Search results for: evolutionary equations of electromagnetic theory of time-domain

Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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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: Mehrdad N. Khajavi, Abbas Hosseini, N.Bani Mostafa

Abstract:

In this paper two different Antilock braking system (ABS) are simulated and compared. One is the ordinary hydraulic ABS system which we call it ABS and the other is Electromagnetic Antilock braking system which is called (EMABS) the basis of performance of an EMABS is based upon Electromagnetic force. In this system there is no need to use servo hydraulic booster which are used in ABS system. In EMABS to generate the desired force we have use a magnetic relay which works with an input voltage through an air gap (g). The generated force will be amplified by the relay arm, and is applied to the brake shoes and thus the braking torque is generated. The braking torque is proportional to the applied electrical voltage E. to adjust the braking torque it is only necessary to regulate the electrical voltage E which is very faster and has a much smaller time constant T than the ABS system. The simulations of these two different ABS systems are done with MATLAB/SIMULINK software and the superiority of the EMABS has been shown.

Keywords: ABS, EMABS, ECU

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Authors: Jagabondhu Hazra, Avinash Sinha

Abstract:

Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional G-Brownian motion, Taylor’s series of fractional order, uncertain volatility.

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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: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

Abstract:

The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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Authors: Maumita Bhattacharya

Abstract:

Optimization is often a critical issue for most system design problems. Evolutionary Algorithms are population-based, stochastic search techniques, widely used as efficient global optimizers. However, finding optimal solution to complex high dimensional, multimodal problems often require highly computationally expensive function evaluations and hence are practically prohibitive. The Dynamic Approximate Fitness based Hybrid EA (DAFHEA) model presented in our earlier work [14] reduced computation time by controlled use of meta-models to partially replace the actual function evaluation by approximate function evaluation. However, the underlying assumption in DAFHEA is that the training samples for the meta-model are generated from a single uniform model. Situations like model formation involving variable input dimensions and noisy data certainly can not be covered by this assumption. In this paper we present an enhanced version of DAFHEA that incorporates a multiple-model based learning approach for the SVM approximator. DAFHEA-II (the enhanced version of the DAFHEA framework) also overcomes the high computational expense involved with additional clustering requirements of the original DAFHEA framework. The proposed framework has been tested on several benchmark functions and the empirical results illustrate the advantages of the proposed technique.

Keywords: Evolutionary algorithm, Fitness function, Optimization, Meta-model, Stochastic method.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil

Abstract:

In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

Keywords: Reduced Order Modeling, Stability, Mihailov Stability Criterion, Continued Fraction Expansions, Differential Evolution, Integral Squared Error.

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Authors: S. Damodaran, T. V. S.Sekhar

Abstract:

The motion of a sphere moving along the axis of a rotating viscous fluid is studied at high Reynolds numbers and moderate values of Taylor number. The Higher Order Compact Scheme is used to solve the governing Navier-Stokes equations. The equations are written in the form of Stream function, Vorticity function and angular velocity which are highly non-linear, coupled and elliptic partial differential equations. The flow is governed by two parameters Reynolds number (Re) and Taylor number (T). For very low values of Re and T, the results agree with the available experimental and theoretical results in the literature. The results are obtained at higher values of Re and moderate values of T and compared with the experimental results. The results are fourth order accurate.

Keywords: Navier_Stokes equations, Taylor number, Reynolds number, Higher order compact scheme, Rotating Fluid.

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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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.I Sulaiman, T.K Abdul Rahman, I. Musirin, S. Shaari

Abstract:

This paper presents performance analysis of the Evolutionary Programming-Artificial Neural Network (EPANN) based technique to optimize the architecture and training parameters of a one-hidden layer feedforward ANN model for the prediction of energy output from a grid connected photovoltaic system. The ANN utilizes solar radiation and ambient temperature as its inputs while the output is the total watt-hour energy produced from the grid-connected PV system. EP is used to optimize the regression performance of the ANN model by determining the optimum values for the number of nodes in the hidden layer as well as the optimal momentum rate and learning rate for the training. The EPANN model is tested using two types of transfer function for the hidden layer, namely the tangent sigmoid and logarithmic sigmoid. The best transfer function, neural topology and learning parameters were selected based on the highest regression performance obtained during the ANN training and testing process. It is observed that the best transfer function configuration for the prediction model is [logarithmic sigmoid, purely linear].

