Journal of Computational Methods in Physics The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. On the Use of Recursive Evaluation of Derivatives and Padé Approximation to Solve the Blasius Problem Tue, 26 Jan 2016 13:43:35 +0000 The Blasius problem is one of the well-known problems in fluid mechanics in the study of boundary layers. It is described by a third-order ordinary differential equation derived from the Navier-Stokes equation by a similarity transformation. Crocco and Wang independently transformed this third-order problem further into a second-order differential equation. Classical series solutions and their Padé approximants have been computed. These solutions however require extensive algebraic manipulations and significant computational effort. In this paper, we present a computational approach using algorithmic differentiation to obtain these series solutions. Our work produces results superior to those reported previously. Additionally, using increased precision in our calculations, we have been able to extend the usefulness of the method beyond limits where previous methods have failed. Asai Asaithambi Copyright © 2016 Asai Asaithambi. All rights reserved. A New Flux Splitting Scheme Based on Toro-Vazquez and HLL Schemes for the Euler Equations Tue, 02 Dec 2014 09:03:29 +0000 This paper presents a new flux splitting scheme for the Euler equations. The proposed scheme termed TV-HLL is obtained by following the Toro-Vazquez splitting (Toro and Vázquez-Cendón, 2012) and using the HLL algorithm with modified wave speeds for the pressure system. Here, the intercell velocity for the advection system is taken as the arithmetic mean. The resulting scheme is more accurate when compared to the Toro-Vazquez schemes and also enjoys the property of recognition of contact discontinuities and shear waves. Accuracy, efficiency, and other essential features of the proposed scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. The accuracy of the scheme is shown in 1D test cases designed by Toro. Pascalin Tiam Kapen and Tchuen Ghislain Copyright © 2014 Pascalin Tiam Kapen and Tchuen Ghislain. All rights reserved. Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation Wed, 15 Oct 2014 09:10:27 +0000 We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011). Ivan M. Uzunov and Zhivko D. Georgiev Copyright © 2014 Ivan M. Uzunov and Zhivko D. Georgiev. All rights reserved. Fourier Splitting Method for Kawahara Type Equations Tue, 26 Aug 2014 05:33:25 +0000 In this work, we integrate numerically the Kawahara and generalized Kawahara equation by using an algorithm based on Strang’s splitting method. The linear part is solved using the Fourier transform and the nonlinear part is solved with the aid of the exponential operator method. To assess the accuracy of the solution, we compare known analytical solutions with the numerical solution. Further, we show that as t increases the conserved quantities remain constant. Pablo U. Suárez and J. Héctor Morales Copyright © 2014 Pablo U. Suárez and J. Héctor Morales. All rights reserved. Comparative DFT Study of Phytochemical Constituents of the Fruits of Cucumis trigonus Roxb. and Cucumis sativus Linn. Tue, 12 Aug 2014 09:26:52 +0000 The hepatoprotective active phytochemical constituents from the ethanolic extracts of the fruits of Cucumis trigonus Roxb. and Cucumis sativus Linn. were identified by GC-MS analysis. The density functional theory (DFT) of these molecules was calculated by density functional B3LYP methods using B3LYP/6-311++G(d,p) basis set. The optimized geometries of phytochemical constituents were evaluated. Physicochemical properties such as HOMO, LUMO, ionization potential, electron affinity, electronegativity, electrochemical potential, hardness, softness, electrophilicity, total energy, and dipole moment have also been recorded. These are very important parameters to understand the chemical reactivity and biological activity of the phytochemical constituents. Glycodeoxycholic acid and 2-(2-methylcyclohexylidene)-hydrazinecarboxamide were found to be effective drugs selected on the basis of their HOMO and LUMO energy gap and softness. The effective properties of these compounds may be due to the presence of amino, carbonyl, and alcohol as a functional group. Subarayan Bothi Gopalakrishnan, Thangaraj Kalaiarasi, and Ramasamy Subramanian Copyright © 2014 Subarayan Bothi Gopalakrishnan et al. All rights reserved. Solving Fractional Diffusion Equation via the Collocation Method Based on Fractional Legendre Functions Thu, 24 Jul 2014 10:08:45 +0000 A formulation of the fractional Legendre functions is constructed to solve the generalized time-fractional diffusion equation. The fractional derivative is described in the Caputo sense. The method