Partial Differential Equations Commons^™

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

Biology and Medicine Through Mathematics Conference

No abstract provided.

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

Biology and Medicine Through Mathematics Conference

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.

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

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 ...

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 ...

C.V., Wojciech M. Budzianowski

Wojciech Budzianowski

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Abstract Template Resrb 2017, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Order Form Resrb 2017, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

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 ...

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 ...

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.

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, 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 ...

On The Propagation Of Atmospheric Gravity Waves In A Non-Uniform Wind Field: Introducing A Modified Acoustic-Gravity Wave Equation, Ahmad Talaei

All Graduate Plan B and other Reports

Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies.

We utilize the complete set of governing equations for a compressible atmosphere with non-uniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is ...

Foundations Of Wave Phenomena: Complete Version, Charles G. Torre

Foundations of Wave Phenomena

This is the complete version of Foundations of Wave Phenomena. Version 8.2.

Please click here to explore the components of this work.

Microstructural Analysis Of Thermoelastic Response, Nonlinear Creep, And Pervasive Cracking In Heterogeneous Materials, Alden C. Cook

Electronic Theses and Dissertations

This dissertation is concerned with the development of robust numerical solution procedures for the generalized micromechanical analysis of linear and nonlinear constitutive behavior in heterogeneous materials. Although the methods developed are applicable in many engineering, geological, and materials science fields, three main areas are explored in this work. First, a numerical methodology is presented for the thermomechanical analysis of heterogeneous materials with a special focus on real polycrystalline microstructures obtained using electron backscatter diffraction techniques. Asymptotic expansion homogenization and finite element analysis are employed for micromechanical analysis of polycrystalline materials. Effective thermoelastic properties of polycrystalline materials are determined and compared ...

Fast Method Of Particular Solutions For Solving Partial Differential Equations, Anup Raja Lamichhane

Dissertations

Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the large-scale problems are some of the challenges which need to overcome. In this dissertation, we have used several techniques to overcome such challenges.

The closed-form particular solutions for the Matérn and Gaussian RBFs were not known yet. With the help of the symbolic computational tools, we have derived the closed-form particular solutions of the Matérn and Gaussian RBFs for the Laplace and biharmonic ...

Spreading Speeds Along Shifting Resource Gradients In Reaction-Diffusion Models And Lattice Differential Equations., Jin Shang

Electronic Theses and Dissertations

A reaction-diffusion model and a lattice differential equation are introduced to describe the persistence and spread of a species along a shifting habitat gradient. The species is assumed to grow everywhere in space and its growth rate is assumed to be monotone and positive along the habitat region. We show that the persistence and spreading dynamics of a species are dependent on the speed of the shifting edge of the favorable habitat, c, as well as c^*(∞) and c^*(−∞), which are formulated in terms of the dispersal kernel and species growth rates in both directions. When the favorable habitat edge ...