Keywords: Artificial neural network (ANN), Correlation coefficient (R), Evolutionary programming-ANN (EPANN), Photovoltaic (PV), logarithmic sigmoid and tangent sigmoid.

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Authors: Ivan Yatchev, Ewen Ritchie

Abstract:

Comparison of two approaches for the simulation of the dynamic behaviour of a permanent magnet linear actuator is presented. These are full coupled model, where the electromagnetic field, electric circuit and mechanical motion problems are solved simultaneously, and decoupled model, where first a set of static magnetic filed analysis is carried out and then the electric circuit and mechanical motion equations are solved employing bi-cubic spline approximations of the field analysis results. The results show that the proposed decoupled model is of satisfactory accuracy and gives more flexibility when the actuator response is required to be estimated for different external conditions, e.g. external circuit parameters or mechanical loads.

Keywords: Coupled problems, dynamic models, finite elementanalysis, linear actuators, permanent magnets.

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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: Parvinder Singh Sandhu, Sumeet Kaur Sehra, Karmjit Kaur

Abstract:

Phylogenetic tree is a graphical representation of the evolutionary relationship among three or more genes or organisms. These trees show relatedness of data sets, species or genes divergence time and nature of their common ancestors. Quality of a phylogenetic tree requires parsimony criterion. Various approaches have been proposed for constructing most parsimonious trees. This paper is concerned about calculating and optimizing the changes of state that are needed called Small Parsimony Algorithms. This paper has proposed enhanced small parsimony algorithm to give better score based on number of evolutionary changes needed to produce the observed sequence changes tree and also give the ancestor of the given input.

Keywords: Phylogenetic Analysis, Small Parsimony, EnhancedFitch Algorithm, Enhanced Sakoff Algorithm.

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Authors: Emanuele Stomeo, Tatiana Kalganova, Cyrille Lambert

Abstract:

Evolvable hardware (EHW) is a developing field that applies evolutionary algorithm (EA) to automatically design circuits, antennas, robot controllers etc. A lot of research has been done in this area and several different EAs have been introduced to tackle numerous problems, as scalability, evolvability etc. However every time a specific EA is chosen for solving a particular task, all its components, such as population size, initialization, selection mechanism, mutation rate, and genetic operators, should be selected in order to achieve the best results. In the last three decade the selection of the right parameters for the EA-s components for solving different “test-problems" has been investigated. In this paper the behaviour of mutation rate for designing logic circuits, which has not been done before, has been deeply analyzed. The mutation rate for an EHW system modifies the number of inputs of each logic gates, the functionality (for example from AND to NOR) and the connectivity between logic gates. The behaviour of the mutation has been analyzed based on the number of generations, genotype redundancy and number of logic gates for the evolved circuits. The experimental results found provide the behaviour of the mutation rate during evolution for the design and optimization of simple logic circuits. The experimental results propose the best mutation rate to be used for designing combinational logic circuits. The research presented is particular important for those who would like to implement a dynamic mutation rate inside the evolutionary algorithm for evolving digital circuits. The researches on the mutation rate during the last 40 years are also summarized.

Keywords: Design of logic circuit, evolutionary computation, evolvable hardware, mutation rate.

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Authors: Amna Noreen , Kare Olaussen

Abstract:

We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.

Keywords: Eigenvalue problems, bound states, trapezoidal rule, poisson resummation.

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Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay

Abstract:

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.

