Showing papers in "Mathematical Problems in Engineering in 2009"

Approximate Analysis of MHD Squeeze Flow between Two Parallel Disks with Suction or Injection by Homotopy Perturbation Method

Abstract: An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.

Some Relatively New Techniques for Nonlinear Problems

Abstract: This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems of physical nature. In particular, we will focus on the variational iteration method (VIM) and its modifications, the homotopy perturbation method (HPM), the parameter expansion method, and exp-function method. These relatively new but very reliable techniques proved useful for solving a wide class of nonlinear problems and are capable to cope with the versatility of the physical problems. Several examples are given to reconfirm the efficiency of these algorithms. Some open problems are also suggested for future research work.

Modeling Nonlinear Dynamics and Chaos: A Review

Abstract: This paper reviews the major developments of modeling techniques applied to nonlinear dynamics and chaos. Model representations, parameter estimation techniques, data requirements, and model validation are some of the key topics that are covered in this paper, which surveys slightly over two decades since the pioneering papers on the subject appeared in the literature.

Chaotic Image Encryption Design Using Tompkins-Paige Algorithm

Abstract: In this paper, we have presented a new permutation-substitution image encryption architecture using chaotic maps and Tompkins-Paige algorithm. The proposed encryption system includes two major parts, chaotic pixels permutation and chaotic pixels substitution. A logistic map is used to generate a bit sequence, which is used to generate pseudorandom numbers in Tompkins-Paige algorithm, in 2D permutation phase. Pixel substitution phase includes two process, the tent pseudorandom image (TPRI) generator and modulo addition operation. All parts of the proposed chaotic encryption system are simulated. Uniformity of the histogram of the proposed encrypted image is justified using the chi-square test, which is less than 𝜒 2 (255, 0.05). The vertical, horizontal, and diagonal correlation coefficients, as well as their average and RMS values for the proposed encrypted image are calculated that is about 13% less than previous researches. To quantify the difference between the encrypted image and the corresponding plain-image, three measures are used. These are MAE, NPCR, and UACI, which are improved in our proposed system considerably. NPCR of our proposed system is exactly the ideal value of this criterion. The key space of our proposed method is large enough to protect the system against any Brute-force and statistical attacks.

Conjugate Problems in Convective Heat Transfer: Review

Abstract: A review of conjugate convective heat transfer problems solved during the early and current time of development of this modern approach is presented. The discussion is based on analytical solutions of selected typical relatively simple conjugate problems including steady-state and transient processes, thermal material treatment, and heat and mass transfer in drying. This brief survey is accompanied by the list of almost two hundred publications considering application of different more and less complex analytical and numerical conjugate models for simulating technology processes and industrial devices from aerospace systems to food production. The references are combined in the groups of works studying similar problems so that each of the groups corresponds to one of selected analytical solutions considered in detail. Such structure of review gives the reader the understanding of early and current situation in conjugate convective heat transfer modeling and makes possible to use the information presented as an introduction to this area on the one hand, and to find more complicated publications of interest on the other hand.

Thermal Radiation Effects on Heat and Mass Transfer over an Unsteady Stretching Surface

Abstract: The unsteady heat, mass, and fluid transfer over a horizontal stretching sheet has been numerically investigated. Using a similarity transformation the governing time-dependent boundary layer equations for the momentum, heat, and mass transfer were reduced to a sets of ordinary differential equations. These set of ordinary differential equations were then solved using the Chebyshev pseudo-spectral collocation method, and a parametric analysis was carried out. The study observed, among other observations that the local Sherwood number increases as the values of the stretching parameter 𝐴 and the Schmidt number 𝑆𝑐 increase. Also the fluid temperature was found to be significantly reduced by increases in the values of the Prandtl number 𝑃𝑟, the unsteadiness parameter 𝐴, and the radiation parameter 𝑅. The velocity and concentration profiles were found to be reduced by increasing values of the unsteadiness parameter 𝐴.

Dynamical Aspects of an Equilateral Restricted Four-Body Problem

Abstract: The spatial equilateral restricted four-body problem (ERFBP) is a four body problem where a mass point of negligible mass is moving under the Newtonian gravitational attraction of three positive masses (called the primaries) which move on circular periodic orbits around their center of mass fixed at the origin of the coordinate system such that their configuration is always an equilateral triangle. Since fourth mass is small, it does not affect the motion of the three primaries. In our model we assume that the two masses of the primaries and are equal to and the mass is . The Hamiltonian function that governs the motion of the fourth mass is derived and it has three degrees of freedom depending periodically on time. Using a synodical system, we fixed the primaries in order to eliminate the time dependence. Similarly to the circular restricted three-body problem, we obtain a first integral of motion. With the help of the Hamiltonian structure, we characterize the region of the possible motions and the surface of fixed level in the spatial as well as in the planar case. Among other things, we verify that the number of equilibrium solutions depends upon the masses, also we show the existence of periodic solutions by different methods in the planar case.

