Examples Of Solving The Wave Equation In The Hyperbolic Plane, 2018 Liberty University

#### Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey

*Senior Honors Theses*

The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To ...

Classifying Textual Fast Food Restaurant Reviews Quantitatively Using Text Mining And Supervised Machine Learning Algorithms, 2018 East Tennessee State University

#### Classifying Textual Fast Food Restaurant Reviews Quantitatively Using Text Mining And Supervised Machine Learning Algorithms, Lindsey Wright

*Undergraduate Honors Theses*

Companies continually seek to improve their business model through feedback and customer satisfaction surveys. Social media provides additional opportunities for this advanced exploration into the mind of the customer. By extracting customer feedback from social media platforms, companies may increase the sample size of their feedback and remove bias often found in questionnaires, resulting in better informed decision making. However, simply using personnel to analyze the thousands of relative social media content is financially expensive and time consuming. Thus, our study aims to establish a method to extract business intelligence from social media content by structuralizing opinionated textual data using ...

Properties And Convergence Of State-Based Laplacians, 2018 University of Nebraska - Lincoln

#### Properties And Convergence Of State-Based Laplacians, Kelsey Wells

*Dissertations, Theses, and Student Research Papers in Mathematics*

The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different ...

Harmonic Functions And Harmonic Measure, 2018 University of Connecticut

#### Harmonic Functions And Harmonic Measure, David Mcdonald

*Honors Scholar Theses*

The purpose of this thesis is to give a brief introduction to the field of harmonic measure. In order to do this we first introduce a few important properties of harmonic functions and show how to find a Green’s function for a given domain. Following this we calculate the harmonic measure for some easy cases and end by examining the connection between harmonic measure and Brownian motion.

The Computational Study Of Fly Swarms & Complexity, 2018 Linfield College

#### The Computational Study Of Fly Swarms & Complexity, Austin Bebee

*Senior Theses*

A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the ...

Extending The Applicability Of The Lagrange Multipliers Method, 2018 The College at Brockport

#### Extending The Applicability Of The Lagrange Multipliers Method, Ashley Case

*Senior Honors Theses*

In this work we studied the use of the Lagrange Multipliers Method. We proved that substitutions can result in the ability to use this method when the method had previously failed. We also look at situations where this is not the case, and the method fails to maximize or minimize the function. In such cases, we will discuss what to do from there.

Physical Applications Of The Geometric Minimum Action Method, 2018 The Graduate Center, City University of New York

#### Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

*All Dissertations, Theses, and Capstone Projects*

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...

Characterization Of Volcanic Terrains Using Lidar Reflectivity: A Statistical Approach, 2018 Indiana University of Pennsylvania

#### Characterization Of Volcanic Terrains Using Lidar Reflectivity: A Statistical Approach, Michael Barber

*Theses and Dissertations (All)*

In recent decades, lidar has revolutionized topographic mapping of the Earth and planets through the use of digital elevation models (DEMs). However, the return amplitudes of the reflected laser pulses, typically collected as part of a lidar dataset, have seldom beenused as a means of identifying and characterizing volcanic surface features such as lava flows, rafted tephra and agglutinate, and pyroclastic deposits consisting of tephra and ashfall. Here, we find an effective process for remotely characterizing volcanic terrains using a simple but rigorous cluster analysis of lidar return amplitudes and DEM data to define the parameters for a self-organizing mapping ...

Analysis Of Daily Precipitation Data From Selected Sites In The United States, 2018 Montclair State University

#### Analysis Of Daily Precipitation Data From Selected Sites In The United States, Sahar Ahmed

*Theses, Dissertations and Culminating Projects*

Global warming is a contentious topic since modern climate records only exist for the last 100 years in contrast to ice-core analysis that establishes ice ages tens of thousands of years ago. Nevertheless, patterns associated with events such as El Niño Southern Oscillation (ENSO), precipitation, tornadoes, and snowfall amounts over the last century can provide a useful and objective indicator of climate “change”. This project focuses on daily precipitation totals for the state of New Jersey over the last 100 to 150 years from nineteen meteorological recording stations and involves large data sets with a million observations. This research utilizes ...

