Physical Sciences and Mathematics Commons^™

Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe

Theses and Dissertations

In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …

Time Dependent Solution For An Incompressible Viscous Fluid Flow In A Cavity, Bishnu Parajuli

Theses and Dissertations

The Finite Element Method is used to find the time dependent solution for an incompressible viscous fluid flow in a cavity in two dimension. The governing equations for this system are the continuity equation and the momentum equation. We use finite element method to obtain the dependent variables. Here we derive weak formulation and develop finite element model by using Galerkin Method. Then we compute velocity components of the fluid for a square cavity. The numerical results are presented.

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun

Theses and Dissertations

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas …

Applications Of The Homotopy Analysis Method To Optimal Control Problems, Shubham Singh

Open Access Theses

Traditionally, trajectory optimization for aerospace applications has been performed using either direct or indirect methods. Indirect methods produce highly accurate solutions but suer from a small convergence region, requiring initial guesses close to the optimal solution. In past two decades, a new series of analytical approximation methods have been used for solving systems of dierential equations and boundary value problems.

The Homotopy Analysis Method (HAM) is one such method which has been used to solve typical boundary value problems in nance, science, and engineering. In this investigation, a methodology is created to solve indirect trajectory optimization problems using the Homotopy …

Regularity Of Solutions And The Free Boundary For A Class Of Bernoulli-Type Parabolic Free Boundary Problems With Variable Coefficients, Thomas H. Backing

Open Access Dissertations

In this work the regularity of solutions and of the free boundary for a type of parabolic free boundary problem with variable coefficients is proved. After introducing the problem and its history in the introduction, we proceed in Chapter 2 to prove the optimal Lipschitz regularity of viscosity solutions under the main assumption that the free boundary is Lipschitz. In Chapter 3, we prove that Lipschitz free boundaries possess a classical normal in both space and time at each point and that this normal varies with a Hölder modulus of continuity. As a consequence, the viscosity solution is in fact …

Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine

Doctoral Dissertations

Statistical analysis is influenced by implementation of the algorithms used to execute the computations associated with various statistical techniques. Over many years; very important criteria for model comparison has been studied and examined, and two algorithms on a single dataset have been performed numerous times. The goal of this research is not comparing two or more models on one dataset, but comparing models with numerical algorithms that have been used to solve them on the same dataset.

In this research, different models have been broadly applied in modeling and their contrasting which are affected by the numerical algorithms in different …

Two Dimensional Mathematical Model Of Fluid Flow In A Growing Solid Tumor, Adriana Gracia

Theses and Dissertations - UTB/UTPA

We investigate the problem of steady and unsteady fluid flow in a growing solid tumor. We develop a mathematical model for the two dimensional fluid flow in a spherical tumor where the spatial variations of the interstitial velocity, interstitial pressure and the drug concentration within the tumor are, in general, with respect to the radial distance and the latitudinal angle in the spherical coordinates. The expressions for radial and latitudinal variations of the interstitial velocity, interstitial pressure, and the two investigated drug concentrations were determined analytically. We calculated these quantities in the tumor as well as in a corresponding normal …

Dynamics For The Compound Burgers-Kdv Equation, Xiangqian Zheng

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation and Two-Dimensional Compound Burgers-Korteweg-de Vries (2D-Compound BKdV) by analyzing the first integral equation, which indicates that under some particular conditions, the 2D-BKdV equation and 2D-Compound BKdV have exact traveling wave solutions. By using the elliptic integral and some transformations, traveling wave solution to the 2D-BKdV equation and 2DCompound BKdV are expressed explicitly.

Radar Image Processing And Its Applications Based On Convolution Back Projection, Qitong Li

Theses and Dissertations - UTB/UTPA

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and a SAR image processing algorithm called Convolution Back Projection (CBP) will be introduced in this thesis, which can be applied to data gathered by a Synthetic Aperture Radar (SAR) system to produce high resolution images. The purpose of this thesis is starting from Maxwell’s equations to study the CBP algorithm as it is applied to SAR image processing. Two different image simulation results will be provided by this method.

The Born Approximation, Multiple Scattering, And The Butterfly Algorithm, Alejandro F. Martinez

Theses and Dissertations - UTB/UTPA

Radar works by focusing a beam of light and seeing how long it takes to reflect. To see a large region the beam is pointed in different directions. The focus of the beam depends on the size of the antenna (called an aperture). Synthetic aperture radar (SAR) works by moving the antenna through some region of space. A fundamental assumption in SAR is that waves only bounce once. Several imaging algorithms have been designed using that assumption. The scattering process can be described by iterations of a badly behaving integral. Recently a method for efficiently evaluating these types of integrals …

Performance Modeling And Optimization Techniques For Heterogeneous Computing, Supada Laosooksathit

Doctoral Dissertations

Since Graphics Processing Units (CPUs) have increasingly gained popularity amoung non-graphic and computational applications, known as General-Purpose computation on GPU (GPGPU), CPUs have been deployed in many clusters, including the world's fastest supercomputer. However, to make the most efficiency from a GPU system, one should consider both performance and reliability of the system.

