Physical Sciences and Mathematics Commons^™

Mhd Flow Over Exponential Radiating Stretching Sheet Using Homotopy Analysis Method, Fazle Mabood

Fazle Mabood

No abstract provided.

Approximate Analytic Solutions For Influence Of Heat Transfer On Mhd Stagnation Point Flow In Porous Medium, Fazle Mabood

Fazle Mabood

No abstract provided.

Homotopy Analysis Method For Boundary Layer Flow And Heat Transfer Over A Permeable Flat Plate In A Darcian Porous Medium With Radiation Effects, Fazle Mabood

Fazle Mabood

No abstract provided.

Mhd Boundarylayer Flowandheattransferofnanofluids Overanonlinearstretchingsheet:Anumericalstudy, Fazle Mabood

Fazle Mabood

No abstract provided.

Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He

Ji-Huan He

A homotopy perturbation method with two expanding parameters is suggested. The method is especially effective for a nonlinear equation with two nonlinear terms, which might have different effects on the solution. A nonlinear oscillator is used as an example to elucidate the solution procedure.

Criterion For An Oscillatory Charged Jet During The Bubble Spinning Process, Ji-Huan He, H.Y. Kong

Ji-Huan He

The oscillatory diameter of the charged jet during the bubble electrospinning results in beads on the obtained nanofibers. We demonstrate that the applied voltage and the initial flow rate of the jet are the crucial parameters that are necessary to control morphology of the nanofibers. We also find that there is a criterion for production of smooth nanofibers without beads. The theory developed in this paper can be extended to the classical electrospinning and the blown bubble-spinning.

Variational Iteration Method For Bratu-Like Equation Arising In Electrospinning, Ji-Huan He, Hai-Yan Kong, Rou-Xi Chen, Ming-Sheng Hu, Qiao-Ling Chen

Ji-Huan He

This paper points out that the so called enhanced variational iteration method (Colantoni & Boubaker, 2014) for a nonlinear equation arising in electrospinning and vibration-electrospinning process is the standard variational iteration method. An effective algorithm using the variational iteration algorithm-II is suggested for Bratu-like equation arising in electrospinning. A suitable choice of initial guess results in a relatively accurate solution by one or few iteration.

Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li

Ji-Huan He

Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional …

Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong

Chongyang Liu

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control …

Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu

Chongyang Liu

Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a …

Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the …

A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time-delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system …

Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary …

Compound Interest And The Power Of Saving, Richard H. Serlin

Richard H. Serlin

This is an article with an included assignment that I give to my personal finance 1 students. The first part talks about the power of compound interest. I go into depth about the intuition why it's so powerful, why it takes off, and has been called the eighth wonder of the world. I've haven't seen anywhere else an extensive explanation of the intuition like I have here.

In the second part I give the students a nice assignment to see how much their savings can grow if they invest even a modest amount consistently, month in and month out, in …

A New Class Of Scalable Parallel Pseudorandom Number Generators Based On Pohlig-Hellman Exponentiation Ciphers, Paul Beale

Paul Beale

Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes. We propose a new scalable class of parallel pseudorandom number generators based on Pohlig--Hellman exponentiation ciphers. The method generates uniformly distributed floating point pseudorandom streams by encrypting simple sequences of integer \textit{messages} into \textit{ciphertexts} by exponentiation modulo prime numbers. The advantages of the method are: the method is trivially parallelizable by parameterization with each pseudorandom number generator derived from an independent prime modulus, the method is fully scalable on massively parallel computing clusters due to the large number of primes available …

Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Mechaniczno-Energetycznego Pwr., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Tematyka Prac Dyplomowych Dla Studentów Wydziału Chemicznego Pwr., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Mechanika Płynów Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Fibonacci Sequence And Orderliness As Observed In The Creations Of Allah, Mohd Rezuan Masran Mr.

Mr. Mohd Rezuan Masran

There are numerous verses in the Quran that encourage Muslims to observe the many creations of Allah. This article is an exploratory discuss ion on the observation of a sequence of numbers known as the Fibonacci sequence (also known as the Fibonacci numbers ) which can be observed in the creations of Allah. The history of Fibonacci sequence dated back to 1202 in the magnum opus of the Italian mathematician, Leonardo Pisano Fibonacci, entitled Liber Abaci ( Book of Calculation ). This article discusses verses in the Quran that encourage us to observe Allah’s creations. T here are many occurrences …

Variational Iteration Method For The Burgers' Flow With Fractional Derivatives—New Lagrange Multipliers, Guo-Cheng Wu, Dumitru Baleanu

G.C. Wu

The flow through porous media can be better described by fractional models than the classical ones since they include inherently memory effects caused by obstacles in the structures. The variational iteration method was extended to find approximate solutions of fractional differential equations with the Caputo derivatives, but the Lagrange multipliers of the method were not identified explicitly. In this paper, the Lagrange multiplier is determined in a more accurate way and some new variational iteration formulae are presented.

Application Of The Local Fractional Series Expansion Method And The Variational Iteration Method To The Helmholtz Equation Involving Local Fractional Derivative Operators, Yang Xiaojun

Xiao-Jun Yang

We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.

A Proposition For Using Mathematical Models Based On A Fuzzy System With Application, R. W. Hndoosh

R. W. Hndoosh

Some mathematical models based on fuzzy set theory, fuzzy systems and neural network techniques seem very well suited for typical technical problems. This study aims to build two different models, the Fuzzy Inference System (FIS) and the Adaptive Fuzzy System using neural network. We have proposed a new model of a fuzzy system that is extended from 2-dimensions to 3-dimensions, using Mamdani's minimum implication, the minimum inference system, the Singleton fuzzifier and the Center Average Defuzzifier. Also, we have extended the theorem accuracy of the fuzzy system to 3- dimensions along with changing the type of fuzzy inference system. We …

Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng

Chongyang Liu

The main control goal in fed-batch fermentation is to maximize yield of target product and reduce operation costs. In this paper, we propose a controlled nonlinear time-delay system, in which the flow rate of glycerol is taken as the control function and the terminal time of the fermentation as the optimization variable, to model the 1,3-propanediol (1,3-PD) production in fed-batch process. Taking the mass of 1,3-PD per unit time as the performance index, we formulate a constrained optimal control model with free terminal time to optimize the production process. Using a time-scale transformation, the optimal control problem is equivalently transcribed …

Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun

Xiao-Jun Yang

The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.

An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of L-moments and L-correlation. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of L-skew, L-kurtosis, …

Fractional, Bahram Agheli

Bahram Agheli

No abstract provided.

Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.

Mohammed O. Al-Amr

In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for...

Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation, Abdulghafor M. Al-Rozbayani Ph.D., Mohammed O. Al-Amr M.Sc.

Mohammed O. Al-Amr

In this paper, the discrete Adomian decomposition method (DADM) is applied to a fully implicit scheme of the generalized Burger’s–Huxley equation. The numerical results of two test problems are compared with the exact solutions. The comparisons reveal that the proposed method is very accurate and effective for this kind of problems.

Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang

Xiao-Jun Yang

The local fractional Schr¨odinger equations in the one-dimensional Cantorian systemare investigated.The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.