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

A New Spectral-Homotopy Perturbation Method and Its Application to Jeffery-Hamel Nanofluid Flow with High Magnetic Field

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

Quantitative Modeling of Faceted Ice Crystal Growth from Water Vapor Using Cellular Automata

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

Anthony Q. Martin

Wideband Extrapolation of Spatial Responses of Resonant Structures Using Early-Time and Low-Frequency Data

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

Herman Batelaan

Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation

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 <svg     style="vertical-align:-0.0pt;width:10.8625px;" id="M1" height="11.175" version="1.1" viewBox="0 0 10.8625 11.175" width="10.8625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x1D438" d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5&#xA;l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" /></g>

		
	
</svg>-<svg     style="vertical-align:-0.20064pt;width:12.7375px;" id="M2" height="11.375" version="1.1" viewBox="0 0 12.7375 11.375" width="12.7375"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D449" d="M730 650l-8 -28q-52 -4 -72 -18t-64 -77q-79 -113 -321 -539h-33l-119 541q-13 59 -29.5 73t-66.5 20l7 28h245l-8 -28l-28 -5q-33 -6 -40.5 -15.5t-0.5 -38.5l102 -450h2q191 320 246 430q21 42 15.5 56t-43.5 19l-31 4l7 28h240z" /></g>

		
	
</svg> 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

Hadi Akbarzadeh

The Effect of Pressure on Electronic and Magnetic Properties of MnAs Crystal

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

M. K. Chowdhury

MHD-Conjugate Free Convection from  an Isothermal Horizontal Circular Cylinder with  Joule Heating and Heat Generation

The Abrams-Lloyd quantum algorithm computes an eigenvalue and the corresponding eigenstate of a unitary matrix from an approximate eigenvector <svg style="vertical-align:-3.3907pt;width:19.375px;" id="M1" height="15.4" version="1.1" viewBox="0 0 19.375 15.4" width="19.375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D449" d="M730 650l-8 -28q-52 -4 -72 -18t-64 -77q-79 -113 -321 -539h-33l-119 541q-13 59 -29.5 73t-66.5 20l7 28h245l-8 -28l-28 -5q-33 -6 -40.5 -15.5t-0.5 -38.5l102 -450h2q191 320 246 430q21 42 15.5 56t-43.5 19l-31 4l7 28h240z" /></g><g transform="matrix(.012,-0,0,-.012,12.675,15.187)"><path id="x1D44E" d="M483 97q-42 -50 -88.5 -79.5t-68.5 -29.5q-37 0 -17 93l22 102h-2q-54 -79 -144 -149q-59 -46 -100 -46q-24 0 -43 29t-19 86q0 78 34.5 153t94.5 120q41 31 94 51.5t98 20.5q29 0 72 -9q26 -6 39 -6l2 -4q-30 -117 -67 -323q-8 -41 2 -41q16 0 79 58zM374 387&#xA;q-32 15 -73 15q-52 0 -83 -23q-48 -36 -78 -108.5t-30 -152.5q0 -33 8.5 -50.5t20.5 -17.5q31 0 107 79t99 132q15 40 29 126z" /></g></svg>. 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 <svg style="vertical-align:-3.3907pt;width:19.375px;" id="M2" height="15.4" version="1.1" viewBox="0 0 19.375 15.4" width="19.375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D449" /></g><g transform="matrix(.012,-0,0,-.012,12.675,15.187)"><use xlink:href="#x1D44E" /></g></svg> 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

Preparation of Approximate Eigenvector by Unitary Operations on Eigenstate in Abrams-Lloyd Quantum Algorithm

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

Pierre Seimandi

A p-Strategy with a Local Time-Stepping Method in a Discontinuous Galerkin Approach to Solve Electromagnetic Problems

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 <svg     style="vertical-align:-2.3205pt;width:27.2875px;" id="M1" height="15.0875" version="1.1" viewBox="0 0 27.2875 15.0875" width="27.2875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D70E" d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109&#xA;q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" /></g><g transform="matrix(.017,-0,0,-.017,9.667,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,15.548,12.138)"><path id="x1D461" d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" /></g><g transform="matrix(.017,-0,0,-.017,21.345,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg> but also depends on the upper bound of the derivative of the time-varying leakage
delay <svg     style="vertical-align:-5.76984pt;width:16.950001px;" id="M2" height="15.2875" version="1.1" viewBox="0 0 16.950001 15.2875" width="16.950001"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,8.038)"><use xlink:href="#x1D70E"/></g>

			<g transform="matrix(.012,-0,0,-.012,9.663,12.112)"><path id="x1D707" d="M538 96q-38 -45 -84 -76.5t-71 -31.5q-44 0 -15 117q12 49 18 89h-2q-99 -128 -163 -178q-36 -28 -70 -28q-26 0 -44 38h-2q-16 -69 -16 -129q0 -43 11 -75.5t24 -42.5l1 -6q-7 -12 -24.5 -23t-37.5 -11q-40 0 -40 76q0 52 35 202l94 407l78 24l5 -5q-32 -122 -72 -310&#xA;q-7 -33 0 -55t25 -22q36 0 105.5 75t107.5 145l32 146l75 26h10q-50 -197 -78 -347q-7 -38 6 -38q7 0 31 17t47 39z" /></g>

		
	
</svg>. 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

A. R. Sudamani Ramaswamy

Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

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Journal of Computational Methods in Physics