These collisions may result in what is known as Kessler Syndrome. This debris can be removed by a space-based laser targeting system. Hence, the matter is investigated and discussed. The first step in this involves launching a satellite with a high-power laser device into space, above the debris belt. Then the target material is ablated with a focussed laser beam. This step of the process is highly dependent on the attitude and orientation of the debris with respect to the Earth and the device. The laser beam will cause a jet of vapour and plasma to be expelled from the material. Hence, the force is applied in the opposite direction, and in accordance with Newton’s third law of motion, this will cause the material to move towards the Earth and get pulled down due to gravity, where it will get disintegrated in the upper layers of the atmosphere. The larger pieces of the debris can be directed towards the oceans. This method of removal of the orbital debris will enable safer passage for future human-crewed missions into space.

Keywords: altitude, Kessler syndrome, laser ablation, Newton’s third law of motion, satellites, Space debris

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Authors: Aymen Laadhari

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During the last decade, an increasing number of contributions have been made in the fields of scientific computing and numerical methodologies applied to the study of the hemodynamics in the heart. In contrast, the numerical aspects concerning the interaction of pulsatile blood flow with highly deformable thin leaflets have been much less explored. This coupled problem remains extremely challenging and numerical difficulties include e.g. the resolution of full Fluid-Structure Interaction problem with large deformations of extremely thin leaflets, substantial mesh deformations, high transvalvular pressure discontinuities, contact between leaflets. Although the Lagrangian description of the structural motion and strain measures is naturally used, many numerical complexities can arise when studying large deformations of thin structures. Eulerian approaches represent a promising alternative to readily model large deformations and handle contact issues. We present a fully Eulerian finite element methodology tailored for the simulation of pulsatile blood flow in the aorta and sinus of Valsalva interacting with highly deformable thin leaflets. Our method enables to use a fluid solver on a fixed mesh, whilst being able to easily model the mechanical properties of the valve. We introduce a semi-implicit time integration scheme based on a consistent NewtonRaphson linearization. A variant of the classical Newton method is introduced and guarantees a third-order convergence. High-fidelity computational geometries are built and simulations are performed under physiological conditions. We address in detail the main features of the proposed method, and we report several experiments with the aim of illustrating its accuracy and efficiency.

Keywords: eulerian, level set, newton, valve

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Authors: Surendra Mund

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At the beginning, the physical entity force was defined mathematically by Sir Isaac Newton in his Principia Mathematica as F ⃗=(dp ⃗)/dt in form of his second law of motion. Newton also defines his Universal law of Gravitational force exist in same outstanding book, but at the end of 20th century and beginning of 21st century, we have tried a lot to specify and unify four or five Fundamental forces or Interaction exist in universe, but we failed every time. Usually, Gravity creates problems in this unification every single time, but in my previous papers and presentations, I defined and derived Field and force equations for Gravitational like Interactions for each and every kind of central systems. This force is named as Variational Force by me, and this force is generated by variation in the scalar field density around the body. In this particular paper, at first, I am specifying which type of Interactions are Fundamental in Universal sense (or in all type of central systems or bodies predicted by my N-time Inflationary Model of Universe) and then unify them in Universal framework (defined and derived by me as Universal Mechanics in a separate paper) as well. This will also be valid in Universal dynamical sense which includes inflations and deflations of universe, central system relativity, Universal relativity, ϕ-ψ transformation and transformation of spin, physical perception principle, Generalized Fundamental Dynamical Law and many other important Generalized Principles of Generalized Quantum Mechanics (GQM) and Central System Theory (CST). So, In this article, at first, I am Generalizing some Fundamental Principles, and then Unifying Variational Forces (General form of Gravitation like Interactions) and Flow Generated Force (General form of EM like Interactions), and then Unify all Fundamental Forces by specifying Weak and Strong Interactions in form of more basic terms - Variational, Flow Generated and Transformational Interactions.

Keywords: Central System Force, Disturbance Force, Flow Generated Forces, Generalized Nuclear Force, Generalized Weak Interactions, Generalized EM-Like Interactions, Imbalance Force, Spin Generated Forces, Transformation Generated Force, Unified Force, Universal Mechanics, Uniform And Non-Uniform Variational Interactions, Variational Interactions

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Authors: Mohamed Belhorma, Aboubakar S. Bouchikhi, Belkacem Bounab

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This paper addresses modeling a Double A-Arm suspension, a three-dimensional nonlinear model has been developed using the multibody systems formalism. Dynamical study of the different components responses was done, particularly for the wheel assembly. To validate those results, the system was constructed and simulated by RecurDyn, a professional multibody dynamics simulation software. The model has been used as the Objectif function in an optimization algorithm for ride quality improvement.

