Physical Sciences and Mathematics Commons^™

Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel

Applications and Applied Mathematics: An International Journal (AAM)

The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution.

A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt

University Faculty Publications and Creative Works

Let M3 S C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily …

An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.

Multistage Homotopy Analysis Method For Solving Nonlinear Integral Equations, H. Jafari, M. A. Firoozjaee

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present an efficient modification of the homotopy analysis method (HAM) that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy analysis method. This modification of the homotopy analysis method is applied to nonlinear integral equations and mixed Volterra-Fredholm integral equations, which yields a series solution with accelerated convergence. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work.

Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim.

Revised Variational Iteration Method For Solving Systems Of Ordinary Differential Equations, Elham Salehpoor, Hossein Jafari, Merieh A. Afrapoli

Applications and Applied Mathematics: An International Journal (AAM)

A modification of the variational iteration method applied to systems of linear/non-linear ordinary differential equations, which yields a series solution with accelerated convergence, has been presented. Illustrative examples have been given.

The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the variational iteration method is applied for finding the solution of an Integro-differential parabolic problem with integral conditions. Convergence of the proposed method is also discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method.

Forced Oscillations Of Nonlinear Hyperbolic Equations With Functional Arguments Via Riccati Method, Yutaka Shoukaku

Applications and Applied Mathematics: An International Journal (AAM)

By using integral averaging method and a generalized Riccati technique, sufficient conditions are established for the oscillation of solutions of forced nonlinear hyperbolic equations with functional arguments.

Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is applied to some nonlinear second order initial value problems and the numerical results reveal that the modified method is accurate and efficient for second order initial value problems.

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

Quantum Codes From Two-Point Hermitian Codes, Justine Hyde-Volpe

All Theses

We explore the background on error-correcting codes, including linear codes and quantum codes from curves. Then we consider the parameters of quantum codes constructed from two-point Hermitian codes.

Optimal Control Of Species Augmentation Conservation Strategies, Erin Nicole Bodine

Doctoral Dissertations

Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this dissertation, species augmentation is analyzed in an optimal control setting to determine the optimal augmentation strategies given various constraints and settings. In each setting, we consider the effects on both the target/endangered population and a reserve population from which the individuals translocated in the augmentation are harvested. Four different optimal control formulations are explored. The first two optimal control formulations model the underlying population dynamics with a system of ordinary differential equations. Each of these …

A Global Characterization Of Tubed Surfaces In ℂ2, Michael Bolt

University Faculty Publications and Creative Works

Let M3 S C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-Hermitian part of the second fundamental form transforms under Möbius transformations. The surfaces for which these forms are constant multiples of each other were identified in previous work, provided the constant is not unimodular. Here it is proved that if the surface is assumed to be complete and if the constant is unimodular, then the surface is tubed over a strongly convex curve. The converse statement is true, too, and is easily …

Contaminant Flow And Transport Simulation In Cracked Porous Media Using Locally Conservative Schemes, Pu Song

All Theses

The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous media, such as the influence of fracture network on the advection and diffusion of contaminant species, the adsorption impact of contaminant wastes on the overall transport flow and so on. In order to precisely describe the whole process, we firstly need to build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation, the other is reactive transport equation. The first …

Numerical Modeling Of Contaminant Transport In Fractured Porous Media Using Mixed Finite Element And Finite Volume Methods, Chen Dong

All Theses

A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods, i.e. mixed finite element (MFE) and the finite volume methods. Adaptive triangle mesh is used for effective treatment of the fractures. A hybrid MFE method is employed to provide an accurate approximation of velocities field for both the fractures and matrix which are crucial to the convection part of the transport equation. The finite volume method and the standard MFE method are used to approximate the convection and dispersion terms respectively. Numerical examples in different fractured media …

Conservation Based Uncertainty Propagation In Dynamic Systems, Lillian J. Ratliff

UNLV Theses, Dissertations, Professional Papers, and Capstones

Uncertainty is present in our everyday decision making process as well as our understanding of the structure of the universe. As a result an intense and mathematically rigorous study of how uncertainty propagates in the dynamic systems present in our lives is warranted and arguably necessary. In this thesis we examine existing methods for uncertainty propagation in dynamic systems and present the results of a literature survey that justifies the development of a conservation based method of uncertainty propagation. Conservation methods are physics based and physics drives our understanding of the physical world. Thus, it makes perfect sense to formulate …

Propagation Of Periodic Waves Using Wave Confinement, Paula Cysneiros Sanematsu

Masters Theses

This thesis studies the behavior of the Eulerian scheme, with "Wave Confinement" (WC), when propagating periodic waves. WC is a recently developed method that was derived from the scheme "vorticity confinement" used in fluid mechanics, and it efficiently solves the linear wave equation. This new method is applicable for numerous simulations such as radio wave propagation, target detection, cell phone and satellite communications.

