**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**263

# Search results for: number of iteration

##### 263 Trajectory-Based Modified Policy Iteration

**Abstract:**

**Keywords:**
Markov Decision Process (MDP),
Mobile robot,
Policy iteration,
Simulation.

##### 262 A Kernel Classifier using Linearised Bregman Iteration

**Authors:**
K. A. D. N. K Wimalawarne

**Abstract:**

**Keywords:**
Compressive sensing,
Bregman iteration,
Generalisedhinge loss,
sparse,
kernels,
shrinkage functions

##### 261 Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space

**Authors:**
Alemayehu Geremew Negash

**Abstract:**

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

**Keywords:**
Common fixed point,
Mann iteration,
Multivalued mapping,
weak convergence.

##### 260 Optimal Design of UPFC Based Damping Controller Using Iteration PSO

**Authors:**
Amin Safari,
Hossein Shayeghi

**Abstract:**

This paper presents a novel approach for tuning unified power flow controller (UPFC) based damping controller in order to enhance the damping of power system low frequency oscillations. The design problem of damping controller is formulated as an optimization problem according to the eigenvalue-based objective function which is solved using iteration particle swarm optimization (IPSO). The effectiveness of the proposed controller is demonstrated through eigenvalue analysis and nonlinear time-domain simulation studies under a wide range of loading conditions. The simulation study shows that the designed controller by IPSO performs better than CPSO in finding the solution. Moreover, the system performance analysis under different operating conditions show that the δE based controller is superior to the mB based controller.

**Keywords:**
UPFC,
Optimization Problem,
Iteration ParticleSwarm Optimization,
Damping Controller,
Low FrequencyOscillations.

##### 259 Investigation of a Transition from Steady Convection to Chaos in Porous Media Using Piecewise Variational Iteration Method

**Authors:**
Mohamed M. Mousa,
Aidarkhan Kaltayev Shahwar F. Ragab

**Abstract:**

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

**Keywords:**
Variational iteration method,
free convection,
Chaos,
Lorenz equations.

##### 258 On Algebraic Structure of Improved Gauss-Seidel Iteration

**Authors:**
O. M. Bamigbola,
A. A. Ibrahim

**Abstract:**

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

**Keywords:**
Linear system of equations,
Gauss-Seidel iteration,
algebraic structure,
convergence.

##### 257 Variational Iteration Method for the Solution of Boundary Value Problems

**Authors:**
Olayiwola M.O.,
Gbolagade A .W.,
Akinpelu F. O.

**Abstract:**

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

**Keywords:**
Variational iteration method,
boundary value
problems,
convergence,
restricted variation.

##### 256 Studying the Effect of Froude Number and Densimetric Froude Number on Local Scours around Circular Bridge Piers

**Authors:**
Md Abdullah Al Faruque

**Abstract:**

A very large percentage of bridge failures are attributed to scouring around bridge piers and this directly influences public safety. Experiments are carried out in a 12-m long rectangular open channel flume made of transparent tempered glass. A 300 mm thick bed made up of sand particles is leveled horizontally to create the test bed and a 50 mm hollow plastic cylinder is used as a model bridge pier. Tests are carried out with varying flow depths and velocities. Data points of various scour parameters such as scour depth, width, and length are collected based on different flow conditions and visual observations of changes in the stream bed downstream the bridge pier are also made as the scour progresses. Result shows that all three major flow characteristics (flow depth, Froude number and densimetric Froude number) have one way or other affect the scour profile.

**Keywords:**
Bridge pier scour,
densimetric Froude number,
flow depth,
Froude Number,
sand.

##### 255 Convergence of a One-step Iteration Scheme for Quasi-asymptotically Nonexpansive Mappings

**Authors:**
Safeer Hussain Khan

**Abstract:**

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

**Keywords:**
One-step iteration scheme,
asymptotically quasi non expansive mapping,
common fixed point,
condition (a'),
weak and strong convergence.

##### 254 A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations

**Authors:**
Jinfeng Wang,
Yang Liu,
Hong Li

**Abstract:**

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

**Keywords:**
Hyperbolic wave equation,
Nonlinear,
He’s variational
iteration method,
Transformations

##### 253 Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method

**Authors:**
Desmond Adair,
Kairat Ismailov,
Martin Jaeger

**Abstract:**

Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

**Keywords:**
Timoshenko beam,
variational iteration method,
two-parameter elastic foundation model.

##### 252 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations

**Authors:**
Sara Barati,
Karim Ivaz

**Abstract:**

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

**Keywords:**
Variational iteration method,
delay differential equations,
multiple delays,
Runge-Kutta method.

##### 251 A Contractor Iteration Method Using Eigenpairs for Positive Solutions of Nonlinear Elliptic Equation

**Authors:**
Hailong Zhu,
Zhaoxiang Li,
Kejun Zhuang

**Abstract:**

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

**Keywords:**
Positive solutions,
newton's method,
contractor iteration method,
Eigenpairs.

##### 250 Comparison of Newton Raphson and Gauss Seidel Methods for Power Flow Analysis

**Authors:**
H. Abaali,
T. Talbi,
R.Skouri

**Abstract:**

This paper presents a comparative study of the Gauss Seidel and Newton-Raphson polar coordinates methods for power flow analysis. The effectiveness of these methods are evaluated and tested through a different IEEE bus test system on the basis of number of iteration, computational time, tolerance value and convergence.

