Search results for: phase differential.

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: V.V. Lyahov, V.M. Neshchadim

Abstract:

The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: Yanling Zhu

Abstract:

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: S. A. Eftekhari

Abstract:

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Keywords: Dam-reservoir system, Differential quadrature method, Fluid-structure interaction, Galerkin method, Integral quadrature method.

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Authors: R. Kongnuy, E. Naowanich, T. Kruehong

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An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: Bing Yu , Xingshi He

Abstract:

In this paper, Differential Evolution (DE) algorithm, a new promising evolutionary algorithm, is proposed to train Radial Basis Function (RBF) network related to automatic configuration of network architecture. Classification tasks on data sets: Iris, Wine, New-thyroid, and Glass are conducted to measure the performance of neural networks. Compared with a standard RBF training algorithm in Matlab neural network toolbox, DE achieves more rational architecture for RBF networks. The resulting networks hence obtain strong generalization abilities.

Keywords: differential evolution, neural network, Rbf function

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Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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Authors: S. Khamsawang, S. Jiriwibhakorn

Abstract:

This paper proposes an application of the differential evolution (DE) algorithm for solving the economic dispatch problem (ED). Furthermore, the regenerating population procedure added to the conventional DE in order to improve escaping the local minimum solution. To test performance of DE algorithm, three thermal generating units with valve-point loading effects is used for testing. Moreover, investigating the DE parameters is presented. The simulation results show that the DE algorithm, which had been adjusted parameters, is better convergent time than other optimization methods.

Keywords: Differential evolution, Economic dispatch problem, Valve-point loading effect, Optimization method.

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Authors: Davod Khojasteh Salkuyeh

Abstract:

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.

Keywords: Ordinary differential equations, optimal stepsize, error, stochastic arithmetic, CESTAC, CADNA.

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Authors: M. Y. Ismail, M. Inam, A. F. M. Zain, N. Misran

Abstract:

Progressive phase distribution is an important consideration in reflectarray antenna design which is required to form a planar wave in front of the reflectarray aperture. This paper presents a detailed mathematical model in order to determine the required reflection phase values from individual element of a reflectarray designed in Ku-band frequency range. The proposed technique of obtaining reflection phase can be applied for any geometrical design of elements and is independent of number of array elements. Moreover the model also deals with the solution of reflectarray antenna design with both centre and off-set feed configurations. The theoretical modeling has also been implemented for reflectarrays constructed on 0.508mm thickness of different dielectric substrates. The results show an increase in the slope of the phase curve from 4.61°/mm to 22.35°/mm by varying the material properties.

Keywords: Mathematical modeling, Progressive phase distribution, Reflectarray antenna, Reflection phase.

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Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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Authors: Xiguang Li

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.

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Authors: H. Megherbi, A. C. Megherbi, N. Megherbi, K. Benmahamed

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This paper presents three-phase evolution search methodology to automatically design fuzzy logic controllers (FLCs) that can work in a wide range of operating conditions. These include varying load, parameter variations, and unknown external disturbances. The three-phase scheme consists of an exploration phase, an exploitation phase and a robustness phase. The first two phases search for FLC with high accuracy performances while the last phase aims at obtaining FLC providing the best compromise between the accuracy and robustness performances. Simulations were performed for direct-drive two-axis robot arm. The evolved FLC with the proposed design technique found to provide a very satisfactory performance under the wide range of operation conditions and to overcome problem associated with coupling and nonlinearities characteristics inherent to robot arms.

Keywords: Fuzzy logic control, evolutionary algorithms, robustness, exploration/exploitation phase.

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Authors: Ondrej Baran, Miroslav Kasal, Petr Vagner, Tomas Urbanec

Abstract:

This paper deals with the modeling and the evaluation of a multiplicative phase noise influence on the bit error ratio in a general space communication system. Our research is focused on systems with multi-state phase shift keying modulation techniques and it turns out, that the phase noise significantly affects the bit error rate, especially for higher signal to noise ratios. These results come from a system model created in Matlab environment and are shown in a form of constellation diagrams and bit error rate dependencies. The change of a user data bit rate is also considered and included into simulation results. Obtained outcomes confirm theoretical presumptions.

Keywords: Additive thermal noise, AWGN, BER, bit error rate, multiplicative phase noise, phase shift keying.

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Authors: Rahul Bansal, Sudipta Majumdar

Abstract:

This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Mohd Tariq

Abstract:

The three phase system drives produce the problem of more torque pulsations and harmonics. This issue prevents the smooth operation of the drives and it also induces the amount of heat generated thus resulting in an increase in power loss. Higher phase system offers smooth operation of the machines with greater power capacity. Five phase variable-speed induction motor drives are commonly used in various industrial and commercial applications like tractions, electrical vehicles, ship propulsions and conveyor belt drive system. In this work, a comparative analysis of the different modulation schemes applied on the five-level five-phase Packed U Cell (PUC) inverter fed induction motor drives is presented. The performance of the inverter is greatly affected with the modulation schemes applied. The system is modeled, designed, and implemented in MATLAB^®/Simulink environment. Experimental validation is done for the prototype of single phase, whereas five phase experimental validation is proposed in the future works.

Keywords: Packed U-Cell inverter, pulse width modulation, five-phase system, induction motor.

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Authors: Emin Özyılmaz

Abstract:

In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.

Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.