Mannheim Offsets of Ruled Surfaces

Abstract: In a recent works Liu and Wang (2008; 2007) study the Mannheim partner curves in the three dimensional space. In this paper, we extend the theory of the Mannheim curves to ruled surfaces and define two ruled surfaces which are offset in the sense of Mannheim. It is shown that, every developable ruled surface have a Mannheim offset if and only if an equation should be satisfied between the geodesic curvature and the arc-length of spherical indicatrix of it. Moreover, we obtain that the Mannheim offset of developable ruled surface is constant distance from it. Finally, examples are also given.

Optimal Pricing and Production Master Planning in a Multiperiod Horizon Considering Capacity and Inventory Constraints

Abstract: We formulate and solve a single-item joint pricing and master planning optimization problem with capacity and inventory constrains. The objective is to maximize profits over a discrete-time multiperiod horizon. The solution process consists of two steps. First, we solve the single-period problem exactly. Second, using the exact solution of the single-period problem, we solve the multiperiod problem using a dynamic programming approach. The solution process and the importance of considering both capacity and inventory constraints are illustrated with numerical examples.

Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model

Abstract: We introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.

Retailer's Optimal Pricing and Ordering Policies for Non-Instantaneous Deteriorating Items with Price-Dependent Demand and Partial Backlogging

Abstract: An inventory system for non-instantaneous deteriorating items with price-dependent demand is formulated and solved. A model is developed in which shortages are allowed and partially backlogged, where the backlogging rate is variable and dependent on the waiting time for the next replenishment. The major objective is to determine the optimal selling price, the length of time in which there is no inventory shortage, and the replenishment cycle time simultaneously such that the total profit per unit time has a maximum value. An algorithm is developed to find the optimal solution, and numerical examples are provided to illustrate the theoretical results. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.

Using of H-Infinity Control Method in Attitude Control System of Rigid-Flexible Satellite

Abstract: The attitude control systems of satellites with rigid and flexible components are demanding more and more better performance resulting in the development of several methods control. For that reason, control design methods presently available, including parameters and states estimation, robust and adaptive control, as well as linear and nonlinear theory, need more investigation to know their capability and limitations. In this paper the investigated technique is H-Infinity method in the performance of the Attitude Control System of a Rigid-Flexible Satellite.

Applications of the Moore-Penrose Inverse in Digital Image Restoration

Abstract: This paper presents a fast computational method that finds application in a broad scientific field such as digital image restoration. The proposed method provides a new approach to the problem of image reconstruction by using the Moore-Penrose inverse. The resolution of the reconstructed image remains at a very high level but the main advantage of the method was found on the computational load that has been decreased considerably compared to the classic techniques.

Numerical Solutions of the Generalized Burgers-Huxley Equation by a Differential Quadrature Method

Abstract: Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this technique have been compared with the exact solution to show the required accuracy of it. Since the scheme is explicit, linearization is not needed and the approximate solution to the nonlinear equation is obtained easily. The effectiveness of this method is verified through illustrative examples. The present method is seen to be a very reliable alternative method to some existing techniques for such realistic problems.

Free Vibration Analysis of Rectangular Orthotropic Membranes in Large Deflection

Abstract: This paper reviewed the research on the vibration of orthotropic membrane, which commonly applied in the membrane structural engineering. We applied the large deflection theory of membrane to derive the governing vibration equations of orthotropic membrane, solved it, and obtained the power series formula of nonlinear vibration frequency of rectangular membrane with four edges fixed. The paper gave the computational example and compared the two results from the large deflection theory and the small one, respectively. Results obtained from this paper provide some theoretical foundation for the measurement of pretension by frequency method; meanwhile, the results provide some theoretical foundation for the research of nonlinear vibration of membrane structures and the response solving of membrane structures under dynamic loads.

Nonlinear Conjugate Gradient Methods with Sufficient Descent Condition for Large-Scale Unconstrained Optimization

Abstract: Two nonlinear conjugate gradient-type methods for solving unconstrained optimization problems are proposed. An attractive property of the methods, is that, without any line search, the generated directions always descend. Under some mild conditions, global convergence results for both methods are established. Preliminary numerical results show that these proposed methods are promising, and competitive with the well-known PRP method.

Pursuit-Evasion Differential Game with Many Inertial Players

Abstract: We consider pursuit-evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players.

Chaos Synchronization between Two Different Fractional Systems of Lorenz Family

Abstract: This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lu system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenz-like system. The analytical conditions for the synchronization of these pairs of different fractional order chaotic systems are derived by utilizing Laplace transform. Numerical simulations are used to verify the theoretical analysis using different values of the fractional order parameter.

Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

Abstract: Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.

Order Level Inventory Models for Deteriorating Seasonable/Fashionable Products with Time Dependent Demand and Shortages

Abstract: An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.

Optimal On-Off Attitude Control for the Brazilian Multimission Platform Satellite

Abstract: This work deals with the analysis and design of a reaction thruster attitude control for the Brazilian Multimission platform satellite. The three-axis attitude control systems are activated in pulse mode. Consequently, a modulation of the torque command is compelling in order to avoid high nonlinear control action. This work considers the Pulse-Width Pulse-Frequency (PWPF) modulator which is composed of a Schmidt trigger, a first-order filter, and a feedback loop. PWPF modulator holds several advantages over classical bang-bang controllers such as close to linear operation, high accuracy, and reduced propellant consumption. The Linear Gaussian Quadratic (LQG) technique is used to synthesize the control law during stabilization mode and the modulator is used to modulate the continuous control signal to discrete one. Numerical simulations are used to analyze the performance of the attitude control. The LQG/PWPF approach achieves good stabilization-mode requirements as disturbances rejection and regulation performance.

New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

Abstract: We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter in practical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners.

A semianalytical approach to large deflections in compliant beams under point load

Abstract: The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block inmore complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

The Estimation of Product Standard Time by Artificial Neural Networks in the Molding Industry

Abstract: Determination of exact standard time with direct measurement procedures is particularly difficult in companies which do not have an adequate environment suitable for time measurement studies or which produce goods requiring complex production schedules. For these companies new and special measurement procedures need to be developed. In this study, a new time estimation method based on different robust algorithms of artificial neural networks (ANNs) is developed. For the proposed method, the products that have similar production processes were chosen from among the whole product range within the cleansing department of a molding company. While using ANNs, to train the network, some of the chosen products' standard time that had been previously measured is used to estimate the standard time of the remaining products. The different ANN algorithms are trained and four of them, which are converged the data, are stated and compared in different architectures. In this way, it is concluded that this estimation method could be applied accurately in many similar processes using the relevant algorithms.

Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

Abstract: The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

Modeling and Control of Distillation Column in a Petroleum Process

Abstract: This paper introduces a calculation procedure for modeling and control simulation of a condensate distillation column based on the energy balance (𝐿-𝑉) structure. In this control, the reflux rate 𝐿 and the boilup rate 𝑉 are used as the inputs to control the outputs of the purity of the distillate overhead and the impurity of the bottom products. The modeling simulation is important for process dynamic analysis and the plant initial design. In this paper, the modeling and simulation are accomplished over three phases: the basic nonlinear model of the plant, the full-order linearised model, and the reduced-order linear model. The reduced-order linear model is then used as the reference model for a model-reference adaptive control (MRAC) system to verify the applicable ability of a conventional adaptive controller for a distillation column dealing with the disturbance and the model-plant mismatch as the influence of the plant feed disturbances.

Adomian Decomposition Method for a Nonlinear Heat Equation with Temperature Dependent Thermal Properties

Abstract: The solutions of nonlinear heat equation with temperature dependent diffusivity are investigated using the modified Adomian decomposition method. Analysis of the method and examples are given to show that the Adomian series solution gives an excellent approximation to the exact solution. This accuracy can be increased by increasing the number of terms in the series expansion. The Adomian solutions are presented in some situations of interest.

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

Abstract: Several software reliability growth models (SRGMs) have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Ito type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

An Unconditionally Stable Parallel Difference Scheme for Telegraph Equation

Abstract: We use an unconditionally stable parallel difference scheme to solve telegraph equation. This method is based on domain decomposition concept and using asymmetric Saul'yev schemes for internal nodes of each sub-domain and alternating group implicit method for sub-domain's interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability and better accuracy than original Saul'yev schemes. The details of implementation and proving stability are briefly discussed. Numerical experiments on stability and accuracy are also presented.

Singular Positone and Semipositone Boundary Value Problems of Nonlinear Fractional Differential Equations

Abstract: We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problem D 𝛼 0 + 𝑢 ( 𝑡 ) = 𝜇 𝑎 ( 𝑡 ) 𝑓 ( 𝑡 , 𝑢 ( 𝑡 ) ) , 0 𝑡 1 , 𝑢 ( 0 ) = 𝑢 ( 1 ) = 𝑢  ( 0 ) = 𝑢  ( 1 ) = 0 , where 𝜇 > 0 , 𝑎 , and 𝑓 are continuous, 𝛼 ∈ ( 3 , 4 ] is a real number, and D 𝛼 0 + is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main results.