Keywords: double A-Arm suspension, multibody systems, ride quality optimization, dynamic simulation

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: algorithm, determinant, computation, eigenvalue, time complexity

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Authors: Puneet Chawla, Balwinder Singh

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Recently, increased attention has been devoted to the voltage instability phenomenon in power systems. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. In this paper, P-V and Q-V curves have been generated for a 57 bus Patiala Rajpura circle of India. The power-flow program is developed in MATLAB using Newton-Raphson method. Using Q-V curves, the weakest bus of the power system and the maximum reactive power change permissible on that bus is calculated. STATCOMs are placed on the weakest bus to improve the voltage and hence voltage stability and also the power transmission capability of the line.

Keywords: voltage stability, reactive power, power flow, weakest bus, STATCOM

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Authors: Sean Kinney

Abstract:

In 1666, Newton created the Law of Universal Gravitation. And in 1915, Einstein improved it to incorporate factors such as time dilation and gravitational lensing. But currently, there is a problem with this “universal” law. The math doesn’t work outside the confines of our solar system. And something is missing; any evidence of what gravity actually is and how it manifest. This paper explores the notion that gravity must obey the law of conservation of energy as all other forces in this universe have been shown to do. Explaining exactly what gravity is and how it manifests itself. And looking at many different implications that would be created are explained. And finally, using the math of Dynamic Gravity to calculate Dark Energy and Dark Matter effects to explain all observations without the need of exotic measures.

Keywords: gravity, dynamic gravity, dark matter, dark energy

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Authors: Sean Michael Kinney

Abstract:

In 1666, Newton created the Law of Universal Gravitation. And in 1915, Einstein improved it to incorporate factors such as time dilation and gravitational lensing. But currently, there is a problem with this “universal” law. The math doesn’t work outside the confines of our solar system. And something is missing; any evidence of what gravity actually is and how it manifests. This paper explores the notion that gravity must obey the law of conservation of energy as all other forces in this universe have been shown to do. Explaining exactly what gravity is and how it manifests itself. And looking at many different implications that would be created are explained. And finally, use the math of Dynamic gravity to calculate Dark Energy and Dark Matter effects to explain all observations without the need for exotic measures.

Keywords: dynamic gravity, gravity, dark matter, dark energy

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Al Omari Moahmmed Ahmed

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In the Bayesian, we developed an approach by using non-informative prior with covariate and obtained by using Gauss quadrature method to estimate the parameters of the covariate and reliability function of the Weibull regression distribution with Type-I censored data. The maximum likelihood seen that the estimators obtained are not available in closed forms, although they can be solved it by using Newton-Raphson methods. The comparison criteria are the MSE and the performance of these estimates are assessed using simulation considering various sample size, several specific values of shape parameter. The results show that Bayesian with non-informative prior is better than Maximum Likelihood Estimator.

Keywords: non-informative prior, Bayesian method, type-I censoring, Gauss quardature

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Mai Abdul Latif, Yuntian Feng

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Applied Element Method (AEM) is a method that was developed to aid in the analysis of the collapse of structures. Current available methods cannot deal with structural collapse accurately; however, AEM can simulate the behavior of a structure from an initial state of no loading until collapse of the structure. The elements in AEM are connected with sets of normal and shear springs along the edges of the elements, that represent the stresses and strains of the element in that region. The elements are rigid, and the material properties are introduced through the spring stiffness. Nonlinear dynamic analysis has been widely modelled using the finite element method for analysis of progressive collapse of structures; however, difficulties in the analysis were found at the presence of excessively deformed elements with cracking or crushing, as well as having a high computational cost, and difficulties on choosing the appropriate material models for analysis. The Applied Element method is developed and coded to significantly improve the accuracy and also reduce the computational costs of the method. The scheme works for both linear elastic, and nonlinear cases, including elasto-plastic materials. This paper will focus on elastic and elasto-plastic material behaviour, where the number of springs required for an accurate analysis is tested. A steel cantilever beam is used as the structural element for the analysis. The first modification of the method is based on the Gaussian Quadrature to distribute the springs. Usually, the springs are equally distributed along the face of the element, but it was found that using Gaussian springs, only up to 2 springs were required for perfectly elastic cases, while with equal springs at least 5 springs were required. The method runs on a Newton-Raphson iteration scheme, and quadratic convergence was obtained. The second modification is based on adapting the number of springs required depending on the elasticity of the material. After the first Newton Raphson iteration, Von Mises stress conditions were used to calculate the stresses in the springs, and the springs are classified as elastic or plastic. Then transition springs, springs located exactly between the elastic and plastic region, are interpolated between regions to strictly identify the elastic and plastic regions in the cross section. Since a rectangular cross-section was analyzed, there were two plastic regions (top and bottom), and one elastic region (middle). The results of the present study show that elasto-plastic cases require only 2 springs for the elastic region, and 2 springs for the plastic region. This showed to improve the computational cost, reducing the minimum number of springs in elasto-plastic cases to only 6 springs. All the work is done using MATLAB and the results will be compared to models of structural elements using the finite element method in ANSYS.

