Search results for: first order adjoint equation method

Authors: Chiharu Okuma, Naoki Yamamoto, Jun Murakami

Abstract:

As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

Keywords: Singular value decomposition (SVD), higher-orderSVD (HOSVD), outer product expansion, power method.

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Authors: Sudipta Majumdar, Harish Parthasarathy

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In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Keywords: Least squares method, linear system, system identification, wavelet transform.

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Authors: P. W. C. Prasad, A. Assi, M. Raseen, A. Harb

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The goal of this work is to describe a new algorithm for finding the optimal variable order, number of nodes for any order and other ROBDD parameters, based on a tabular method. The tabular method makes use of a pre-built backend database table that stores the ROBDD size for selected combinations of min-terms. The user uses the backend table and the proposed algorithm to find the necessary ROBDD parameters, such as best variable order, number of nodes etc. Experimental results on benchmarks are given for this technique.

Keywords: Tabular Method, Binary Decision Diagram, BDD Manipulation, Boolean Function.

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Authors: Ali Safdari-Vaighani

Abstract:

Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: Radial basis function, basket option, jump diffusion, RBF-PUM.

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Authors: N. Khatiashvili, K. Pirumova, D. Janjgava

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The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

Keywords: Stokes system, viscous fluid.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

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In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Huei-Fu Lu

Abstract:

This study links up the theories of social psychology, economics and sport management to assess the impact of sport participation on subjective well-being (SWB) and use a simple statistic method to estimate the relative monetary value that sport participation derives SWB for Taiwan-s college students. By constructing proper measurements on sport participation and SWB respectively, a structural equation model (SEM) is developed to perform a confirmatory factory analysis, and the causal relationship between sport participation and SWB as well as the effect of the demographic variables on these two concepts are also discussed.

Keywords: Demographics, Economic value, Sport participation, Structural equation modeling (SEM), Subjective well-being.

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: Nonlinear optics, propagation equation, plasmonic waveguide.

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Authors: K. Kaabeche-Djerafi, N. Bendjaballah-Lalaoui, S. Semra

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The paper aims at investigating influence of medium capacity on linear adsorbed solute dispersion into chemically heterogeneous fixed beds. A discrete chemical heterogeneity distribution is considered in the one-dimensional advectivedispersive equation. The partial differential equation is solved using finite volumes method based on the Adam-Bashforth algorithm. Increased dispersion is estimated by comparing breakthrough curves second order moments and keeping identical hydrodynamic properties. As a result, dispersion increase due to chemical heterogeneity depends on the column size and surprisingly on the solid capacity. The more intense capacity is, the more important solute dispersion is. Medium length which is known to favour this effect vanishing according to the linear adsorption in fixed bed seems to create nonmonotonous variation of dispersion because of the heterogeneity. This nonmonotonous behaviour is also favoured by high capacities.

Keywords: linear adsorption; chemical heterogeneity;dispersion; fixed bed; porous media

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

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By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

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Authors: S. N. Deepa, G. Sugumaran

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This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.

Keywords: Higher order systems, model order formulation, modified particle swarm optimization, PID controller, pole-zero cancellation.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: Masoud Abedini, Azrul A. Mutalib, Shahrizan Baharom, Hong Hao

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This study was conducted published to investigate there liability of the equation pressure-impulse (PI) reinforced concrete column inprevious studies. Equation involves three different levels of damage criteria known as D =0. 2, D =0. 5 and D =0. 8.The damage criteria known as a minor when 0-0.2, 0.2-0.5is known as moderate damage, high damage known as 0.5-0.8, and 0.8-1 of the structure is considered a failure. In this study, two types of reliability analyzes conducted. First, using pressure-impulse equation with different parameters. The parameters involved are the concrete strength, depth, width, and height column, the ratio of longitudinal reinforcement and transverse reinforcement ratio. In the first analysis of the reliability of this new equation is derived to improve the previous equations. The second reliability analysis involves three types of columns used to derive the PI curve diagram using the derived equation to compare with the equation derived from other researchers and graph minimum standoff versus weapon yield Federal Emergency Management Agency (FEMA). The results showed that the derived equation is more accurate with FEMA standards than previous researchers.

Keywords: Blast load, RC column, P-I curve, Analytical formulae, Standard FEMA.

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Authors: Süha Yılmaz, Melih Turgut

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The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained.

