Search results for: third order ordinary differential equations

Authors: Mohammed Abdulhameed, Sagir M. Abdullahi

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In this paper, based on the applications of nanoparticle, the blood flow along with nanoparticles through stenosed artery is studied. The blood is acted by periodic body acceleration, an oscillating pressure gradient and an external magnetic field. The mathematical formulation is based on Caputo-Fabrizio fractional derivative without singular kernel. The model of ordinary blood, corresponding to time-derivatives of integer order, is obtained as a limiting case. Analytical solutions of the blood velocity and temperature distribution are obtained by means of the Hankel and Laplace transforms. Effects of the order of Caputo-Fabrizio time-fractional derivatives and three different nanoparticles i.e. Fe3O4, TiO4 and Cu are studied. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. It is observed that the addition of Fe3O4 nanoparticle reduced the resistance impedance of the blood flow and temperature distribution through bell shape stenosed arteries as compared to TiO4 and Cu nanoparticles. On entering in the stenosed area, blood temperature increases slightly, but, increases considerably and reaches its maximum value in the stenosis throat. The shears stress has variation from a constant in the area without stenosis and higher in the layers located far to the longitudinal axis of the artery. This fact can be an important for some clinical applications in therapeutic procedures.

Keywords: nanoparticles, blood flow, stenosed artery, mathematical models

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Authors: Wararit Panichkitkosolkul

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The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulation. Simulation results show that all unit root tests can control the probability of Type I error for all situations. The empirical power of the unit root tests based on the robust estimator are higher than the unit root tests based on the OLS estimator.

Keywords: autoregressive, ordinary least squares, type i error, power of the test, Monte Carlo simulation

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Authors: Leonardo Herrera, Shield B. Lin, Stephen J. Montgomery-Smith, Ziraguen O. Williams

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A one-directional dynamic model of a Stewart Platform was developed to assist NASA in analyzing the dynamic response in spacecraft docking operations. A simplified mechanical drawing was created, capturing the physical structure's main features. A simplified schematic diagram was developed into a lumped mass model from the mechanical drawing. Three differential equations were derived according to the schematic diagram. A Simulink diagram was created using MATLAB to represent the three equations. System parameters, including spring constants and masses, are derived in detail from the physical system. The model can be used for further analysis via computer simulation in predicting dynamic response in its main docking direction, i.e., up-and-down motion.

Keywords: stewart platform, docking operation, spacecraft, spring constant

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Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

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This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: load frequency control, fuzzy-pid controller, type 2 fuzzy system, harmony search algorithm

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Authors: Chimeri Muzano Leonard

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The study was carried out to investigate the perceptions of male and female Ordinary Level students on the effects of alcohol abuse at Gatsi Secondary School. The study showed that alcohol abuse has academic, social, psychological and health effects on Ordinary Level students. The negative effects comprises of death, dropping out, poor grades, poor concentration, risky behaviors, impairment of the brain and central nervous system , risky behaviors and Impairment of reproductive functioning Only students who enrolled for Ordinary Level in the 2014 academic year participated in this study. Fifty students (25 males and 25 females) were randomly selected to participate in the study. A formal survey questionnaire was used to collect data. The respondents were asked to use a scale of 0 (totally disagree) to 10 (completely agree) to indicate the extent to which they agreed with each perception. The Statistical Package for Social Sciences (SPSS) version 19.0 was used for data analysis. The Mann Whitney U test was used to test for the significance of differences in the perceptions of male and female students. No statistically significant differences were detected between males and females in most of their perceptions regarding the effects of alcohol abuse on Ordinary Level students. However, there were three perceptions found to be significantly different between male and female. They comprises of “Peers influence one to drink alcohol”, “Alcohol abuse is a major problem among male students compared to their female peers” and “ Female students should not drink beer”.It was evident from this study that Gatsi Secondary School needs to implement more effective interventions that combat alcohol abuse. A deeper analysis of the issues that predispose Ordinary Level students to alcohol abuse should inform the interventions. Consequently, unravelling the problem of negative effects of alcohol abuse was desirable because of its potential usefulness in developing strategies that might help curb the problem and presumably improve the performance of Ordinary Level students and above all the quality of education at Gatsi Secondary School.