**Keywords:**
Convergence time,
Gauss-Seidel Method,
Newton-Raphson Method,
number of iteration,
power flow analysis.

##### 249 Analyses of Natural Convection Heat Transfer from a Heated Cylinder Mounted in Vertical Duct

**Authors:**
H. Bhowmik,
A. Faisal,
Ahmed Al Yaarubi,
Nabil Al Alawi

**Abstract:**

Experiments are conducted to analyze the steady-state and the power-on transient natural convection heat transfer from a horizontal cylinder mounted in a vertical up flow circular duct. The heat flux ranges from 177 W/m^{2} to 2426 W/m^{2} and the Rayleigh number ranges from 1×10^{4} to 4.35×10^{4}. For natural air flow and constant heat flux condition, the effects of heat transfer around the cylinder under steady-state condition are investigated. The steady-state results compare favorably with that of the available data. The effects of transient heat transfer data on different angular position of the thermocouple (0^{o}, 90^{o}, 180^{o}) are also reported. It is observed that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. In the transient region, the rate of heat transfer obtained at 90^{o} and 180^{o} are higher than that of stagnation point (0^{o}). Finally, the dependence of the average Nusselt number on Rayleigh number for steady and transient natural convection heat transfer are analyzed, and a correlation equation is presented.

**Keywords:**
Steady-state,
transient,
natural convection,
Rayleigh number,
Nusselt number,
Fourier Number.

##### 248 Fluid Flow and Heat Transfer Structures of Oscillating Pipe Flows

**Authors:**
Yan Su,
Jane H. Davidson,
F. A. Kulacki

**Abstract:**

**Keywords:**
Keulegan-Carpenter number,
Nusselt number,
Oscillating pipe flows,
Reynolds number

##### 247 A Dynamically Reconfigurable Arithmetic Circuit for Complex Number and Double Precision Number

**Authors:**
Haruo Shimada,
Akinori Kanasugi

**Abstract:**

**Keywords:**
arithmetic circuit,
complex number,
double precision,
dynamic reconfiguration

##### 246 Numerical Study of Transient Laminar Natural Convection Cooling of high Prandtl Number Fluids in a Cubical Cavity: Influence of the Prandtl Number

**Authors:**
O. Younis,
J. Pallares,
F. X. Grau

**Abstract:**

This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5·106 and 5·107) and six different Prandtl numbers (3 · 105 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (N u) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.

**Keywords:**
Transient natural convection,
High Prandtl number,
variable viscosity.

##### 245 Natural Convection Heat Transfer from Inclined Cylinders: A Unified Correlation

**Authors:**
Neetu Rani,
Hema Setia,
Marut Dutt. R.K. Wanchoo

**Abstract:**

An empirical correlation for predicting the heat transfer coefficient for a cylinder under free convection, inclined at any arbitrary angle with the horizontal has been developed in terms of Nusselt number, Prandtl number and Grashof number. Available experimental data was used to determine the parameters for the proposed correlation. The proposed correlation predicts the available data well within ±10%, for Prandtl number in the range 0.68-0.72 and Grashof number in the range 1.4×10^{4}–1.2×10^{10}.

**Keywords:**
Heat transfer,
inclined cylinders,
natural convection,
Nusselt number,
Prandtl number,
Grashof number.

##### 244 Deterministic Random Number Generators for Online Applications

**Authors:**
Natarajan Vijayarangan,
Prasanna S. Bidare

**Abstract:**

Cryptography, Image watermarking and E-banking are filled with apparent oxymora and paradoxes. Random sequences are used as keys to encrypt information to be used as watermark during embedding the watermark and also to extract the watermark during detection. Also, the keys are very much utilized for 24x7x365 banking operations. Therefore a deterministic random sequence is very much useful for online applications. In order to obtain the same random sequence, we need to supply the same seed to the generator. Many researchers have used Deterministic Random Number Generators (DRNGs) for cryptographic applications and Pseudo Noise Random sequences (PNs) for watermarking. Even though, there are some weaknesses in PN due to attacks, the research community used it mostly in digital watermarking. On the other hand, DRNGs have not been widely used in online watermarking due to its computational complexity and non-robustness. Therefore, we have invented a new design of generating DRNG using Pi-series to make it useful for online Cryptographic, Digital watermarking and Banking applications.

**Keywords:**
E-tokens,
LFSR,
non-linear,
Pi series,
pseudo
random number.

##### 243 Sinusoidal Roughness Elements in a Square Cavity

**Abstract:**

Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm based on a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was 16.66 percent at Ra number 10^5.

