A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows,
2016
West Chester University of Pennsylvania
A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou
Mathematics Faculty Publications
We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on the …
2. Population,
2016
Illinois Mathematics and Science Academy
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
3: Drugs And De's,
2016
Illinois Mathematics and Science Academy
3: Drugs And De's, Ruth Dover
Differential Equations
Making a connection between discrete recursion and differential equations.
1. Coffee,
2016
Illinois Mathematics and Science Academy
A High Accuracy Minimally Invasive Regularization Technique For Navier-Stokes Equations At High Reynolds Number,
2016
Michigan Technological University
A High Accuracy Minimally Invasive Regularization Technique For Navier-Stokes Equations At High Reynolds Number, Mustafa Aggul
Dissertations, Master's Theses and Master's Reports
A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier-Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes (a frequent requirement in the simulation of turbulent flows in complex geometries). The two-step method is considered here; in order to obtain a regularization that is second order accurate in space and time, the method computes a low-order accurate, stable and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher …
Galvanically Induced/Accelerated Crevice Corrosion,
2016
The University of Akron
Galvanically Induced/Accelerated Crevice Corrosion, Zachary R. Roland
Williams Honors College, Honors Research Projects
In this thesis, a one dimensional model is developed to investigate the initial stages of corrosion in a fastener assembly consisting of a stainless steel fastener and aluminum 7075 as the plate. Differential equations are formulated and solved to determine the profiles for the potential, the oxygen concentration, and the aluminum ion concentration in the crevice, and also the potential in the bulk electrolyte. This fastener system exhibits galvanic corrosion, pitting corrosion, and crevice corrosion. It is found that the potential decreases monotonically down the length of the crevice, the oxygen concentration decreases exponentially down the length of the crevice, …
Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease,
2016
The University of Akron
Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops
Williams Honors College, Honors Research Projects
In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore …
Defect-Deferred Correction Method For The Two-Domain Convection-Dominated Convection-Diffusion Problem,
2016
Michigan Technological University
Defect-Deferred Correction Method For The Two-Domain Convection-Dominated Convection-Diffusion Problem, Dilek Erkmen
Dissertations, Master's Theses and Master's Reports
We present a method for solving a fluid-fluid interaction problem (two convection-dominated convection-diusion problems adjoined by an interface), which is a simplifed version of the atmosphere ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid-fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied …
Exact Implicit Solution Of Nonlinear Heat Transfer In Rectangular Straight Fin Using Symmetry Reduction Methods,
2015
Mansoura University
Exact Implicit Solution Of Nonlinear Heat Transfer In Rectangular Straight Fin Using Symmetry Reduction Methods, M. S. Abdel Latif, A. H. Abdel Kader, H. M. Nour
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the exact implicit solution of the second order nonlinear ordinary differential equation which governing heat transfer in rectangular fin is obtained using symmetry reduction methods. General relationship among the temperature at the fin tip, the temperature gradient at the fin base, the mode of heat transfer, 𝑛 and the fin parameters 𝑁 and ℰ is obtained. Some numerical examples are discussed and it is shown that the temperature of fin increases when approaching from the heat source. The relationship between the fin efficiency and the temperature of fin tip is obtained for any value of the mode …
Boundary-Layer Flow Of Nanofluids Over A Moving Surface In The Presence Of Thermal Radiation, Viscous Dissipation And Chemical Reaction,
2015
Osmania University
Boundary-Layer Flow Of Nanofluids Over A Moving Surface In The Presence Of Thermal Radiation, Viscous Dissipation And Chemical Reaction, Eshetu Haile, B. Shankar
Applications and Applied Mathematics: An International Journal (AAM)
The flow problem presented in the paper is boundary-layer flow of nanofluids over a moving surface in the presence of thermal radiation, viscous dissipation and chemical reaction. The plate is assumed to move in the same or opposite direction to the free stream which depends on the sign of the velocity parameter. The partial differential equations appearing in the governing equations are transformed into a couple of nonlinear ordinary differential equations using similarity transformations. The transformed equations in turn are solved numerically by the shooting method along with the fourth order Runge-Kutta integration technique. Influences of the pertinent parameters in …
Local Fractional Variational Iteration Method For Solving Nonlinear Partial Differential Equations Within Local Fractional Operators,
2015
University of Mazandaran
Local Fractional Variational Iteration Method For Solving Nonlinear Partial Differential Equations Within Local Fractional Operators, Hossein Jafari, Hassan K. Jassim
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the proposed method is capable of solving effectively a large number of nonlinear differential equations with high accuracy. In addition, we show that local fractional variational iteration method is able to solve a large class of nonlinear problems involving local fractional operators effectively, more easily and accurately, and …
Nonlinear Partial Differential Equations, Their Solutions, And Properties,
2015
Boise State University
Nonlinear Partial Differential Equations, Their Solutions, And Properties, Prasanna Bandara
Boise State University Theses and Dissertations
Although valuable understanding of real-world phenomena can be gained experimentally, it is often the case that experimental investigations can be found to be limited by financial, ethical or other constraints making such an approach impractical or, in some cases, even impossible. To nevertheless understand and make predictions of the natural world around us, countless processes encountered in the physical and biological sciences, engineering, economics and medicine can be efficiently described by means of mathematical models written in terms of ordinary or/and partial differential equations or their systems. Fundamental questions that arise in the modeling process need care that relies on …
An Economic Regression Model To Predict Market Movements,
2015
Embry-Riddle Aeronautical University
An Economic Regression Model To Predict Market Movements, Timothy A. Smith, Andrew Hawkins
Publications
In finance, multiple linear regression models are frequently used to determine the value of an asset based on its underlying traits. We built a regression model to predict the value of the S&P 500 based on economic indicators of gross domestic product, money supply, produce price and consumer price indices. Correlation between the error in this regression model and the S&P’s volatility index (VIX) provides an efficient way to predict when large changes in the price of the S&P 500 may occur. As the true value of the S&P 500 deviates from the predicted value, obtained by the regression model, …
Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings,
2015
Tallinn University of Technology
Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski
Publications
Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.
Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids,
2015
The University of New Orleans
Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu
LSU New Orleans Theses and Dissertations
The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.
On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes,
2015
University of Southern Mississippi
On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo
Dissertations
Meshless methods utilizing Radial Basis Functions~(RBFs) are a numerical method that require no mesh connections within the computational domain. They are useful for solving numerous real-world engineering problems. Over the past decades, after the 1970s, several RBFs have been developed and successfully applied to recover unknown functions and to solve Partial Differential Equations (PDEs).
However, some RBFs, such as Multiquadratic (MQ), Gaussian (GA), and Matern functions, contain a free variable, the shape parameter, c. Because c exerts a strong influence on the accuracy of numerical solutions, much effort has been devoted to developing methods for determining shape parameters which provide …
Local And Nonlocal Models In Thin-Plate And Bridge Dynamics,
2015
University of Nebraska-Lincoln
Local And Nonlocal Models In Thin-Plate And Bridge Dynamics, Jeremy Trageser
Department of Mathematics: Dissertations, Theses, and Student Research
This thesis explores several models in continuum mechanics from both local and nonlocal perspectives. The first portion settles a conjecture proposed by Filippo Gazzola and his collaborators on the finite-time blow-up for a class of fourth-order differential equations modeling suspension bridges. Under suitable assumptions on the nonlinearity and the initial data, a finite-time blowup is demonstrated as a result of rapid oscillations with geometrically growing amplitudes. The second section introduces a nonlocal peridynamic (integral) generalization of the biharmonic operator. Its action converges to that of the classical biharmonic as the radius of nonlocal interactions---the ``horizon"---tends to zero. For the corresponding …
Kink, Singular Soliton And Periodic Solutions To Class Of Nonlinear Equations,
2015
Jordan University of Science and Technology
Kink, Singular Soliton And Periodic Solutions To Class Of Nonlinear Equations, Marwan Alquran, Safwan Al-Shara, Sabreen Al-Nimrat
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we extend the ordinary differential Duffing equation into a partial differential equation. We study the traveling wave solutions to this model by using the G'/G expansion method. Then, based on the obtained results given for the Duffing equation, we generate kink, singular soliton and periodic solutions for a coupled integrable dispersionless nonlinear system. All the solutions given in this work are verified.
New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods,
2015
University of Guilan
New Exact Solutions Of The Perturbed Nonlinear Fractional Schr¨Odinger Equation Using Two Reliable Methods, Nasir Taghizadeh, Mona N. Foumani, Vahid S. Mohammadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the fractional derivatives in the sense of the modified Riemann-Liouville derivative and the first integral method and the Bernoulli sub-ODE method are employed for constructing the exact complex solutions of the perturbed nonlinear fractional Schr ¨odinger equation and comparing the solutions.
Solution Of Fractional Drinfeld-Sokolov-Wilson Equation Using Homotopy Perturbation Transform Method,
2015
Indian Institute of Technology
Solution Of Fractional Drinfeld-Sokolov-Wilson Equation Using Homotopy Perturbation Transform Method, P. K. Singh, K. Vishal, T. Som
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the approximate solutions of the non-linear Drinfeld-Sokolov-Wilson equation with fractional time derivative have been obtained. The fractional derivative is described in the Caputo sense. He’s polynomial is used to tackle the nonlinearity which arise in our considered problems. A time fractional nonlinear partial differential equation has been computed numerically. The numerical procedures illustrate the effectiveness and reliability of the method. Effects of fractional order time derivatives on the solutions for different particular cases are presented through graphs.