Keywords: perceived effects, alcohol, Gatsi Secondary School, alcohol abuse

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Authors: Sara Bilal, Abdi Omar Shuriye, Raihan Othman

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Numerical Methods is a course that can be conducted using workshops and group discussion. This study has been implemented on undergraduate students of level two at the Faculty of Engineering, International Islamic University Malaysia. The Numerical Method course has been delivered to two Sections 1 and 2 with 44 and 22 students in each section, respectively. Systematic steps have been followed to apply the student centered learning approach in teaching Numerical Method course. Initially, the instructor has chosen the topic which was Euler’s Method to solve Ordinary Differential Equations (ODE) to be learned. The students were then divided into groups with five members in each group. Initial instructions have been given to the group members to prepare their subtopics before meeting members from other groups to discuss the subtopics in an expert group inside the classroom. For the time assigned for the classroom discussion, the setting of the classroom was rearranged to accommodate the student centered learning approach. Teacher strength was by monitoring the process of learning inside and outside the class. The students have been assessed during the migrating to the expert groups, recording of a video explanation outside the classroom and during the final examination. Euler’s Method to solve the ODE was set as part of Question 3(b) in the final exam. It is observed that none of the students from both sections obtained a zero grade in Q3(b), compared to Q3(a) and Q3(c). Also, for Section 1(44 students), 29 students obtained the full mark of 7/7, while only 10 obtained 7/7 for Q3(a) and no students obtained 6/6 for Q3(c). Finally, we can recommend that the Numerical Method course be moved toward more student-centered Learning classrooms where the students will be engaged in group discussion rather than having a teacher one man show.

Keywords: teacher centered learning, student centered learning, mathematic, numerical methods

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Esmaeil Bahmyari

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The natural frequency analysis of the functionally graded (FG) rotating cylindrical shells subjected to thermal loads is studied based on the three-dimensional elasticity theory. The temperature-dependent assumption of the material properties is graded in the thickness direction, which varies based on the simple power law distribution. The governing equations and the appropriate boundary conditions, which include the effects of initial thermal stresses, are derived employing Hamilton’s principle. The initial thermo-mechanical stresses are obtained by the thermo-elastic equilibrium equation’s solution. As an efficient and accurate numerical tool, the differential quadrature method (DQM) is adopted to solve the thermo-elastic equilibrium equations, free vibration equations and natural frequencies are obtained. The high accuracy of the method is demonstrated by comparison studies with those existing solutions in the literature. Ultimately, the parametric studies are performed to demonstrate the effects of boundary conditions, temperature rise, material graded index, the thickness-to-length and the aspect ratios for the rotating cylindrical shells on the natural frequency.

Keywords: free vibration, DQM, elasticity theory, FG shell, rotating cylindrical shell

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Authors: Marcin Sowa

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The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

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Authors: Rizwan Rizwan

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This paper provides an overview of Federated Learning (FL) and its application in enhancing data security, privacy, and efficiency. FL utilizes three distinct architectures to ensure privacy is never compromised. It involves training individual edge devices and aggregating their models on a server without sharing raw data. This approach not only provides secure models without data sharing but also offers a highly efficient privacy--preserving solution with improved security and data access. Also we discusses various frameworks used in FL and its integration with machine learning, deep learning, and data mining. In order to address the challenges of multi--party collaborative modeling scenarios, a brief review FL scheme combined with an adaptive gradient descent strategy and differential privacy mechanism. The adaptive learning rate algorithm adjusts the gradient descent process to avoid issues such as model overfitting and fluctuations, thereby enhancing modeling efficiency and performance in multi-party computation scenarios. Additionally, to cater to ultra-large-scale distributed secure computing, the research introduces a differential privacy mechanism that defends against various background knowledge attacks.