Inertial Particle Transport By Lagrangian Coherent Structures In Geophysical Flows, 2018 Montclair State University

#### Inertial Particle Transport By Lagrangian Coherent Structures In Geophysical Flows, Alexa Aucoin

*Theses, Dissertations and Culminating Projects*

Lagrangian Coherent Structures (LCS) provide a skeleton for the underlying structures in geophysical flows. It is known that LCS govern the movement of fluid particles within a flow, but it is not well understood how these same LCS influence the movement of inertial particles within a fluid flow. In this thesis, we consider two geophysical flows, the double-gyre model, and a single-layer quasi-geostrophic PDE model. In particular, we use finite-time Lyapunov exponents (FTLE) to characterize the attracting and repelling LCS for these models and show how inertial particles aggregate with respect to LCS. We numerically investigate the dynamics of inertial ...

Seasonal Switching Affects Bacterial-Fungal Dominance In An Ecological System, 2018 Montclair State University

#### Seasonal Switching Affects Bacterial-Fungal Dominance In An Ecological System, Kristin Carfora

*Theses, Dissertations and Culminating Projects*

We consider a model inspired by producer-herbivore-decomposer soil food webs and determine the effect of ecological parameters on the decomposer pool. In particular, we observe how seasonal changes in the stoichiometric quality of the producer coupled with the efficiency of herbivory over the calendar year can induce a shift in the composition of the decomposer pool. Decomposers have a significant effect on the movement of essential nutrients throughout an ecosystem; we further determine how this shift between a bacterially dominated decomposer pool and a fungally dominated pool affects primary production and relative distribution of biomass of the other compartments.

The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, 2018 The Graduate Center, City University of New York

#### The Advection-Diffusion Equation And The Enhanced Dissipation Effect For Flows Generated By Hamiltonians, Michael Kumaresan

*All Dissertations, Theses, and Capstone Projects*

We study the Cauchy problem for the advection-diffusion equation when the diffusive parameter is vanishingly small. We consider two cases - when the underlying flow is a shear flow, and when the underlying flow is generated by a Hamiltonian. For the former, we examine the problem on a bounded domain in two spatial variables with Dirichlet boundary conditions. After quantizing the system via the Fourier transform in the first spatial variable, we establish the enhanced-dissipation effect for each mode. For the latter, we allow for non-degenerate critical points and represent the orbits by points on a Reeb graph, with vertices representing ...

Power Corrections To Tmd Factorization For Z-Boson Production, 2018 Old Dominion University

#### Power Corrections To Tmd Factorization For Z-Boson Production, I. Balitsky, A. Tatasov

*Physics Faculty Publications*

A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to the TMD factorization formula become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in *N*_{c} power corrections are expressed in ...

Energy Calculations And Wave Equations, 2018 Missouri State University

#### Energy Calculations And Wave Equations, Ellen R. Hunter

*MSU Graduate Theses*

The focus of this thesis is to show how methods of Fourier analysis, in particular Parseval’s equality, can be used to provide explicit energy calculations for solutions of wave equations in one dimension. These calculations are discussed for simple examples and then extended to ﬁt the general wave equation with Robin boundary conditions. Ideas from Sobolev space theory are used to provide justiﬁcation of the method.

Ultra-High Dimensional Statistical Learning, 2018 College of William and Mary

#### Ultra-High Dimensional Statistical Learning, Yanxin Xu

*Undergraduate Honors Theses*

Advancements in information technology have enabled scientists to collect data of unprecedented size as well as complexity. Nowadays, high-dimensional data commonly arise in diverse fields as biology, engineering, health sciences, and economics. In this project, we consider both linear and non-parametric models with variable selection in the high-dimensional setting by assuming that only a small number of index coefficients influence the conditional mean of the response variable. Both the numerical results and the real data application demonstrate that the proposed approach selects the correct model with a high frequency and estimates the model coefficients accurately even for moderate sample size ...

Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, 2018 The University of Southern Mississippi

#### Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Montiforte

*Master's Theses*

Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.

Homogenization In Perforated Domains And With Soft Inclusions, 2018 University of Kentucky

#### Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

*Brandon Russell*

The Pope's Rhinoceros And Quantum Mechanics, 2018 Bowling Green State University

#### The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

*Honors Projects*

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time ...

Atmospheric Radiation And Tgfs: Unexplained Radiation In Our Skies, 2018 Harding University

#### Atmospheric Radiation And Tgfs: Unexplained Radiation In Our Skies, Adrian Gallegos

*Honors College Research*

There is a significant correlation between atmospheric electrification via thunderstorms and the occurrence of large emissions of x-ray and gamma ray radiation known as Terrestrial Gamma Ray Flashes (TGFs). Some physical phenomenon may be explained by either the RREA or Thermal Runaway models, but the scientific community as a whole is still largely at work on the theoretical frameworks.

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, 2018 Michigan Technological University

#### Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

*Ramy El-Ganainy*

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other ...