This dissertation makes four major contributions. First, the two-level checkpoint/restart protocol that aims to reduce the checkpoint and recovery costs with a latency hiding strategy in a system between a CPU (Central Processing Unit) and a GPU is proposed. The experimental results and analysis reveals some benefits, …

The Computation Of Fluid Velocity In A Closed Cavity With A Moving Lid, Daniel A. Montez

Theses and Dissertations - UTB/UTPA

We consider a cavity filled with fluid whose three sides are stationary and the lid at the top is moving at a constant speed. The flow in the cavity is modeled using the conservation of mass and momentum equations with proper boundary conditions. We compute the fluid velocity for the steady state case using the finite element method. We seek the weak formulation and develop a finite element model based on the Galerkin method. Furthermore we use the penalty function method to modify our weak formulation to eliminate the pressure. The Gaussian quadrature method is used to evaluate our integrals …

Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers, David Michael Imberti

Open Access Dissertations

In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

Synthetic Aperture Radar With Compressed Sensing, Yufeng Cao

Theses and Dissertations - UTB/UTPA

A general synthetic aperture radar (SAR) signal model is derived from the Maxwell’s equations, and compressed sensing are introduced to the signal model for SAR image reconstruction. Random Partial Fourier Matrices were applied to prove that compressed sensing can be used to this signal model from the viewpoint of mathematics. In the numerical simulation part, we show that the procedure of basis pursuit can reconstruct SAR image, based on our main results, which is shown efficient in comparison with the matched filter algorithm.

On Cubic Multisections, Andrew Alaniz

Theses and Dissertations - UTB/UTPA

In this thesis, a systematic procedure is given for generating cubic multi-sections of Eisenstein series. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three. The resulting series are shown to be rational functions of the Dedekind eta function. A more general treatment of cubic dissection formulas is given by describing the dissection operators in terms of linear transformations.

Lax Pairs For Some Nonlinear Equations, Ana Castillo

Theses and Dissertations - UTB/UTPA

Several methods have been proposed to approach the topic of integrable systems of nonlinear partial differential equations. One of these methods is called the Lax pair. The Lax pair is a pair of matrices or operators, that depend on time and satisfy the Lax equation. Based on the inverse scattering method introduced by Gardner, Greene, Kruskal and Miura (1967), Peter Lax introduced the Lax pair to derive soliton equations from the Lax equation. This thesis provides with a brief background on soliton theory, inverse scattering theory, and Lax pairs. The details missing in the work published by Ablowitz, Kaup, Newell, …

Traveling Wave Solution To Two-Dimensional Burgers-Korteweg-De Vries Equation, Xiaoqian Gong

Theses and Dissertations - UTB/UTPA

In this thesis, we study the Two-Dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analyzing the equivalent Abel equation, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded traveling wave solution. By using the theorem of contractive mapping, a traveling wave solution to the 2D-BKdV equation is expressed explicitly. In the end, the behavior of the proper solution of the 2D-BKdV equation is established by applying the comparison theorem of differential equations.

Distributed Sparse Matrix Solver And Pivoting Algorithms For Large Linear Equations, Esteban Torres

Theses and Dissertations - UTB/UTPA

This thesis presents a distributed sparse direct solver and pivoting strategies for distributed sparse LU factorization. In Chapter I, we introduce some background concepts in linear algebra. In Chapter II, we discuss parallel hardware architectures and introduce our problem for discussion. In Chapter III, we describe the implementation of our sparse direct solver and our pivoting algorithms. Next, we present our simulation methodology and results in Chapter IV and we show that our pivoting algorithm yields up to 50% more accurate results than a current state-of-the-art solver, SuperLU_DIST. Finally, in Chapter V, we present some ideas to further improve the …

A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi

Doctoral Dissertations

DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …

A Model For The Micro-Doppler Effect Of The Quadrupedal Body Motion, Noe Pena

Theses and Dissertations - UTB/UTPA

In radar returns from quadrupedal body motion the micro-Doppler effect is present. This effect can be used to identify and distinguish this motion from others. In this work the model for the micro-Doppler effect due to quadrupedal motion is developed from Maxwell’s equations. The common gait for all quadrupedal mammal motion is described and analyzed. The radar crossection of quadrupedal motion backscattering is discussed. Quadrupedal motion is simulated and the radar returns are analyzed. The micro-Doppler signatures are decomposed and kinematic parameters are extracted

Ultra-Low Voltage Digital Circuits And Extreme Temperature Electronics Design, Aaron J. Arthurs

Graduate Theses and Dissertations

Certain applications require digital electronics to operate under extreme conditions e.g., large swings in ambient temperature, very low supply voltage, high radiation. Such applications include sensor networks, wearable electronics, unmanned aerial vehicles, spacecraft, and energyharvesting systems. This dissertation splits into two projects that study digital electronics supplied by ultra-low voltages and build an electronic system for extreme temperatures. The first project introduces techniques that improve circuit reliability at deep subthreshold voltages as well as determine the minimum required supply voltage. These techniques address digital electronic design at several levels: the physical process, gate design, and system architecture. This dissertation analyzes …

