# Partial Differential Equations Commons™

## All Articles in Partial Differential Equations

502 full-text articles. Page 1 of 17.

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.

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

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

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 ...

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.

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.

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, 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 ...

2017 University of Kentucky

#### Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

##### Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

A Numerical Study Of Construction Of Honey Bee Comb, 2017 Murray State University

#### A Numerical Study Of Construction Of Honey Bee Comb, Pamela Guerrero, Pamela C. Guerrero

##### Murray State Theses and Dissertations

We use finite difference methods in the treatment of an existing system of partial differential equations that captures the dynamics of parallel honeycomb construction in a bee hive. We conduct an uncertainty analysis by calculating the partial rank correlation coefficient for the parameters to find which are most important to the outcomes of the model. We then use an eFAST method to determine both the individual and total sensitivity index for the parameters. Afterwards we examine our numerical model under varying initial conditions and parameter values, and compare ratios found from local data with the golden mean by fitting images ...

2017 University of Kentucky

#### A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

##### Theses and Dissertations--Mechanical Engineering

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model ...

Series Solutions Of Polarized Gowdy Universes, 2017 Virginia Commonwealth University

#### Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro

##### Theses and Dissertations

Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T3 model, and provide an explicit solution to Einstein's equations.

2017 Dublin Institute of Technology

#### Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

##### Articles

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion ...

2017 University of Kentucky

#### Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu

##### Theses and Dissertations--Mathematics

We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.

2017 College of Saint Benedict/Saint John's University

#### High Performance Techniques Applied In Partial Differential Equations Library, Shilei Lin

##### All College Thesis Program

This thesis will explore various Trilinos packages to determine a method for updating the deal.ii library. The deal.ii library specialize in solving partial differential equations by finite element methods. This thesis will begin with introducing some related concepts and the goals of this project, following the methods of achieving those goals by exploring analytical solution of one-dimensional Boussinesq equations and developing of newer prototypes based on Trilinos packages. After demonstrating the reduction of solving time in prototypes, the same methods have been applied to update the deal.ii library. Finally, an example program from the deal.ii library ...

Proceedings Of The 2nd Resrb 2017 Conference, June 19-21, Wrocław, Poland, 2016 Wroclaw University of Technology

#### Proceedings Of The 2nd Resrb 2017 Conference, June 19-21, Wrocław, Poland, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, 2016 Wroclaw University of Technology

#### Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Order Form Resrb 2018, 2016 Wroclaw University of Technology

#### Order Form Resrb 2018, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Abstract Template Resrb 2018, 2016 Wroclaw University of Technology

#### Abstract Template Resrb 2018, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.