is based on the collection Legendre and path following methods. Analysis for the presented method is given and numerical results are presented. Muhammed Syam and Mohammed Al-Refai Copyright © 2014 Muhammed Syam and Mohammed Al-Refai. All rights reserved. Sinc Collocation Method for Solving the Benjamin-Ono Equation Wed, 23 Jul 2014 08:26:57 +0000 We propose a simple, though powerful, technique for numerical solutions of the Benjamin-Ono equation. This approach is based on a global collocation method using Sinc basis functions. Some properties of the Sinc collocation method required for our subsequent development are given and utilized to reduce the computation of the Benjamin-Ono equation to a system of ordinary differential equations. The propagation of one soliton and the interaction of two solitons are used to validate our numerical method. The method is easy to implement and yields accurate results. Edson Pindza and Eben Maré Copyright © 2014 Edson Pindza and Eben Maré. All rights reserved. Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem Mon, 14 Jul 2014 14:33:42 +0000 We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the MHD Jeffery-Hamel flow and the effect of MHD on the flow has been discussed. Comparisons are made between the proposed technique, the previous studies, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the presented approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method at small orders. The MATLAB software has been used to solve all the equations in this study. Ahmed A. Khidir Copyright © 2014 Ahmed A. Khidir. All rights reserved. Prediction of Materials Density according to Number of Scattered Gamma Photons Using Optimum Artificial Neural Network Tue, 10 Jun 2014 05:19:31 +0000 Through the study of scattered gamma beam intensity, material density could be obtained. Most important factor in this densitometry method is determining a relation between recorded intensity by detector and target material density. Such situation needs many experiments over materials with different densities. In this paper, using two different artificial neural networks, intensity of scattered gamma is obtained for whole densities. Mean relative error percentage for test data using best method is 1.27% that shows good agreement between the proposed artificial neural network model and experimental results. Gholam Hossein Roshani, Seyed Amir Hossein Feghhi, Farzin Shama, Abolfazl Salehizadeh, and Ehsan Nazemi Copyright © 2014 Gholam Hossein Roshani et al. All rights reserved. Finite-Difference Simulation of Elastic Wave with Separation in Pure P- and S-Modes Sun, 18 May 2014 13:01:51 +0000 Elastic wave equation simulation offers a way to study the wave propagation when creating seismic data. We implement an equivalent dual elastic wave separation equation to simulate the velocity, pressure, divergence, and curl fields in pure P- and S-modes, and apply it in full elastic wave numerical simulation. We give the complete derivations of explicit high-order staggered-grid finite-difference operators, stability condition, dispersion relation, and perfectly matched layer (PML) absorbing boundary condition, and present the resulting discretized formulas for the proposed elastic wave equation. The final numerical results of pure P- and S-modes are completely separated. Storage and computing time requirements are strongly reduced compared to the previous works. Numerical testing is used further to demonstrate the performance of the presented method. Ke-Yang Chen Copyright © 2014 Ke-Yang Chen. All rights reserved. Tau-Path Following Method for Solving the Riccati Equation with Fractional Order Wed, 05 Mar 2014 07:17:02 +0000 A formulation for the fractional Legendre functions is constructed to find the solution of the fractional Riccati equation. The fractional derivative is described in the Caputo sense. The method is based on the Tau Legendre and path following methods. Theoretical and numerical results are presented. Analysis for the presented method is given. Muhammed I. Syam, Hani I. Siyyam, and Ibrahim Al-Subaihi Copyright © 2014 Muhammed I. Syam et al. All rights reserved. A Single Sweep AGE Algorithm on a Variable Mesh Based on Off-Step Discretization for the Solution of Nonlinear Burgers’ Equation Thu, 16 Jan 2014 08:10:44 +0000 We discuss a new single sweep alternating group explicit iteration method, along with a third-order numerical method based on off-step discretization on a variable mesh to solve the nonlinear ordinary differential equation subject to given natural boundary conditions. Using the proposed method, we have solved Burgers’ equation both in singular and nonsingular cases, which is the main attraction of our work. The convergence of the proposed method is discussed in