Keywords: applied element method, elasto-plastic, Gaussian springs, nonlinear

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

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The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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Authors: Anubhav Shrivastava, Lakshya Bhat, Shivarudraswamy

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Distributed Generation is the need of the hour. With current advancements in the DG technology, there are some major issues that need to be tackled in order to make this method of generation of energy more efficient and feasible. Among other problems, the control in voltage is the major issue that needs to be addressed. This paper focuses on control of voltage using reactive power control of DGs with the help of fuzzy logic. The membership functions have been defined accordingly and the control of the system is achieved. Finally, with the help of simulation results in Matlab, the control of voltage within the tolerance limit set (+/- 5%) is achieved. The voltage waveform graphs for the IEEE 14 bus system are obtained by using simple algorithm with MATLAB and then with fuzzy logic for 14 bus system. The goal of this project was to control the voltage within limits by controlling the reactive power of the DG using fuzzy logic.

Keywords: distributed generation, fuzzy logic, matlab, newton raphson, IEEE 14 bus, voltage regulation, radial network

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Authors: Satyendra Pratap Singh, S. P. Singh

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This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: gravitational search algorithm (GSA), law of motion, law of gravity, observability, phasor measurement unit

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Authors: Prashant G. Metri

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A numerical model is developed to study nano liquid film flow over an unsteady stretching sheet in the presence of hydromagnetic have been investigated. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg and Newton-Raphson schemes. A relationship between film thickness β and the unsteadiness parameter S is found, the effect of unsteadiness parameter S, and the hydromagnetic parameter S, on the velocity and temperature distributions are presented. The present analysis shows that the combined effect of magnetic field and viscous dissipation has a significant influence in controlling the dynamics of the considered problem. Comparison with known results for certain particular cases is in excellent agreement.

Keywords: boundary layer flow, nanoliquid, thin film, unsteady stretching sheet

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Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

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This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

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Authors: Abbas Moradi, Mohsen Safajoy, Reza Yazdanparast

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Analysis of blade-disc dovetail joints is one of the biggest challenges facing designers of aero-engines. To avoid comparatively expensive experimental full-scale tests, numerical methods can be used to simulate loaded disc-blades assembly. Mortar method provides a powerful and flexible tool for solving frictional contact problems. In this study, 2D frictional contact in dovetail has been analysed based on the mortar algorithm. In order to model the friction, the classical law of coulomb and moving friction cone algorithm is applied. The solution is then obtained by solving the resulting set of non-linear equations using an efficient numerical algorithm based on Newton–Raphson Method. The numerical results show that this approach has better convergence rate and accuracy than other proposed numerical methods.

Keywords: computational contact mechanics, dovetail joints, nonlinear FEM, mortar approach

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Authors: Jing-Gang Xie

Abstract:

The research, in this case, considers the integration of the Quantum Field Theory and the General Relativity Theory. As two successful models in explaining behaviors of particles, they are incompatible since they work at different masses and scales of energy, with the evidence that regards the description of black holes and universe formation. It is so considering previous efforts in merging the two theories, including the likes of the String Theory, Quantum Gravity models, and others. In a bid to prove an actionable experiment, the paper’s approach starts with the derivations of the existing theories at present. It goes on to test the derivations by applying the same initial assumptions, coupled with several deviations. The resulting equations get similar results to those of classical Newton model, quantum mechanics, and general relativity as long as conditions are normal. However, outcomes are different when conditions are extreme, specifically with no breakdowns even for less than Schwarzschild radius, or at Planck length cases. Even so, it proves the possibilities of integrating the two theories.

Keywords: general relativity theory, particles, photons, Quantum Gravity Model, gravitational frequency shift

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Authors: Eric Asare, Jamie Evans, Mark Newton, Emiliano Bilotti

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Two types of filler shapes (sphere and flakes) and three different sizes are employed to study the size effect on PTC. The composite is prepared using a mini-extruder with high-density polyethylene (HDPE) as the matrix. A computer modelling is used to fit the experimental results. The percolation threshold decreases with decreasing filler size and this was observed for both the spherical particles as well as the flakes. This was caused by the decrease in interparticle distance with decreasing filler size. The 100 µm particles showed a larger PTC intensity compared to the 5 µm particles for the metal coated glass sphere and flake. The small particles have a large surface area and agglomeration and this makes it difficult for the conductive network to e disturbed. Increasing the filler content decreased the PTC intensity and this is due to an increase in the conductive network within the polymer matrix hence more energy is needed to disrupt the network.

Keywords: positive temperature coefficient (PTC) effect, conductive polymer composite (CPC), electrical conductivity

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