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Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: S. Firouzi, M.R. Alizadeh, S. Minaei

Abstract:

A study was carried out at the Rice Research Institute of Iran (RRII) to investigate the effect of rollers differential peripheral speed of commercial rubber roll husker and paddy moisture content on the husking index and percentage of broken rice. The experiment was conducted at six levels of rollers differential speed (1.5, 2.2, 2.9, 3.6, 4.3 and 5 m/s) and three levels of paddy moisture content (8-9, 10-11 and 12-13% w.b.). Two common paddy varieties namely, Binam and Khazer, were selected for this study. Results revealed that the effect of rollers differential speed and moisture content significantly (P<0.01) affected percentage of broken brown rice and paddy husking index. Average broken kernel percentage increased from 13 to 14.61% while husking index decreased from 71.64 to 61.81%, as paddy moisture content increased from 8-9 to 12-13%. It was observed that amount of broken rice decreased from 18.83 to 9.97%, when rollers differential speed varied from 1.5 to 5 m/s, while the husking index initially increased and then started to decrease. The mean value of husking index for Khazar variety (64.71%) was significantly lower than that for Binam variety (69.2%). It was concluded that rollers differential speed of 2.9 m/s and moisture content of 8-9% was the most appropriate combination for paddy husking of Binam and Khazar varieties in rubber roll husker.

Keywords: husking index, moisture content, paddy, rubber roll husker.

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Authors: R. S. Hassani, S. Chikh, L. Tadrist, S. Radev

Abstract:

A bubbly flow in a vertical miniature tube is analyzed theoretically. The liquid and gas phase are co-current flowing upward. The gas phase is injected via a nozzle whose inner diameter is 0.11mm and it is placed on the axis of the tube. A force balance is applied on the bubble at its detachment. The set of governing equations are solved by use of Mathematica software. The bubble diameter and the bubble generation frequency are determined for various inlet phase velocities represented by the inlet mass quality. The results show different behavior of bubble growth and detachment depending on the tube size.

Keywords: Two phase flow, bubble growth, minichannel, generation frequency.

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Authors: Saleh A. Al-Jufout

Abstract:

This paper presents a procedure of forming the mathematical model of radial electric power systems for simulation of both transient and steady-state conditions. The research idea has been based on nodal voltages technique and on differentiation of Kirchhoff's current law (KCL) applied to each non-reference node of the radial system, the result of which the nodal voltages has been calculated by solving a system of algebraic equations. Currents of the electric power system components have been determined by solving their respective differential equations. Transforming the three-phase coordinate system into Cartesian coordinate system in the model decreased the overall number of equations by one third. The use of Cartesian coordinate system does not ignore the DC component during transient conditions, but restricts the model's implementation for symmetrical modes of operation only. An example of the input data for a four-bus radial electric power system has been calculated.

Keywords: Mathematical Modelling, Radial Power System, Steady-State, Transients

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Authors: M. Yousefi, N. Nasirzadeh

Abstract:

In this paper, behavior of an oscillator under injection of another signal has been investigated. Also, variation of output signal amplitude versus injected signal phase variation, the effect of varying the amplitude of injected signal and quality factor of the oscillator has been investigated. The results show that the locking time depends on phase and the best locking time happens at 180-degrees phase. Also, the effect of injected lock has been discussed. Simulations show that the locking time decreases with signal injection to bulk. Locking time has been investigated versus various phase differences. The effect of phase and amplitude changes on locking time of a typical LC oscillator in 180 nm technology has been investigated.

Keywords: Injection-lock oscillator, oscillator, analysis, phase modulation.

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Authors: Zakir Husain

Abstract:

This paper presents modeling and analysis of 12-phase distribution static compensator (DSTATCOM), which is capable of balancing the source currents in spite of unbalanced loading and phase outages. In addition to balance the supply current, the power factor can be set to a desired value. The theory of instantaneous symmetrical components is used to generate the twelve-phase reference currents. These reference currents are then tracked using current controlled voltage source inverter, operated in a hysteresis band control scheme. An ideal compensator in place of physical realization of the compensator is used. The performance of the proposed DTATCOM is validated through MATLAB simulation and detailed simulation results are given.

Keywords: DSTATCOM, Modeling, Load balancing, Multiphase, Power factor correction.

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Authors: Hideki Yoshikawa, Masahiro Kaminaga, Arimitsu Shikoda, Toshinori Suzuki

Abstract:

Round addition differential fault analysis using operation skipping for lightweight block ciphers with on-the-fly key scheduling is presented. For 64-bit KLEIN, it is shown that only a pair of correct and faulty ciphertexts can be used to derive the secret master key. For PRESENT, one correct ciphertext and two faulty ciphertexts are required to reconstruct the secret key. Furthermore, secret key extraction is demonstrated for the LBlock Feistel-type lightweight block cipher.

Keywords: Differential Fault Analysis (DFA), round addition, block cipher, on-the-fly key schedule.

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Authors: K.H.Khairul Anuar, K.I.Othman, F.Ishak, Z.B.Ibrahim, Z.Majid

Abstract:

Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum error

Keywords: Adam Block Method, BDF, Ordinary Differential Equations, Partitioning Block Intervalwise

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Authors: A. Jawahar

Abstract:

In this paper, the dependence of soliton pulses with respect to phase in a 10Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the ‘I’ also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point (I).

Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system.

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