detail. We compared the results of the proposed iteration method with the results of the corresponding double sweep alternating group explicit iteration methods to demonstrate computationally the efficiency of the proposed method. R. K. Mohanty and Jyoti Talwar Copyright © 2014 R. K. Mohanty and Jyoti Talwar. All rights reserved. Static Kirchhoff Rods under the Action of External Forces: Integration via Runge-Kutta Method Thu, 09 Jan 2014 13:27:25 +0000 This paper shows how to apply a simple Runge-Kutta algorithm to get solutions of Kirchhoff equations for static filaments subjected to arbitrary external and static forces. This is done by suitably integrating at once Kirchhoff and filament reference system equations under appropriate initial boundary conditions. To show the application of the method, we display several numerical solutions for filaments including cases showing the effect of gravity. Ademir L. Xavier Jr. Copyright © 2014 Ademir L. Xavier Jr.. All rights reserved. A New Spectral-Homotopy Perturbation Method and Its Application to Jeffery-Hamel Nanofluid Flow with High Magnetic Field Mon, 30 Dec 2013 13:29:29 +0000 We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method, and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the Jeffery-Hamel flow considering the effects of magnetic field and nanoparticle. Comparisons are made between the proposed technique, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the present approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method. Ahmed A. Khidir Copyright © 2013 Ahmed A. Khidir. All rights reserved. Quantitative Modeling of Faceted Ice Crystal Growth from Water Vapor Using Cellular Automata Wed, 04 Dec 2013 14:07:39 +0000 We describe a numerical model of faceted crystal growth using a cellular automata method. The model was developed for investigating the diffusion-limited growth of ice crystals from water vapor, when the surface boundary conditions are determined primarily by strongly anisotropic molecular attachment kinetics. We restricted our model to cylindrically symmetric crystal growth with relatively simple growth morphologies, as this was sufficient for making quantitative comparisons between models and ice growth experiments. Overall this numerical model appears to reproduce ice growth behavior with reasonable fidelity over a wide range of conditions. More generally, the model could easily be adapted for other material systems, and the cellular automata technique appears well suited for investigating crystal growth dynamics when strongly anisotropic surface attachment kinetics yields faceted growth morphologies. Kenneth G. Libbrecht Copyright © 2013 Kenneth G. Libbrecht. All rights reserved. Wideband Extrapolation of Spatial Responses of Resonant Structures Using Early-Time and Low-Frequency Data Tue, 22 Oct 2013 09:30:45 +0000 An efficient procedure is presented to extrapolate a wideband electromagnetic response defined over an arbitrary spatial region using early-time and low-frequency data. The previous procedures presented in the literature are efficient for single-point extrapolation and can readily be applied to spatial regions but are terribly inefficient when a response is desired at many spatial locations. In this work, an optimized algorithm is presented to quickly extrapolate over a large number of spatial locations. The time and frequency behavior of the response is fitted by polynomials and pole terms, and the spatial variation is represented with spatially dependent polynomial coefficients and pole residues. A single set of poles, common to all spatial locations of interest, is shown to sufficiently describe the resonant behavior of response over the entire spatial region. A multisignal formulation of the matrix pencil method is applied to determine poles from early time data. Numerical examples are presented to demonstrate the procedure. Additionally, an automated approach to distinguish physical poles, which correspond to structural resonances, from nonphysical fitting poles is presented. The spatially dependent residues of physical pole terms, referred to here as modal residues, are shown to provide important insight into the resonant behavior of a structure. J. Michael Frye and Anthony Q. Martin Copyright © 2013 J. Michael Frye and Anthony Q. Martin. All rights reserved. Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation Mon, 07 Oct 2013 09:37:22 +0000 Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED. Wayne Cheng-Wei Huang and Herman Batelaan Copyright © 2013 Wayne Cheng-Wei Huang and Herman Batelaan. All rights reserved. The Effect of Pressure on Electronic and Magnetic Properties of MnAs Crystal Thu, 26 Sep 2013 09:28:27 +0000 The structural, electronic, and magnetic properties of MnAs crystal are studied. The WIEN2k code which uses a full-potential LAPW program based on density functional theory with GGA is used for the calculations. At first, the total energy of a MnAs crystal in different lattices is calculated and the corresponding - diagram is drawn for two different structures of MnAs. The effect of pressuring this crystal is determined. The calculations confirm that, MnAs has the NiAs-type structure at ambient pressure but transforms into the zinc-blend structure of a specific pressure value. Also, the electric field gradient (EFG) and hyperfine field (HFF) at the nuclear site of Mn and As are calculated. Finally, the effect of pressure on EFG and HFF is studied. Farzad Moradiannejad, S. Javad Hashemifar, and Hadi Akbarzadeh Copyright © 2013 Farzad Moradiannejad et al. All rights reserved. MHD-Conjugate Free Convection from an Isothermal Horizontal Circular Cylinder with Joule Heating and Heat Generation Tue, 17 Sep 2013 11:18:34 +0000 The present work is devoted to the numerical study of laminar magnetohydrodynamic (MHD) conjugate natural convection flow from a horizontal circular cylinder taking into account Joule heating and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made nondimensional forms using a set of dimensionless variables. Thus, the nondimensional governing equations are solved numerically using finite difference method with Keller box scheme. Numerical outcomes are found for different values of the magnetic parameter, conjugate conduction parameter, Prandtl number, Joule heating parameter, and heat generation parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat transfer along the surface. It is found that the skin friction increases, and heat transfer rate decreases for escalating value of Joule heating parameter and heat generation parameter. Results are presented graphically with detailed discussion. NHM. A. Azim and M. K. Chowdhury Copyright © 2013 NHM. A. Azim and M. K. Chowdhury. All rights reserved. Preparation of Approximate Eigenvector by Unitary Operations on Eigenstate in Abrams-Lloyd Quantum Algorithm Wed, 11 Sep 2013 08:51:19 +0000 The Abrams-Lloyd quantum algorithm computes an eigenvalue and the corresponding eigenstate of a unitary matrix from an approximate eigenvector . The eigenstate is a basis vector in the orthonormal eigenspace. Finding another eigenvalue, using a random approximate eigenvector, may require many trials as the trial may repeatedly result in the eigenvalue measured earlier. We present a method involving orthogonalization of the eigenstate obtained in a trial. It is used as the for the next trial. Because of the orthogonal construction, Abrams-Lloyd algorithm will not repeat the eigenvalue measured earlier. Thus, all the eigenvalues are obtained in sequence without repetitions. An operator that anticommutes with a unitary operator orthogonalizes the eigenvectors of the unitary. We implemented the method on the programming language model of quantum computation and tested it on a unitary matrix representing the time evolution operator of a small spin chain. All the eigenvalues of the operator were obtained sequentially. Another use of the first eigenvector from Abrams-Lloyd algorithm is preparing a state that is the uniform superposition of all the eigenvectors. This is possible by nonorthogonalizing the first eigenvector in all dimensions and then applying the Abrams-Lloyd algorithm steps stopping short of the last measurement. Latha S. Warrier Copyright © 2013 Latha S. Warrier. All rights reserved. A p-Strategy with a Local Time-Stepping Method in a Discontinuous Galerkin Approach to Solve Electromagnetic Problems Tue, 30 Jul 2013 11:56:00 +0000 We present a local spatial approximation or p-strategy Discontinuous Galerkin method to solve the time-domain Maxwell equations. First, the Discontinuous Galerkin method with a local time-stepping strategy is recalled. Next, in order to increase the efficiency of the method, a local spatial approximation strategy is introduced and studied. While preserving accuracy and by using different spatial approximation orders for each cell, this strategy is very efficient to reduce the computational time and the required memory in numerical simulations using very distorted meshes. Several numerical examples are given to show the interest and the capacity of such method. Benoit Mallet, Xavier Ferrieres, Sebastien Pernet, Jean-Baptiste Laurent, Bernard Pecqueux, and Pierre Seimandi Copyright © 2013 Benoit Mallet et al. All rights reserved. Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays Thu, 18 Jul 2013 12:46:54 +0000 This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria. N. Mala and A. R. Sudamani Ramaswamy Copyright © 2013 N. Mala and A. R. Sudamani Ramaswamy. All rights reserved.