Keywords: Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.

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Authors: H. Ozbasaran

Abstract:

IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: Cantilever, IPN, IPE, lateral torsional buckling

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai

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One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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

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

Keywords: Boundary conditions, buckling, non-local, the differential transform method.

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

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This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman

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In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.

Keywords: Backward Differentiation Formula, block, secondorder.

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Authors: Hamioud Saida, Khalfallah Salah

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In this study, a spectral element method (SEM) is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: Elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation.

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Authors: Prawal Sinha, Getachew Adamu

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Heating is inevitable in any bearing operation. This leads to not only the thinning of the lubricant but also could lead to a thermal deformation of the bearing. The present work is an attempt to analyze the influence of thermal deformation on the thermohydrodynamic lubrication of infinitely long tilted pad slider rough bearings. As a consequence of heating the slider is deformed and is assumed to take a parabolic shape. Also the asperities expand leading to smaller effective film thickness. Two different types of surface roughness are considered: longitudinal roughness and transverse roughness. Christensen-s stochastic approach is used to derive the Reynolds-type equations. Density and viscosity are considered to be temperature dependent. The modified Reynolds equation, momentum equation, continuity equation and energy equation are decoupled and solved using finite difference method to yield various bearing characteristics. From the numerical simulations it is observed that the performance of the bearing is significantly affected by the thermal distortion of the slider and asperities and even the parallel sliders seem to carry some load.

Keywords: Thermal Deformation, Tilted pad slider bearing, longitudinal roughness, transverse roughness, load capacity

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

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The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: Axially moving beam, Galerkin method, non-linear vibration, super harmonic resonances.

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Authors: I. Otete, A. I. Ejere, I. S. Okunzuwa

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In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

Keywords: Schrödinger's equation, bound state, Hulthen-Yukawa potential, Nikiforov-Uvarov, D-dimensions

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Authors: Okay Gunes

Abstract:

In this article, a new method is proposed for the measuring of well-being inequality through a model composed of superimposing satisfaction waves. The displacement of households’ satisfactory state (i.e. satisfaction) is defined in a satisfaction string. The duration of the satisfactory state for a given period is measured in order to determine the relationship between utility and total satisfactory time, itself dependent on the density and tension of each satisfaction string. Thus, individual cardinal total satisfaction values are computed by way of a one-dimensional form for scalar sinusoidal (harmonic) moving wave function, using satisfaction waves with varying amplitudes and frequencies which allow us to measure wellbeing inequality. One advantage to using satisfaction waves is the ability to show that individual utility and consumption amounts would probably not commute; hence, it is impossible to measure or to know simultaneously the values of these observables from the dataset. Thus, we crystallize the problem by using a Heisenberg-type uncertainty resolution for self-adjoint economic operators. We propose to eliminate any estimation bias by correlating the standard deviations of selected economic operators; this is achieved by replacing the aforementioned observed uncertainties with households’ perceived uncertainties (i.e. corrected standard deviations) obtained through the logarithmic psychophysical law proposed by Weber and Fechner.

Keywords: Heisenberg Uncertainty Principle, superimposing satisfaction waves, Weber–Fechner law, well-being inequality.

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Authors: Maatoug Hassine, Mourad Hrizi

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In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: Geometric inverse source problem, heat equation, topological sensitivity, topological optimization, Kohn-Vogelius formulation.

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Authors: M. Sedighizadeh, A. Rezazadeh

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Due to the increasing penetration of wind energy, it is necessary to possess design tools that are able to simulate the impact of these installations in utility grids. In order to provide a net contribution to this issue a detailed wind park model has been developed and is briefly presented. However, the computational costs associated with the performance of such a detailed model in describing the behavior of a wind park composed by a considerable number of units may render its practical application very difficult. To overcome this problem integral manifolds theory has been applied to reduce the order of the detailed wind park model, and therefore create the conditions for the development of a dynamic equivalent which is able to retain the relevant dynamics with respect to the existing a.c. system. In this paper integral manifold method has been introduced for order reduction. Simulation results of the proposed method represents that integral manifold method results fit the detailed model results with a higher precision than singular perturbation method.

Keywords: Wind, Reduced Order, Integral Manifold.

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Authors: Fabrice Poirion, Benedicte Puig

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Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.

Keywords: Simulation, nonGaussian, random field, multivariate, stochastic process.

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