Showing papers in "Mathematical Problems in Engineering in 2008"
TL;DR: In this article, the flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated, and the unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions.
Abstract: The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.
136 citations
TL;DR: It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands and this generalization coincides with the Shannon wavelet reconstruction of functions.
Abstract: Shannon wavelets are studied together with their differential properties (known as connection coefficients). It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of functions. The differential properties of Shannon wavelets are also studied through the connection coefficients. It is shown that Shannon wavelets are -functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series. These coefficients make it possible to define the wavelet reconstruction of the derivatives of the -functions.
98 citations
TL;DR: In this paper, a variational homotopy perturbation method (VHPM) was proposed for solving higher dimensional initial boundary value problems with variable coefficients, which is suitable for use in these problems.
Abstract: We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM). We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.
87 citations
TL;DR: A method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system is described.
Abstract: Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC) or an adaptive fuzzy sliding mode controller (AFSMC) capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.
74 citations
TL;DR: In this article, a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order is presented.
Abstract: This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed.
62 citations
TL;DR: The main aim of as discussed by the authors is to use some general results from the general theory of elliptic equations in order to obtain some qualitative results in a concrete and very applicative situation.
Abstract: The main aim of our study is to use some general results from the general theory
of elliptic equations in order to obtain some qualitative results in a concrete
and very applicative situation. In fact, we will prove the existence and uniqueness
of the generalized solutions for the boundary value problems in elasticity of initially
stressed bodies with voids (porous materials).
57 citations
TL;DR: In this paper, three different artificial neural network (ANN) methods, namely, feed-forward back-propagation (FFBP), radial basis function (RBF), and generalized regression neural networks (GRNNs), were applied to predict peak ground acceleration (PGA).
Abstract: Three different artificial neural network (ANN) methods, namely, feed-forward back-propagation (FFBP), radial basis function (RBF), and generalized regression neural networks (GRNNs) were applied to predict peak ground acceleration (PGA). Ninety five three-component records from 15 ground motions that occurred in Northwestern Turkey between 1999 and 2001 were used during the applications. The earthquake moment magnitude, hypocentral distance, focal depth, and site conditions were used as inputs to estimate PGA for vertical (U-D), east-west (E-W), and north-south (N-S) directions. The direction of the maximum PGA of the three components was also added to the input layer to obtain the maximum PGA. Testing stage results of three ANN methods indicated that the FFBPs were superior to the GRNN and the RBF for all directions. The PGA values obtained from the FFBP were modified by linear regression analysis. The results showed that these modifications increased the prediction performances.
56 citations
TL;DR: In this article, it was shown that the parameters and the odds ratio estimates obtained via conditional exact logistic regression are different from those obtained via unconditional asymptotic logistic regressions.
Abstract: The general approach to modeling binary data for the purpose of estimating the propagation of an internal solitary wave (ISW) is based on the maximum likelihood estimate (MLE) method. In cases where the number of observations in the data is small, any inferences made based on the asymptotic distribution of changes in the deviance may be unreliable for binary data (the model's lack of fit is described in terms of a quantity known as the deviance). The deviance for the binary data is given by D. Collett (2003). may be unreliable for binary data. Logistic regression shows that the -values for the likelihood ratio test and the score test are both 0.05. However, the null hypothesis is not rejected in the Wald test. The seeming discrepancies in -values obtained between the Wald test and the other two tests are a sign that the large-sample approximation is not stable. We find that the parameters and the odds ratio estimates obtained via conditional exact logistic regression are different from those obtained via unconditional asymptotic logistic regression. Using exact results is a good idea when the sample size is small and the approximate -values are 0.10. Thus in this study exact analysis is more appropriate.
48 citations
TL;DR: In this article, the modified variational iteration method (MVIM) was applied for solving the singular and nonsingular initial and boundary value problems in the problem of boundary value estimation.
Abstract: We apply the modified variational iteration method (MVIM) for solving the singular and nonsingular initial and boundary value problems in this paper. The proposed modification is made by introducing Adomian's polynomials in the correct functional. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the solution without any discretization, linearization, perturbation, or restrictive assumptions. Several examples are given to verify the efficiency and reliability of the suggested algorithm.
47 citations
TL;DR: In this article, the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays are investigated, and the stability results are formulated based on Gronwall's lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time.