**Keywords:**
Lattice Boltzmann Method Natural convection,
Nusselt Number Rayleigh number,
Roughness.

##### 242 Investigating Iraqi EFL Undergraduates' Performance in the Production of Number Forms in English

**Authors:**
Adnan Z. Mkhelif

**Abstract:**

The production of number forms in English tends to be problematic for Iraqi learners of English as a foreign language (EFL), even at the undergraduate level. To help better understand and consequently address this problem, it is important to identify its sources. This study aims at: (1) statistically analysing Iraqi EFL undergraduates' performance in the production of number forms in English; (2) classifying learners' errors in terms of their possible major causes; and (3) outlining some pedagogical recommendations relevant to the teaching of number forms in English. It is hypothesized in this study that (1) Iraqi EFL undergraduates still face problems in the production of number forms in English and (2) errors pertaining to the context of learning are more numerous than those attributable to the other possible causes. After reviewing the literature available on the topic, a written test comprising 50 items has been constructed and administered to a randomly chosen sample of 50 second-year college students from the Department of English, College of Education, Wasit University. The findings of the study showed that Iraqi EFL undergraduates still face problems in the production of number forms in English and that the possible major sources of learners’ errors can be arranged hierarchically in terms of the percentages of errors to which they can be ascribed as follows: (1) context of learning (50%), (2) intralingual transfer (37%), and (3) interlingual transfer (13%). It is hoped that the implications of the study findings will be beneficial to researchers, syllabus designers, as well as teachers of English as a foreign/second language.

**Keywords:**
L2 morphology,
L2 number forms,
L2 vocabulary learning,
productive knowledge.

##### 241 An Overview of Some High Order and Multi-Level Finite Difference Schemes in Computational Aeroacoustics

**Authors:**
Appanah Rao Appadu,
Muhammad Zaid Dauhoo

**Abstract:**

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.

**Keywords:**
Optimised time derivative,
dissipation,
dispersion,
cfl number,
Nomenclature: k : time step,
h : spatial step,
β :advection velocity,
r: cfl/Courant number,
hkrβ= ,
w =θ,
h : exact wave number,
n :time level,
RPE : Relative phase error per unit time step,
AFM :modulus of amplification factor

##### 240 Numerical and Experimental Investigations on Jet Impingement Cooling

**Authors:**
Arun Jacob,
Leena R.,
Krishnakumar T.S.,
Jose Prakash M.

**Abstract:**

**Keywords:**
CFD,
heat transfer coefficient,
Nusselt number,
ratio of jet diameter to jet spacing (Z/D),
Reynolds number,
turbulence model.

##### 239 Effect of Prandtl Number on Natural Convection Heat Transfer from a Heated Semi-Circular Cylinder

**Authors:**
Avinash Chandra,
R. P. Chhabra

**Abstract:**

**Keywords:**
Constant heat flux,
Constant surface temperature,
Grashof number,
natural convection,
Prandtl number,
Semi-circular
cylinder

##### 238 Effect of Blade Number on a Straight-Bladed Vertical-Axis Darreius Wind Turbine

**Authors:**
Marco Raciti Castelli,
Stefano De Betta,
Ernesto Benini

**Abstract:**

**Keywords:**
CFD,
VAWT,
NACA 0021,
blade number

##### 237 Behavior of Ice Melting in Natural Convention

**Authors:**
N. Dizadji,
P. Entezar

**Abstract:**

**Keywords:**
Nusselt Number,
Heat Transfer,
Grashof Number,
Heat Transfer Coefficient.

##### 236 Completion Number of a Graph

**Authors:**
Sudhakar G

**Abstract:**

In this paper a new concept of partial complement of a graph G is introduced and using the same a new graph parameter, called completion number of a graph G, denoted by c(G) is defined. Some basic properties of graph parameter, completion number, are studied and upperbounds for completion number of classes of graphs are obtained , the paper includes the characterization also.

**Keywords:**
Completion Number,
Maximum Independent subset,
Partial complements,
Partial self complementary

##### 235 Public Key Cryptosystem based on Number Theoretic Transforms

**Authors:**
C. Porkodi,
R. Arumuganathan

**Abstract:**

**Keywords:**
Cryptography,
decryption,
discrete logarithm
problem encryption,
Integer Factorization problem,
Key agreement,
Number Theoretic Transform.

##### 234 Numerical Investigation of the Effect of Number of Waves on Heat Transfer in a Wavy Wall Enclosure

**Authors:**
Ali Reza Tahavvor,
Saeed Hosseini,
Afshin Karimzadeh Fard

**Abstract:**

In this paper the effect of wall waviness of side walls in a two-dimensional wavy enclosure is numerically investigated. Two vertical wavy walls and straight top wall are kept isothermal and the bottom wall temperature is higher and spatially varying with cosinusoidal temperature distribution. A computational code based on Finite-volume approach is used to solve governing equations and SIMPLE method is used for pressure velocity coupling. Test is performed for several different numbers of undulations. The Prandtl number was kept constant and the Ra number denotes that the flow is laminar. Temperature and velocity fields are determined. Therefore, according to the obtained results a correlation is proposed for average Nusselt number as a function of number of side wall waves. The results indicate that the Nusselt number is highly affected by number of waves and increasing it decreases the wavy walls Nusselt number; although the Nusselt number is not highly affected by surface waviness when the number of undulations is below one.

**Keywords:**
Cavity,
natural convection,
Nusselt number,
wavy
wall.