Journal of Computational Methods in Physics
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The latest articles from Hindawi Publishing Corporation
© 2014 , Hindawi Publishing Corporation . All rights reserved.

TauPath Following Method for Solving the Riccati Equation with Fractional Order
Wed, 05 Mar 2014 07:17:02 +0000
http://www.hindawi.com/journals/jcmp/2014/207916/
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 AlSubaihi
Copyright © 2014 Muhammed I. Syam et al. All rights reserved.

A Single Sweep AGE Algorithm on a Variable Mesh Based on OffStep Discretization for the Solution of Nonlinear Burgers’ Equation
Thu, 16 Jan 2014 08:10:44 +0000
http://www.hindawi.com/journals/jcmp/2014/853198/
We discuss a new single sweep alternating group explicit iteration method, along with a thirdorder numerical method based on offstep 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 Burgersâ€™ 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 RungeKutta Method
Thu, 09 Jan 2014 13:27:25 +0000
http://www.hindawi.com/journals/jcmp/2014/650365/
This paper shows how to apply a simple RungeKutta 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 SpectralHomotopy Perturbation Method and Its Application to JefferyHamel Nanofluid Flow with High Magnetic Field
Mon, 30 Dec 2013 13:29:29 +0000
http://www.hindawi.com/journals/jcmp/2013/939143/
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 JefferyHamel 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
http://www.hindawi.com/journals/jcmp/2013/174806/
We describe a numerical model of faceted crystal growth using a cellular automata method. The model was developed for investigating the diffusionlimited 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 EarlyTime and LowFrequency Data
Tue, 22 Oct 2013 09:30:45 +0000
http://www.hindawi.com/journals/jcmp/2013/563724/
An efficient procedure is presented to extrapolate a wideband electromagnetic response defined over an arbitrary spatial region using earlytime and lowfrequency data. The previous procedures presented in the literature are efficient for singlepoint 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 ZeroPoint Radiation
Mon, 07 Oct 2013 09:37:22 +0000
http://www.hindawi.com/journals/jcmp/2013/308538/
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 doublepeak 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 ChengWei Huang and Herman Batelaan
Copyright © 2013 Wayne ChengWei 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
http://www.hindawi.com/journals/jcmp/2013/879164/
The structural, electronic, and magnetic properties of MnAs crystal are studied. The WIEN2k code which uses a fullpotential 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 NiAstype structure at ambient pressure but transforms into the zincblend 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.

MHDConjugate Free Convection from an Isothermal Horizontal Circular Cylinder with Joule Heating and Heat Generation
Tue, 17 Sep 2013 11:18:34 +0000
http://www.hindawi.com/journals/jcmp/2013/180516/
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 AbramsLloyd Quantum Algorithm
Wed, 11 Sep 2013 08:51:19 +0000
http://www.hindawi.com/journals/jcmp/2013/235624/
The AbramsLloyd 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, AbramsLloyd 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 AbramsLloyd 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 AbramsLloyd algorithm steps stopping short of the last measurement.
Latha S. Warrier
Copyright © 2013 Latha S. Warrier. All rights reserved.

A pStrategy with a Local TimeStepping Method in a Discontinuous Galerkin Approach to Solve Electromagnetic Problems
Tue, 30 Jul 2013 11:56:00 +0000
http://www.hindawi.com/journals/jcmp/2013/563480/
We present a local spatial approximation or pstrategy Discontinuous Galerkin method to solve the timedomain Maxwell equations. First, the Discontinuous Galerkin method with a local timestepping 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, JeanBaptiste Laurent, Bernard Pecqueux, and Pierre Seimandi
Copyright © 2013 Benoit Mallet et al. All rights reserved.

Passivity Analysis of Markovian Jumping Neural Networks with Leakage TimeVarying Delays
Thu, 18 Jul 2013 12:46:54 +0000
http://www.hindawi.com/journals/jcmp/2013/172906/
This paper is concerned with the passivity analysis of Markovian
jumping neural networks with leakage timevarying delays. Based on a Lyapunov
functional that accounts for the mixed time delays, a leakage delaydependent
passivity conditions are derived in terms of linear matrix inequalities (LMIs). The
mixed delays includes leakage timevarying delays, discrete timevarying delays,
and distributed timevarying delays. By employing a novel LyapunovKrasovskii
functional having tripleintegral terms, new passivity leakage delaydependent
criteria are established to guarantee the passivity performance. This performance
not only depends on the upper bound of the timevarying leakage delay but also depends on the upper bound of the derivative of the timevarying leakage
delay . While estimating the upper bound of derivative of the LyapunovKrasovskii 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.