Abstract: This paper investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwall's lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky-Lyapunov functional for all the above-mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time-varying systems are also discussed.
47 citations
TL;DR: In this article, Ghorbani et al. applied the variational iteration method using He's polynomials (VIMHP) for solving the fifth-order boundary value problems.
Abstract: We apply the variational iteration method using He's polynomials (VIMHP) for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to Ghorbani (2007). The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.
TL;DR: In this article, robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty, by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope.
Abstract: Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.
TL;DR: In this paper, a geometrically exact formulation of cables suffering axis stretching and flexural curvature is presented, which is based on nonlinearly viscoelastic constitutive laws for the tension and bending moment with the additional constitutive nonlinearity accounting for the no-compression condition.
Abstract: A geometrically exact formulation of cables suffering axis stretching and flexural curvature is presented. The dynamical formulation is based on nonlinearly viscoelastic constitutive laws for the tension and bending moment with the additional constitutive nonlinearity accounting for the no-compression condition. A continuation method, combined with a mixed finite-difference spatial discretization, is then employed to path-follow the static responses of cables subject to forces or support displacements. These computations, conducted in the quasistatic regime, are based on cables with linearly elastic material behaviors, whereas the nonlinearity is in the geometric stiffness terms and the no-compression behavior. The finite-difference results have been confirmed employing a weak formulation based on quadratic Lagrangian finite elements. The influence of the flexural stiffness on the nonlinear static responses is assessed comparing the results with those obtained for purely extensible cables. The properties of the frequencies of the linear normal modes of cables with flexural stiffness are also investigated and compared with those of purely extensible cables.
TL;DR: In this article, a novel variation of the vehicle routing problem (VRP) is presented, where customers are labeled as either cargo sink or cargo source, depending on their pickup or delivery demand.
Abstract: We present a novel variation of the vehicle routing problem (VRP). Single commodity cargo with pickup and delivery service is considered. Customers are labeled as either cargo sink or cargo source, depending on their pickup or delivery demand. This problem is called a single commodity vehicle routing problem with pickup and delivery service (1-VRPPD). 1-VRPPD deals with multiple vehicles and is the same as the single-commodity traveling salesman problem (1-PDTSP) when the number of vehicles is equal to 1. Since 1-VRPPD specializes VRP, it is 𝒩𝒫 hard in the strong sense. Iterative modified simulated annealing (IMSA) is presented along with greedy random-based initial solution algorithm. IMSA provides a good approximation to the global optimum in a large search space. Experiment is done for the instances with different number of customers and their demands. With respect to average values of IMSA execution times, proposed method is appropriate for practical applications.
TL;DR: Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory as discussed by the authors.
Abstract: Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory Comparison is made between the exact solutions and the results of the variational iteration method (VIM) The results reveal that this method is very effective and simple, and that it yields the exact solutions It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems
TL;DR: In this paper, sufficient linear matrix inequality (LMI) conditions for robust stability analysis and robust synthesis of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented.
Abstract: Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.
TL;DR: In this paper, the main object of the present paper is to theoretically solve the viscous flow of either a finite or infinite depth, which is driven by moving plane(s).
Abstract: The main object of the present study is to theoretically solve the viscous flow of either a finite or infinite depth, which is driven by moving plane(s). Such a viscous flow is usually named as Stokes' first or second problems, which indicates the fluid motion driven by the impulsive or oscillating motion of the boundary, respectively. Traditional Stokes' problems are firstly revisited, and three extended problems are subsequently examined. Using some mathematical techniques and integral transforms, complete solutions which can exactly capture the flow characteristics at any time are derived. The corresponding steady-state and transient solutions are readily determined on the basis of complete solutions. Current results have wide applications in academic researches and are of significance for future studies taking more boundary conditions and non-Newtonian fluids into account.
TL;DR: In this paper, He's variational iteration method (VIM) was extended to find the approximate solutions for nonlinear differential-difference equation, and the results reveal that the method is very effective and simple.
Abstract: We extend He's variational iteration method (VIM) to find the approximate solutions for nonlinear differential-difference equation. Simple but typical examples are applied to illustrate the validity and great potential of the generalized variational iteration method in solving nonlinear differential-difference equation. The results reveal that the method is very effective and simple. We find the extended method for nonlinear differential-difference equation is of good accuracy.