Keywords: federated learning, differential privacy, gradient descent strategy, convergence, stability, threats

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Authors: A. Selmi

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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Farhad Imanshoar

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The regime or equilibrium geometry of alluvial rivers remains a topic of fundamental scientific and engineering interest. There are several approaches to analyze the problem, namely: empirical formulas, semi-theoretical methods and rational (extreme) procedures. However, none of them is widely accepted at present, due to lack of knowledge of some physical processes associated with channel formation and the simplification hypotheses imposed in order to reduce the high quantity of involved variables. The study presented in this paper shows a new approach to estimate stable width and depth of sand-bed rivers by using developed stream power equation (DSPE). At first, a new procedure based on theoretical analysis and by considering DSPE and ultimate sediment concentration were developed. Then, experimental data for regime condition in sand-bed rivers (flow depth, flow width, sediment feed rate for several cases) were gathered. Finally, the results of this research (regime equations) are compared with the field data and other regime equations. A good agreement was observed between the field data and the values resulted from developed regime equation.

Keywords: regime equations, developed stream power equation, sand-bed rivers, semi-theoretical methods

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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: Tayeb Bensattalah, Mohamed Zidour, Mohamed Ait Amar Meziane, Tahar Hassaine Daouadji, Abdelouahed Tounsi

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In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Influence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.

Keywords: boundary conditions, buckling, non-local, differential transform method

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Temur Chilachava

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In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two various widespread languages, taking into account demographic factor is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state formation, an autonomy), exposed to bilateral assimilation from two rather powerful states. Earlier by us it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model "predator - the victim", thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilator. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model "a predator – the victim", with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states.

Keywords: nonlinear mathematical model, bilateral assimilation, demographic factor, first integrals, result of assimilation, intervals of change of number of the population

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov

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Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done.

Keywords: dynamics of polymeric liquid, heat dissipation, singularly perturbed problem, pseudospectral method, Chebyshev polynomials, stabilization technique

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Authors: Emmanuel Omokhuale

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A mathematical model is presented to study free convective boundary layer flow in a semi-infinite vertical cylinder with heat sink effect in a porous medium. The governing dimensional governing partial differential equations (PDEs) with corresponding initial and boundary conditions are approximated and solved numerically employing finite difference method (FDM) the implicit type. Stability and convergence of the scheme are also established. Furthermore, the influence of significant physical parameters on the flow characteristics was analysed and shown graphically. The obtained results are benchmarked with previously published works in order to access the accuracy of the numerical method and found to be in good agreement.

Keywords: free convection flow, vertical cylinder, implicit finite difference method, heat sink and porous medium

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent

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Studies concerning the microstructures are becoming more important as the utilization of various micro-electro mechanical systems (MEMS) are increasing. Thus in recent years, thermal buckling and vibration analysis of microstructures have been subject to many investigations that are utilizing different numerical methods. In this study, thermal effects on mechanical response of a functionally graded (FG) Timoshenko micro-beam are presented in the framework of a mixed finite element formulation. Size effects are taken into consideration via modified couple stress theory. The mixed formulation is based on a function which in turn is derived via Gateaux Differential scientifically. After the resolution of all field equations of the beam, a potential operator is carefully constructed. Then this operator is used for the manufacturing of the functional. Usual procedures of finite element approximation are utilized for the derivation of the mixed finite element equations once the potential is obtained. Resulting finite element formulation allows usage of C₀ type simple linear shape functions and avoids shear-locking phenomena, which is a common shortcoming of the displacement-based formulations of moderately thick beams. The developed numerical scheme is used to obtain the effects of thermal loads on the static bending, free vibration and buckling of FG Timoshenko micro-beams for different power-law parameters, aspect ratios and boundary conditions. The versatility of the mixed formulation is presented over other numerical methods such as generalized differential quadrature method (GDQM). Another attractive property of the formulation is that it allows direct calculation of the contribution of micro effects on the overall mechanical response.

Keywords: micro-beam, functionally graded materials, thermal effect, mixed finite element method

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Authors: Vikas Kumar

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The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. Thus, the obtained results are presented numerically and graphically in the paper.