The WC scheme adds a nonlinear term to the discrete wave equation that adds stability with negative and positive diffusion, conserves integral quantities such as total amplitude and wave speed, and it allows wave propagation over long …

Nonlinear Acoustics Of Piston-Driven Gas-Column Oscillations, Andrew William Wilson

Masters Theses

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general …

Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski

Publications

As a preliminary study to more complex situations of interest in small-scale technology, this paper envisages the elementary propagation properties of elastic waves in one-spatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure space-like and time-like material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on …

Multirelational Organization Of Large-Scale Social Networks In An Online World, Renaud Lambiotte

Renaud Lambiotte

The capacity to collect fingerprints of individuals in online media has revolutionized the way researchers explore human society. Social systems can be seen as a nonlinear superposition of a multitude of complex social networks, where nodes represent individuals and links capture a variety of different social relations. Much emphasis has been put on the network topology of social interactions, however, the multidimensional nature of these interactions has largely been ignored, mostly because of lack of data. Here, for the first time, we analyze a complete, multirelational, large social network of a society consisting of the 300,000 odd players of a …

Using Clustering For Modeling Monthly Salary Grade, R. W. Hndoosh

R. W. Hndoosh

Clustering is considered as one of the most scientifically developments which the scientists reached at in the field of recent knowledge and technologies to discover the cluster's group. The clustering concept was introduced firstly by Ronald in 1955. The clustering's fundamental notion is represented in dividing the data into clusters. This research aims to using clustering for actual data modeling for the monthly salary grade of the teaching staff for one of the Mosul University's College in 2009, by using HCM algorithm to these data. Matlab software is used to write down the proposed algorithm programs. Results proved the efficiency …

Optimal Control Of A Switched System In Microbial Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng

Chongyang Liu

The main control goal in fed-batch fermentation process is to get a high concentration of production. In this paper, by taking the feed rate of glycerol as the control function, a nonlinear switched system is proposed to formulate the fed-batch fermentation process of glycerol to 1,3-propanediol (1,3-PD). To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to constraints of continuous state inequality and control function is presented. A computational approach is developed to seek the optimal solution in two aspects. On the one hand, the control parametrization enhancing transform together with the control …

The Generation Of Domestic Electricity Load Profiles Through Markov Chain Modelling, Aidan Duffy, Fintan Mcloughlin, Michael Conlon

Conference Papers

Micro-generation technologies such as photovoltaics and micro-wind power are becoming increasing popular among homeowners, mainly a result of policy support mechanisms helping to improve cost competiveness as compared to traditional fossil fuel generation. National government strategies to reduce electricity demand generated from fossil fuels and to meet European Union 20/20 targets is driving this change. However, the real performance of these technologies in a domestic setting is not often known as high time resolution models for domestic electricity load profiles are not readily available. As a result, projections in terms of reducing electricity demand and financial paybacks for these micro-generation …

Analytic Construction Of Periodic Orbits In The Restricted Three-Body Problem, Mohammed A. Ghazy

Mechanical & Aerospace Engineering Theses & Dissertations

This dissertation explores the analytical solution properties surrounding a nominal periodic orbit in two different planes, the plane of motion of the two primaries and a plane perpendicular to the line joining the two primaries, in the circular restricted three-body problem. Assuming motion can be maintained in the plane and motion of the third body is circular, Jacobi's integral equation can be analytically integrated, yielding a closed-form expression for the period and path expressed with elliptic integral and elliptic function theory. In this case, the third body traverses a circular path with nonuniform speed. In a strict sense, the in-plane …

A Solution Of The Heat Equation With The Discontinuous Galerkin Method Using A Multilivel Calculation Method That Utilizes A Multiresolution Wavelet Basis, Robert Gregory Brown

Mathematics & Statistics Theses & Dissertations

A numerical method to solve the parabolic problem is developed that utilizes the Discontinuous Galerkin Method for space and time discretization. A multilevel method is employed in the space variable. It is shown that use of this process yields the same level of accuracy as the standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.

Post-Processing Techniques And Wavelet Applications For Hammerstein Integral Equations, Khomsan Neamprem

Mathematics & Statistics Theses & Dissertations

This dissertation is focused on the varieties of numerical solutions of nonlinear Hammerstein integral equations. In the first part of this dissertation, several acceleration techniques for post-processed solutions of the Hammerstein equation are discussed. The post-processing techniques are implemented based on interpolation and extrapolation. In this connection, we generalize the results in [29] and [28] to nonlinear integral equations of the Hammerstein type. Post-processed collocation solutions are shown to exhibit better accuracy. Moreover, an extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.

In …

Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He

Scholarship

A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …

Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, Gin Mccollum, Douglas Hanes

Mathematics and Statistics Faculty Publications and Presentations

Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.

Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He

Tian-Xiao He

A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …

Is The Curvature Of The Flagellum Involved In The Apparent Cooperativity Of The Dynein Arms Along The "9+2" Axoneme?, Christian Cibert, Andrei Ludu

Andrei Ludu