TL;DR: The proposed INMF approach is based on a novel constraint criterion and the previous block strategy, and has some good properties, such as low computational complexity, sparse coefficient matrix, and can be applied to incremental learning.
Abstract: Nonnegative matrix factorization (NMF) is a promising approach for local feature extraction in face recognition tasks. However, there are two major drawbacks in almost all existing NMF-based methods. One shortcoming is that the computational cost is expensive for large matrix decomposition. The other is that it must conduct repetitive learning, when the training samples or classes are updated. To overcome these two limitations, this paper proposes a novel incremental nonnegative matrix factorization (INMF) for face representation and recognition. The proposed INMF approach is based on a novel constraint criterion and our previous block strategy. It thus has some good properties, such as low computational complexity, sparse coefficient matrix. Also, the coefficient column vectors between different classes are orthogonal. In particular, it can be applied to incremental learning. Two face databases, namely FERET and CMU PIE face databases, are selected for evaluation. Compared with PCA and some state-of-the-art NMF-based methods, our INMF approach gives the best performance.
TL;DR: In this article, the heat transfer characteristics of natural convection about a vertical permeable flat surface embedded in a saturated porous medium are studied by taking into account the thermal radiation effect.
Abstract: In this article, the heat transfer characteristics of natural convection about a vertical permeable flat surface embedded in a saturated porous medium are studied by taking into account the thermal radiation effect. The plate is assumed to have a power-law temperature distribution. Similarity variables are employed in order to transform the governing partial differential equations into a nonlinear ordinary differential equation. Both Adomian decomposition method (ADM) and He's variational iteration method (VIM) coupled with Pade approximation technique are implemented to solve the reduced system. Comparisons with previously published works are performed, and excellent agreement between the results is obtained.
TL;DR: In this article, a new metering method is presented based on homogeneous and separated flow theory; the acceleration pressure drop and the friction pressure drop of Venturi under two-phase flow conditions are considered in new correlation, and its validity is verified through experiment.
Abstract: When Venturi meters are used in wet gas, the measured differential pressure is higher than it would be in gas phases flowing alone This phenomenon is called over-reading Eight famous over-reading correlations have been studied by many researchers under low- and high-pressure conditions, the conclusion is separated flow model and homogeneous flow model performing well both under high and low pressures In this study, a new metering method is presented based on homogeneous and separated flow theory; the acceleration pressure drop and the friction pressure drop of Venturi under two-phase flow conditions are considered in new correlation, and its validity is verified through experiment For low pressure, a new test program has been implemented in Tianjin University’s low-pressure wet gas loop For high pressure, the National Engineering Laboratory offered their reports on the web, so the coefficients of the new proposed correlation are fitted with all independent data both under high and low pressures Finally, the applicability and errors of new correlation are analyzed
TL;DR: In this article, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting and the results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.
Abstract: Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with
constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The results show that, in new model, there are less computations needed
in comparison to Adomian decomposition method.
TL;DR: In this paper, a mathematical model and a polynomial algorithm for cyclic scheduling of a multihoist electroplating line with constant processing times are presented. But the objective is to minimize the cycle time, or equivalently to maximize the production throughput, for a given number of hoists.
Abstract: Modern automated production lines usually use one or multiple computer-controlled robots or hoists for material handling between workstations. A typical application of such lines is an automated electroplating line for processing printed circuit boards (PCBs). In these systems, cyclic production policy is widely used due to large lot size and simplicity of implementation. This paper addresses cyclic scheduling of a multihoist electroplating line with constant processing times. The objective is to minimize the cycle time, or equivalently to maximize the production throughput, for a given number of hoists. We propose a mathematical model and a polynomial algorithm for this scheduling problem. Computational results on randomly generated instances are reported.
TL;DR: In this paper, the authors developed a model for blood using the theory of interacting continua, that is, the mixture theory, and obtained a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs.
Abstract: Based on ideas proposed by Massoudi and Rajagopal (M-R), we develop a model for blood using the theory of interacting continua, that is, the mixture theory. We first provide a brief review
of mixture theory, and then discuss certain issues in constitutive modeling of a two-component mixture. In the present formulation, we ignore the biochemistry of blood and assume that blood is composed of red blood cells (RBCs) suspended in plasma, where the plasma behaves as a linearly
viscous fluid and the RBCs are modeled as an anisotropic nonlinear density-gradient-type fluid. We
obtain a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs. A simple shear flow is discussed, and an exact solution is obtained for a very
special case; for more general cases, it is necessary to solve the nonlinear coupled equations numerically.