Keywords: axi-symmetric, ferrofluid, magnetic field, porous rotating disk

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Safitri W. Nur, Prathisto Panuntun L. Unggul, M. Ivan Adi Perdana, R. Dary Wira Mahadika

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On soft soil areas, high embankment as a preloading needed to improve the bearing capacity of the soil. For sustainable development, the construction of embankment must not disturb the area around of them. So, the influence area must be known before the contractor applied their embankment design. For several cases in Indonesia, the area around of embankment construction is housing resident and other building. So that, the influence area must be identified to avoid the differential settlement occurs on the buildings around of them. Differential settlement causes the building crack. Each building has a limited tolerance for the differential settlement. For concrete buildings, the tolerance is 0,002 – 0,003 m and for steel buildings, the tolerance is 0,006 – 0,008 m. If the differential settlement stands on the range of that value, building crack can be avoided. In fact, the settlement around of embankment is assumed as zero. Because of that, so many problems happen when high embankment applied on soft soil area. This research used the superposition method combined with plaxis analysis to know the influences area around of embankment in some location with the differential characteristic of the soft soil. The undisturbed soil samples take on 55 locations with undisturbed soil samples at some soft soils location in Indonesia. Based on this research, it was concluded that the effects of embankment variation are if more gentle the slope, the influence area will be greater and vice versa. The largest of the influence area with h initial embankment equal to 2 - 6 m with slopes 1:1, 1:2, 1:3, 1:4, 1:5, 1:6, 1:7, 1:8 is 32 m from the edge of the embankment.

Keywords: differential settlement, embankment, influence area, slope, soft soil

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Authors: Fikret Yalcinkaya, Hamza Unsal

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To understand how neurons work, it is required to combine experimental studies on neural science with numerical simulations of neuron models in a computer environment. In this regard, the simplicity and applicability of spiking neuron modeling functions have been of great interest in computational neuron science and numerical neuroscience in recent years. Spiking neuron models can be classified by exhibiting various neuronal behaviors, such as spiking and bursting. These classifications are important for researchers working on theoretical neuroscience. In this paper, three different spiking neuron models; Izhikevich, Adaptive Exponential Integrate Fire (AEIF) and Hindmarsh Rose (HR), which are based on first order differential equations, are discussed and compared. First, the physical meanings, derivatives, and differential equations of each model are provided and simulated in the Matlab environment. Then, by selecting appropriate parameters, the models were visually examined in the Matlab environment and it was aimed to demonstrate which model can simulate well-known biological neuron behaviours such as Tonic Spiking, Tonic Bursting, Mixed Mode Firing, Spike Frequency Adaptation, Resonator and Integrator. As a result, the Izhikevich model has been shown to perform Regular Spiking, Continuous Explosion, Intrinsically Bursting, Thalmo Cortical, Low-Threshold Spiking and Resonator. The Adaptive Exponential Integrate Fire model has been able to produce firing patterns such as Regular Ignition, Adaptive Ignition, Initially Explosive Ignition, Regular Explosive Ignition, Delayed Ignition, Delayed Regular Explosive Ignition, Temporary Ignition and Irregular Ignition. The Hindmarsh Rose model showed three different dynamic neuron behaviours; Spike, Burst and Chaotic. From these results, the Izhikevich cell model may be preferred due to its ability to reflect the true behavior of the nerve cell, the ability to produce different types of spikes, and the suitability for use in larger scale brain models. The most important reason for choosing the Adaptive Exponential Integrate Fire model is that it can create rich ignition patterns with fewer parameters. The chaotic behaviours of the Hindmarsh Rose neuron model, like some chaotic systems, is thought to be used in many scientific and engineering applications such as physics, secure communication and signal processing.

Keywords: Izhikevich, adaptive exponential integrate fire, Hindmarsh Rose, biological neuron behaviours, spiking neuron models

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Authors: Mohamed Abdel-Monem, Gamal Sowilam, Omar Hegazy

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This paper presents a technical assessment of an electric vehicle with two independent rear-wheel motor and an improved traction control system. The electric differential and the control strategy have been implemented to assure that in a straight trajectory, the two rear-wheels run exactly at the same speed, considering the same/different road conditions under the left and right side of the wheels. In case of turning to right/left, the difference between the two rear-wheels speeds assures a vehicle trajectory without sliding, thanks to a harmony between the electric differential and the control strategy. The present article demonstrates a complete model and analysis of a traction control system, considering four different traction scenarios, for two independent rear-wheels motors for electric vehicles. Furthermore, the vehicle model, including wheel dynamics, load forces, electric differential, and control strategy, is designed and verified by using MATLAB/Simulink environment.

Keywords: electric vehicle, energy saving, multi-motor, electric differential, simulation and control

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Authors: Jorge Gonzalez-Camus

Abstract:

In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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