Heads And Tails, 2017 The California Maritime Academy

#### Heads And Tails, Julie Simons

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

A Method For Sensitivity Analysis And Parameter Estimation Applied To A Large Reaction-Diffusion Model Of Cell Polarization, 2017 The Ohio State University

#### A Method For Sensitivity Analysis And Parameter Estimation Applied To A Large Reaction-Diffusion Model Of Cell Polarization, Marissa Renardy, Tau-Mu Yi, Dongbin Xiu, Ching-Shan Chou

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Modeling Microtubule-Based Transport In The Frog Egg Cell, 2017 Mathematical Biosciences Institute at OSU

#### Modeling Microtubule-Based Transport In The Frog Egg Cell, Maria-Veronica Ciocanel

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, 2017 Embry-Riddle Aeronautical University

#### A Regression Model To Predict Stock Market Mega Movements And/Or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith, Alcuin Rajan

*Publications*

In finance, regression models or time series moving averages can be used to determine the value of an asset based on its underlying traits. In prior work we built a regression model to predict the value of the S&P 500 based on macroeconomic indicators such as gross domestic product, money supply, produce price and consumer price indices. In this present work this model is updated both with more data and an adjustment in the input variables to improve the coefficient of determination. A scheme is also laid out to alternately define volatility rather than using common tools such as ...

Low-Communication, Parallel Multigrid Algorithms For Elliptic Partial Differential Equations, 2017 University of Colorado, Boulder

#### Low-Communication, Parallel Multigrid Algorithms For Elliptic Partial Differential Equations, Wayne Mitchell

*Applied Mathematics Graduate Theses & Dissertations*

When solving elliptic partial differential equations (PDE's) multigrid algorithms often provide optimal solvers and preconditioners capable of providing solutions with O(N) computational cost, where N is the number of unknowns. As parallelism of modern super computers continues to grow towards exascale, however, the cost of communication has overshadowed the cost of computation as the next major bottleneck for multigrid algorithms. Typically, multigrid algorithms require O((log P)^2) communication steps in order to solve a PDE problem to the level of discretization accuracy, where P is the number of processors. This has inspired the development of new algorithms ...

On Honey Bee Colony Dynamics And Disease Transmission, 2017 The University of Western Ontario

#### On Honey Bee Colony Dynamics And Disease Transmission, Matthew I. Betti

*Electronic Thesis and Dissertation Repository*

The work herein falls under the umbrella of mathematical modeling of disease transmission. The majority of this document focuses on the extent to which infection undermines the strength of a honey bee colony. These studies extend from simple mass-action ordinary differential equations models, to continuous age-structured partial differential equation models and finally a detailed agent-based model which accounts for vector transmission of infection between bees as well as a host of other influences and stressors on honey bee colony dynamics. These models offer a series of predictions relevant to the fate of honey bee colonies in the presence of disease ...

Thermodynamics Of Coherent Structures Near Phase Transitions, 2017 Purdue University

#### Thermodynamics Of Coherent Structures Near Phase Transitions, Julia M. Meyer, Ivan Christov

*The Summer Undergraduate Research Fellowship (SURF) Symposium*

Phase transitions within large-scale systems may be modeled by nonlinear stochastic partial differential equations in which system dynamics are captured by appropriate potentials. Coherent structures in these systems evolve randomly through time; thus, statistical behavior of these fields is of greater interest than particular system realizations. The ability to simulate and predict phase transition behavior has many applications, from material behaviors (e.g., crystallographic phase transformations and coherent movement of granular materials) to traffic congestion. Past research focused on deriving solutions to the system probability density function (PDF), which is the ground-state wave function squared. Until recently, the extent to ...

Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., 2017 University of Louisville

#### Some Problems Arising From Mathematical Model Of Ductal Carcinoma In Situ., Heng Li

*Electronic Theses and Dissertations*

Ductal carcinoma in situ (DCIS) is the earliest form of breast cancer. Three mathematical models in the one dimensional case arising from DCIS are proposed. The first two models are in the form of parabolic equation with initial and known moving boundaries. Direct and inverse problems are considered in model 1, existence and uniqueness are proved by using tool from heat potential theory and Volterra integral equations. Also, we discuss the direct problem and nonlocal problem of model 2, existence and uniqueness are proved. And approximation solution of these problems are implemented by Ritz-Galerkin method, which is the first attempt ...

Regularized Solutions For Terminal Problems Of Parabolic Equations., 2017 University of Louisville

#### Regularized Solutions For Terminal Problems Of Parabolic Equations., Sujeewa Indika Hapuarachchi

*Electronic Theses and Dissertations*

The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential equations (PDE) with terminal conditions are those in which the solution depends uniquely but not continuously on the given condition. In this dissertation, we explore how to find an approximation problem for a nonlinear heat equation which is well-posed. By using a small parameter, we construct an approximation problem and use a modified quasi-boundary value method to regularize a time dependent thermal conductivity heat equation and a quasi-boundary value method to regularize a space dependent thermal ...

Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, 2017 University of Southern Mississippi

#### Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, Abdullah M. Aurko

*Master's Theses*

In this thesis, we develop a highly accurate and efficient algorithm for computing the solution of a partial differential equation defined on a two-dimensional domain with discontinuous coefficients. An example of such a problem is for modeling the diffusion of heat energy in two space dimensions, in the case where the spatial domain represents a medium consisting of two different but homogeneous materials, with periodic boundary conditions.

Since diffusivity changes based on the material, it will be represented using a piecewise constant function, and this results in the formation of a complicated mathematical model. Such a model is impossible to ...

Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, 2017 University of Southern Mississippi

#### Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, Thir R. Dangal

*Dissertations*

Polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this dissertation, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solutions are further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. Polynomial basis functions are well-known for yielding ill-conditioned systems when their ...

Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, 2017 Western Kentucky University

#### Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker

*Honors College Capstone Experience/Thesis Projects*

Chronic wounds such as diabetic foot ulcers are the leading cause of non-traumatic amputations in developed countries. For researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can be used to help predict healing responses. The model utilizes equations that are modified from work by Guffey (2015) that consists of four variables – oxygen, bacteria, neutrophils, and chemoattractant within a system of partial differential equations. Our research focuses on numerically solving these partial differential equations using a finite volume approach. This numerical solver will be important for future research in optimization ...

Elimination For Systems Of Algebraic Differential Equations, 2017 The Graduate Center, City University of New York

#### Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data" of ...

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, 2017 Georgia Institute of Technology

#### High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

An Interdisciplinary Approach To Computational Neurostimulation, 2017 Roger Williams University

#### An Interdisciplinary Approach To Computational Neurostimulation, Madison Guitard

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Large Reaction-Diffusion Model For Cell Polarization In Yeast, 2017 The Ohio State University

#### A Large Reaction-Diffusion Model For Cell Polarization In Yeast, Marissa Renardy

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Efficient Denoising And Sharpening Of Color Images Through Numerical Solution Of Nonlinear Diffusion Equations, 2017 The University of Southern Mississippi

#### Efficient Denoising And Sharpening Of Color Images Through Numerical Solution Of Nonlinear Diffusion Equations, Linh T. Duong

*Honors Theses*

The purpose of this project is to enhance color images through denoising and sharpening, two important branches of image processing, by mathematically modeling the images. Modifications are made to two existing nonlinear diffusion image processing models to adapt them to color images. This is done by treating the red, green, and blue (RGB) channels of color images independently, contrary to the conventional idea that the channels should not be treated independently. A new numerical method is needed to solve our models for high resolution images since current methods are impractical. To produce an efficient method, the solution is represented as ...

Hawking Radiation And Classical Tunneling: A Numerical Study, 2017 College of William and Mary

#### Hawking Radiation And Classical Tunneling: A Numerical Study, Dmitriy Zhigunov

*Undergraduate Honors Theses*

Unruh [1] demonstrated that black holes have an analogy in acoustics. Under this analogy the acoustic event horizon is defined by the set of points in which the local background flow exceeds the local sound speed. In past work [2], we demonstrated that under a white noise source, the acoustic event horizon will radiate at a thermal spectrum via a classical tunneling process. In this work, I summarize the theory presented in [2] and nondimensionalize it in order to reduce the dynamical equations to one parameter, the coupling coefficient η2. Since η2 is the sole parameter of the system, we ...

Using Numerical Methods To Explore The Space Of Solutions Of A Nonlinear Partial Differential Equation, 2017 Trinity College, Hartford Connecticut

#### Using Numerical Methods To Explore The Space Of Solutions Of A Nonlinear Partial Differential Equation, Subekshya Bidari

*Senior Theses and Projects*

No abstract provided.

A Study Of The Reduction Of Excessive Energy Generated By Strong Winds On Power Lines Via A Velocity Damping Controller At The Transmission Tower, 2017 Kent State University - Kent Campus

#### A Study Of The Reduction Of Excessive Energy Generated By Strong Winds On Power Lines Via A Velocity Damping Controller At The Transmission Tower, Donald W. Fincher Jr.

*Undergraduate Research Symposium*

In this research, we are pursuing the robustness of a self-excited vibrational system with negative damping. In practice, this is manifested as conductor galloping of overhead power lines, which is an oscillation of the lines caused by strong winds. Improved transmission tower designs are needed which are capable of combating excessive stresses exerted on the tower by the galloping power lines. Our model of this self-excited system shows that the oscillations can be controlled by adding a boundary velocity feedback controller at the transmission tower. Using a decomposition method, we show there is a closed form analytical solution which predicts ...