TL;DR: Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network.
Abstract: Nowadays, digital computer systems and networks are the main engineering tools, being used in planning, design, operation, and control of all sizes of building, transportation, machinery, business, and life maintaining devices. Consequently, computer viruses became one of the most important sources of uncertainty, contributing to decrease the reliability of vital activities. A lot of antivirus programs have been developed, but they are limited to detecting and removing infections, based on previous knowledge of the virus code. In spite of having good adaptation capability, these programs work just as vaccines against diseases and are not able to prevent new infections based on the network state. Here, a trial on modeling computer viruses propagation dynamics relates it to other notable events occurring in the network permitting to establish preventive policies in the network management. Data from three different viruses are collected in the Internet and two different identification techniques, autoregressive and Fourier analyses, are applied showing that it is possible to forecast the dynamics of a new virus propagation by using the data collected from other viruses that formerly infected the network.
TL;DR: In this article, the authors focus on the suboptimization of a class of multivariable discrete-time bilinear systems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only.
Abstract: This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.
TL;DR: In this paper, a variational iteration method is applied to solve ǫ-th order semidifferential equations, which does not need linearization, weak nonlinearity assumptions, or perturbation theory.
Abstract: He's variational iteration method is applied to solve 𝑛th order semidifferential equations. Comparison is made between collocation spline method based on Lagrange interpolation and the present method. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions, or perturbation theory. Some examples are given to illustrate the effectiveness of the method; the results show that He's method provides a straightforward and powerful mathematical tool for solving various semidifferential equations of the 𝑛th order.
TL;DR: In this paper, the Exp-function method was used to obtain a generalized solitary solution for the Huxley equation, and the obtained result includes all solutions in open literature as special cases.
Abstract: Huxley equation is a core mathematical framework for modern biophysically based neural modeling It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings There are many methods to solve the equation, but each method can only lead to a special solution This paper suggests a relatively new method called the Exp-function method for this purpose The obtained result includes all solutions in open literature as special cases, and the generalized solution with some free parameters might imply some fascinating meanings hidden in Huxley equation
TL;DR: In this article, the authors deal with the coupling of two major problems in lubrication theory: cavitation phenomena and roughness of the surfaces in relative motion, and study the behavior of the solution, when highly oscillating roughness effects on the rigid surfaces occur.
Abstract: This paper deals with the coupling of two major problems in lubrication theory: cavitation phenomena and roughness of the surfaces in relative motion. Cavitation is defined as the rupture of the continuous film due to the formation of air bubbles, leading to the presence of a liquid-gas mixture. For this, the Elrod-Adams model (which is a pressure-saturation model) is classically used to describe the behavior of a cavitated thin film flow. In addition, in practical situations, the surfaces of the devices are rough, due to manufacturing processes which induce defaults. Thus, we study the behavior of the solution, when highly oscillating roughness effects on the rigid surfaces occur. In particular, we deal with the reiterated homogenization of this Elrod-Adams problem, using periodic unfolding methods. A numerical simulation illustrates the behavior of the solution. Although the pressure tends to a smooth one, the saturation oscillations are not damped. This does not prevent us from defining an equivalent homogenized saturation and highlights the anisotropic effects on the saturation function in cavitated areas.
TL;DR: In this article, an effective iterative algorithm for the calculation of the rightmost roots of neutral delay differential equations so that the stability of the delay equations can be determined directly, illustrated with two examples.
Abstract: The stability of a delay differential equation can be investigated on the basis of the root location of the characteristic function. Though a number of stability criteria are available, they usually do not provide any information about the characteristic root with maximal real part, which is useful in justifying the stability and in understanding the system performances. Because the characteristic function is a transcendental function that has an infinite number of roots with no closed form, the roots can be found out numerically only. While some iterative methods work effectively in finding a root of a nonlinear equation for a properly chosen initial guess, they do not work in finding the rightmost root directly from the characteristic function. On the basis of Lambert W function, this paper presents an effective iterative algorithm for the calculation of the rightmost roots of neutral delay differential equations so that the stability of the delay equations can be determined directly, illustrated with two examples.