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.
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 …
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows,
2016
University of Vienna
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Articles
We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.
On The N-Wave Equations With Pt-Symmetry,
2016
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, BULGARIA
On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
Articles
We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents,
2016
Technological University Dublin
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov
Articles
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised …
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 …
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 …
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant,
2016
Georgia Southern University
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
College of Graduate Studies: Theses & Dissertations
This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton's Universal Gravitation constant also known as "Big G". This tool set is especially applicable to Bose--Einstein--condensed systems present in NASA's Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrödinger or Gross--Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of the optical …
Black-Scholes Equation And Heat Equation,
2016
Georgia Southern University
Black-Scholes Equation And Heat Equation, Charles D. Joyner
Honors College Theses
First, we present and define the Black-Scholes equation which is used to model assets on the stock market. After that, we derive the heat equation that describes how the temperature increases through a homogeneous material. Finally, we detail how the two equations are related. We introduce and relate the Black-Scholes equation and Heat Equation.
Project Oasis: Optimizing Aquaponic Systems To Improve Sustainability,
2016
University of New Hampshire, Durham
Project Oasis: Optimizing Aquaponic Systems To Improve Sustainability, Siddharth Nigam, Paige Balcom
Honors Theses and Capstones
Started in Fall 2015, Project OASIS (Optimizing Aquaponic Systems to Improve Sustainability) is an interdisciplinary capstone project with the goal of designing a sustainable and affordable small-scale aquaponic system for use in developing nations to tackle the problems of malnutrition and food insecurity. Aquaponics is a symbiotic relationship between fish and vegetables growing together in a recirculating system. The project’s goals were to minimize energy consumption and construction costs while using universally available materials. The computational fluid dynamics (CFD) software OpenFOAM was used to create transient and steady-state models of fish tanks to visualize velocity profiles, streamlines, and particle movement. …
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 …
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 …
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 …