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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: M.R.Isvandzibaei, P.J.Awasare

Abstract:

In this paper a study on the vibration of thin cylindrical shells with ring supports and made of functionally graded materials (FGMs) composed of stainless steel and nickel is presented. Material properties vary along the thickness direction of the shell according to volume fraction power law. The cylindrical shells have ring supports which are arbitrarily placed along the shell and impose zero lateral deflections. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The analysis is carried out using Hamilton-s principle. The governing equations of motion of FGM cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

Keywords: Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.

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Authors: Mounir Zekkaoui, Abdelhadi Fennan

Abstract:

The software evolution control requires a deep understanding of the changes and their impact on different system heterogeneous artifacts. And an understanding of descriptive knowledge of the developed software artifacts is a prerequisite condition for the success of the evolutionary process. The implementation of an evolutionary process is to make changes more or less important to many heterogeneous software artifacts such as source code, analysis and design models, unit testing, XML deployment descriptors, user guides, and others. These changes can be a source of degradation in functional, qualitative or behavioral terms of modified software. Hence the need for a unified approach for extraction and representation of different heterogeneous artifacts in order to ensure a unified and detailed description of heterogeneous software artifacts, exploitable by several software tools and allowing to responsible for the evolution of carry out the reasoning change concerned.

Keywords: Heterogeneous software artifacts, Software evolution control, Unified approach, Meta Model, Software Architecture.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: Da-Xue Chen, Guang-Hui Liu

Abstract:

In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples.

Keywords: Oscillation theorem, second-order nonlinear neutral dynamic equation, variable delay, damping, Riccati transformation.

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Authors: Piotr Podlipniak

Abstract:

This paper proposes that in the course of evolution pitch structure became a human specific tool of communication the function of which is to induce emotional states such as uncertainty and cohesion. By the means of eliciting these emotions during collective music performance people are able to unconsciously give cues concerning social acceptance. This is probably one of the reasons why in all cultures people collectively perform tonal music. It is also suggested that tonal pitch structure had been invented socially before it became an evolutionary innovation of hominines. It means that a predisposition to tonally organize pitches evolved by the means of ‘Baldwin effect’ – a process in which natural selection transforms the learned response of an organism into the instinctive response. In the proposed, hypothetical evolutionary scenario of the emergence of tonal pitch structure social forces such as a need for closer cooperation play the crucial role.

Keywords: Emotion, evolution, tonality, social consolidation.

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Authors: Deepak Kumar, Vivek Kumar, V. P. Singh

Abstract:

This paper describes a steady state model of a multiple effect evaporator system for simulation and control purposes. The model includes overall as well as component mass balance equations, energy balance equations and heat transfer rate equations for area calculations for all the effects. Each effect in the process is represented by a number of variables which are related by the energy and material balance equations for the feed, product and vapor flow for backward, mixed and split feed. For simulation 'fsolve' solver in MATLAB source code is used. The optimality of three sequences i.e. backward, mixed and splitting feed is studied by varying the various input parameters.

Keywords: MATLAB "fsolve" solver, multiple effectevaporators, black liquor, feeding sequences.

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

Abstract:

We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: Run-up waves, Shallow water equations, finite volume method, wet/dry interface, dam-break problem.

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Authors: Jinfeng Wang, Yang Liu, Hong Li

Abstract:

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations

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Authors: Dezhi Liu Guiyuan Yang Wei Zhang

Abstract:

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.

Keywords: Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

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Authors: Xu LiYun, Briand Florent, Fan GuoLiang

Abstract:

The loop-layout design problem (LLDP) aims at optimizing the sequence of positioning of the machines around the cyclic production line. Traffic congestion is the usual criteria to minimize in this type of problem, i.e. the number of additional cycles spent by each part in the network until the completion of its required routing sequence of machines. This paper aims at applying several improvements mechanisms such as a positioned-based crossover operator for the Genetic Algorithm (GA) called a Two Points Crossover (TPC) and an offspring selection process. The performance of the improved GA is measured using well-known examples from literature and compared to other evolutionary algorithms. Good results show that GA can still be competitive for this type of problem against more recent evolutionary algorithms.

Keywords: Crossover, genetic algorithm, layout design problem, loop-layout, manufacturing optimization.

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