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Heads And Tails, Julie Simons 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, Marissa Renardy, Tau-Mu Yi, Dongbin Xiu, Ching-Shan Chou 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, Maria-Veronica Ciocanel 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.


Low-Communication, Parallel Multigrid Algorithms For Elliptic Partial Differential Equations, Wayne Mitchell 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, Matthew I. Betti 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, Julia M. Meyer, Ivan Christov 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., Heng Li 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., Sujeewa Indika Hapuarachchi 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, Abdullah M. Aurko 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, Thir R. Dangal 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, Stefan Stryker 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, Richard Gustavson 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, Abouzar Kaboudian, Flavio H. Fenton 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, Madison Guitard 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, Marissa Renardy 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, Linh T. Duong 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, Dmitriy Zhigunov 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, Subekshya Bidari 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, Donald W. Fincher Jr. 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 ...


A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou 2017 West Chester University of Pennsylvania

A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou

Andreas Aristotelous

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 ...


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