Qualitative Analysis Of The Burgers-Huxley Equation, Jing Tian

Theses and Dissertations - UTB/UTPA

There are many well-known techniques for obtaining exact solutions of differential equations, but some of them only work for a very limited class of problems and are merely special cases of a few power symmetry methods. These approaches can be applied to nonlinear differential of unfamiliar type; they do not rely on special “tricks." Instead, a given differential equation can be made to reveal its symmetries, which are then used to construct exact solutions. In this thesis, we briefly present the theory of the Lie symmetry method for finding exact solutions of nonlinear differential equations, then apply it to the …

Penalized Spline Estimation In The Partially Linear Model, Ashley D. Holland

Faculty Dissertations

Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when the dimension of the regressors is large. In this project, we employ penalized B-splines in the context of the partially linear model to estimate the nonparametric component, when both thenumber of knots and the penalty factor vary with the sample size. We obtain mean-square convergence rates and establish asymptotic distributional approximations, with valid standard errors, for the resulting multivariate estimators of both the parametric and nonparametric components in this model. Our results extend and complement the recent theoretical work in the literature …

Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we study the solution of the two dimensional Laplace equation by the boundary Element method (BEM) and the method of fundamental solutions (MFS). Both the BEM and MFS used to solve boundary value problems involving the Laplace equation 2-D settings. Both methods rely on the use of fundamental solution of the Laplace's equation (the solution of Laplace's equation in the distributional sense). We will contrast and compare the results we get using the BEM with results we get using the MFS.

Mathematics Of Synthetic Aperture Radar Imaging, Guillermo Garza

Theses and Dissertations - UTB/UTPA

In Synthetic Aperture Radar (SAR) imaging, radar antennas are mounted on an airborne platform. The scene to be imaged is illuminated by electromagnetic waves transmitted from an antenna. The goal is to extract information of the scene from the measurements taken of the scattered waves. Reconstructing an image of the scene is an inverse problem. In this thesis, we study a method of image reconstruction developed by formulating the data collected as a Fourier integral operator acting on the scene, then applying an approximate inverse operator to that data. In particular, we examine the effects of bistatic system geometry to …

Modeling Instabilities Of Electrically Driven Jets Under Constant Or Variable Applied Field And Non-Zero Basic State Velocity, Sayantan Das

Theses and Dissertations - UTB/UTPA

We investigate the problem of instability of electrically forced axisymmetric jets with respect to temporally and spatially growing disturbances, within parameter regimes that affects the process of electrospinnning. Deriving a dispersion relation based on the relevant approximated versions of the equations of the electro-hydrodynamics for an electrically forced jet flow. For temporal instability, we find in the non-zero basic state velocity, the growth rate of the unstable mode is unaffected by the value of the basic state velocity. But, the basic state velocity affects the period of the unstable mode in the sense that it decreases the period, and the …

Inverse Synthetic Aperture Radar Imaging Theory And Application, Jaime Xavier Lopez

Theses and Dissertations - UTB/UTPA

Inverse Synthetic Aperture Radar (ISAR) is an electromagnetic sensing system that is capable of producing high resolution microwave images of moving targets. Despite being developed within the engineering community, the theory of radar imaging is a subject of tremendous mathematical richness. The theory of ISAR imaging alone is filled with many applications and open problems that the mathematician and physicist may find interesting. In this thesis, the basis for a filtered back projection imaging algorithm is derived from a popular scalar wave model. This imaging algorithm is based on a filtered-adjoint method for inverting ISAR data, and allows for the …

Improved Algorithms For Ear-Clipping Triangulation, Bartosz Kajak

UNLV Theses, Dissertations, Professional Papers, and Capstones

We consider the problem of improving ear-slicing algorithm for triangulating a simple polygon. We propose two variations of ear-slicing technique for generating “good-quality” triangulation. The first approach is based on searching for the best triangle along the boundary. The second approach considers polygon partitioning on a pre-process before applying the ear-slicing. Experimental investigation reveals that both approaches yield better quality triangulation than the standard ear-slicing method.

Multi-Soliton Solutions To A Model Equation For Shallow Water Waves, Zhijiang Qiao

Theses and Dissertations - UTB/UTPA

In Soliton theory, Hirota direct method is most efficient tool for seeking one soliton solutions or multi-soliton solutions of integrable nonlinear partial differential equations. The key step of the Hirota direct method is to transform the given equation into its Hirota bilinear form. Once the bilinear form of the given equation is found, we can construct the soliton and multi-soliton solutions of that model. Many interesting characteristics of Pfaffians were discovered through studies of soliton equations. In this thesis, a shallow water wave model and its bilinear equation are investigated. Using Hirota direct method, we obtain the multi-soliton solutions and …