Applied Mathematics Commons^™

A Conservative Numerical Scheme For The Multilayer Shallow Water Equations, Evan Butterworth

All Theses

An energy-conserving numerical scheme is developed for the multilayer shallow water equations (SWE’s). The scheme is derived through the Hamiltonian formulation of the inviscid shallow water flows related to the vorticity-divergence variables. Through the employment of the skew-symmetric Poisson bracket, the continuous system for the multilayer SWE’s is shown to preserve an infinite number of quantities, most notably the energy and enstrophy. An energy-preserving numerical scheme is then developed through the careful discretization of the Hamiltonian and the Poisson bracket, ensuring the skew-symmetry of the latter. This serves as the groundwork for developing additional schemes that preserve other conservation properties …

Managing Risk For Power System Operations And Planning: Applications Of Conditional Value-At-Risk And Uncertainty Quantification To Optimal Power Flow And Distributed Energy Resources Investment, Thanh To

All Dissertations

Renewable energy sources are indispensable components of sustainable electrical systems that reduce human dependence on fossil fuels. However, due to their intermittent nature, there are issues that need to be addressed to ensure the security and resiliency of these power systems. This dissertation formulates several practical problems, from an optimization perspective, stemming from the increasing penetration of intermittent renewable energy to power systems. A number of Optimal Power Flow (OPF) formulations are investigated and new formulations are proposed to control both operations and planning risks by utilizing the Conditional Value–at–Risk (CVaR) measure. Our formulations provide system operators and investors analysis …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

All Dissertations

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

A Survey Of The Br´Ezis-Nirenberg Problem And Related Theorems, Edward Huynh

UNLV Theses, Dissertations, Professional Papers, and Capstones

Nonlinear elliptic partial differential equations on bounded domains arise in several different areas of mathematics that include geometry, mathematical physics, and the calculus of variations. The Br ́ezis-Nirenberg problem is concerned with a boundary-value problem that is intimately connected to the existence of positive solutions of the Yamabe problem, of non-minimal solutions to Yang-Mills functionals, and of extremal functions to several important inequalities. Results on existence and uniqueness have been obtained in cases when the exponent is sub-critical, but such results have not been obtained when the exponent is critical due to a lack of compactness. The earliest results obtained …

Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …

Some Graph Laplacians And Variational Methods Applied To Partial Differential Equations On Graphs, Daniel Anthony Corral

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation we will be examining partial differential equations on graphs. We start by presenting some basic graph theory topics and graph Laplacians with some minor original results. We move on to computing original Jost graph Laplacians of friendly labelings of various finite graphs. We then continue on to a host of original variational problems on a finite graph. The first variational problem is an original basic minimization problem. Next, we use the Lagrange multiplier approach to the Kazdan-Warner equation on a finite graph, our original results generalize those of Dr. Grigor’yan, Dr. Yang, and Dr. Lin. Then we …

Dirichlet Type Boundary Value Problems For Linear And Quasi{Linear Hyperbolic Equations Of Higher Order, Reemah Alhuzally

Theses and Dissertations

Dirichlet type problems for quasi-linear hyperbolic equations are considered. For two-dimensional boundary value problems there are established:

(i) Unimprovable sufficient conditions of unique solvability and well-posedness of linear problems in piecewise smooth domains;

(ii) Unimprovable Sufficient conditions of unique solvability of linear problems in smooth convex domains.

(iii) Optimal Sufficient conditions of solvability, unique solvability and strong well-posedness of quasi-linear problems in piecewise smooth domains;

(iv) Optimal sufficient conditions of solvability and unique solvability of quasi- linear problems in smooth convex domains.

For three-dimensional linear boundary value problems there are established:

(i) Unimprovable sufficient conditions of unique solvability and well-posedness …

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Janani Gamage

Mathematics & Statistics Theses & Dissertations

Interface problems have many applications in physics. In this dissertation, we develop a direct method for solving three-dimensional elliptic interface problems and study their application in solving parabolic interface problems. As many of the physical applications of interface problems can be approximated with partial differential equations (PDE) with piecewise constant coefficients, our derivation of the model is focused on interface problems with piecewise constant coefficients but have a finite jump across the interface. The critical characteristic of the method is that our computational framework is based on a finite difference scheme on a uniform Cartesian grid system and does not …

The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception, Julia Ayres

Honors Projects in Mathematics

Professional sports teams are adored nationwide for their talents and the pride they bring to their city for their efforts. However, not all teams take this responsibility seriously and will lose on purpose, or tank, to gain a higher draft pick in the future. Although the long-term goals of tanking are to help the organization, many people take issue with athletes not putting in their best efforts in every game. Teams in both the NBA and NFL are guilty of tanking to gain better draft picks but not all have found success in this process. This leads to important questions …

Tracking Academic Success And Its Relationship With Student Success Center Usage And Demographics, Samuel D. Johnson

Honors Capstone Projects and Theses

No abstract provided.

Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations., Quinnlan Paul Aiken

ONU Student Research Colloquium

Approximation of the functions which are the solutions of complex or difficult problems is a worthwhile endeavor. This has resulted in many ways to effectively approximate the solution of the partial differential equations. One such way to approximate the solution of the partial differential equation is Oscillatory radial basis function method. This method can approximate the solution of the partial differential equation well however relies heavily on a “shape parameter” to achieve acceptable error. Choosing this parameter was traditionally done through a trial-and-error method. Selecting shape parameters in a more analytical way has been desired. One such method is the …

Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello

Undergraduate Research and Scholarship Symposium

Auberle social services is opening the Family Healing Center (FHC), a level 3.5 treatment program in Pittsburgh, PA that provides housing and 24-hour support for families struggling with opioid addiction. We partnered with Auberle to study characteristics of individuals receiving level 3.5 treatment and to determine whether longer treatment lengths correlate with fewer adverse outcomes. We obtained data from the Allegheny County Department of Human Services on 2,016 individuals admitted to level 3.5 treatment in 2019. The data included birth year, race, gender, admittance date, discharge date, and Children Youth and Family (CYF) incidents before and after treatment. We categorized …

Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function, Daniel Siebel-Cortopassi

USF Tampa Graduate Theses and Dissertations

A coupled delay-feedback system of two cantilevers can yield greater sensitivity than that of asingle cantilever system, with potential applications in atomic force microscopy. The Lambert W-function analysis concept for delay differential equations is used to more accurately model the behavior of specific configurations of these cantilever systems. We also use this analysis concept to find parameters which yield stability for greater parameter ranges, of the delay differential equations. The Q factor, or quality factor, is the ratio of energy stored in the system, to the energy lost per fixed oscillation/movement cycle. Having stability of the cantilevers corresponds to the …

A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman

USF Tampa Graduate Theses and Dissertations

The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …

Internet Affects All Areas Of The World: A Quantitative Report On Canadians Internet Usage, Kristina Sims

Symposium of Student Scholars

The Internet has had a significant influence on modern life with Pew research reporting that 99% of American adults between the ages of 18-29 used the internet in 2021 with reported reduced internet use for older Americans. Both positive and negative consequences can be attributed to its widespread use. In attending Kennesaw State University internet use is almost mandatory to successfully complete coursework. Witnessing how active internet use is in collegiate age populations in the US is has sparked some curiosity of use in Canadian residents. The survey on "Canadian Internet Use", in the year 2018 was designed to measure …

On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April

Rose-Hulman Undergraduate Mathematics Journal

While the well-researched Finite Difference Method (FDM) discretizes every independent variable into algebraic equations, Method of Lines discretizes all but one dimension, leaving an Ordinary Differential Equation (ODE) in the remaining dimension. That way, ODE's numerical methods can be applied to solve Partial Differential Equations (PDEs). In this project, Linear Multistep Methods and Method of Lines are used to numerically solve the heat equation. Specifically, the explicit Adams-Bashforth method and the implicit Backward Differentiation Formulas are implemented as Alternative Finite Difference Schemes. We also examine the consistency of these schemes.

Mathematical Analysis Of An Sir Disease Model With Non-Constant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri

Student Research

• Epidemiology: A branch of medicine that studies causes, transmission, and control methods of diseases at the population level.
• Mathematical epidemiology deals with creating a model for a disease through the study of incidence and distribution of the disease throughout a population.
• Here, we have examined the behavior of a measles-like disease[2] that is characterized by a non-constant transmission rate.

Relative Energy Comparison For Various Water Clusters Using Mp2, Df-Mp2, And Ccsd(T):Mp2 Methods, Qihang Wang

Honors Theses

The study of water clusters is an important area of research in many disciplines, such as biology, physical chemistry, and environmental studies. However, due to the difficulty in studying larger water clusters, such as clathrate hydrates, it is beneficial to obtain accurate descriptions of smaller water clusters to use as models for larger systems via computational methods. By starting with small water clusters, such as (H2O)₆, and moving into larger systems it is possible to build up data on various water structures that can determine the energetics of the various geometries within a certain number of water molecules. …

The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang

Mathematics Faculty Research Publications

We study the asymptotic behavior as p → ∞ of the Gelfand problem

−Δ_pu = λe^u in Ω ⊂ Rⁿ, u = 0 on ∂Ω.

Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of

min{|∇_u|−Λe^u, −Δ_∞u} = 0 in Ω, u = 0 on ∂Ω.

We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.

Eigenfunction Restriction Estimates For Curves With Nonvanishing Geodesic Curvatures In Compact Riemannian Surfaces With Nonpositive Sectional Curvatures, Chamsol Park

Mathematics & Statistics ETDs

For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.

A Mathematical Model For The Adoption Of Information And Communication Technology In School Libraries In Nigeria, Helen Olubunmi Jaiyeola Akinade, Jeremiah Ademola Balogun, Peter Adebayo Idowu

Library Philosophy and Practice (e-journal)

This study focused on the development of a mathematical model required for estimating the number of adopters of ICT devices among libraries located in Nigeria. Data for this study was collected from 121 respondents selected based on a research survey approach using simple random sampling. 9 ICT devices were identified, namely: PCs, printers/fax machines, search engines, e-library systems, bulk SMS services, library management systems, bar/QR code readers, projectors and video conferencing. The results showed that the earliest ICT devices were adopted for use in 1997, such as: PCs, printers/fax machines and search engines. The remaining ICT devices were adopted in …

Asymptotic Mean-Value Formulas For Solutions Of General Second-Order Elliptic Equations, Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi

Mathematics Faculty Research Publications

We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.

Thickness Of Fluvial Deposits Records Climate Oscillations, Xiaoping Yuan, Laure Guerit, Jean Braun, Delphine Rouby, Charles Shobe

Faculty & Staff Scholarship

Fluvial deposits offer Earth’s best-preserved geomorphic record of past climate change over geological timescales. However, quantitatively extracting this information remains challenging in part due to the complexity of erosion, sediment transport and deposition processes and how each of them responds to climate. Furthermore, sedimentary basins have the potential to temporarily store sediments, and rivers subsequently rework those sediments. This may introduce time lags into sedimentary signals and obscure any direct correlation with climate forcing. Here, using a numerical model that combines all three processes—and a new analytical solution—we show that the thickness of fluvial deposits at the outlet of a …

Representing And Analyzing The Dynamics Of An Agent-Based Adaptive Social Network Model With Partial Integro-Differential Equations, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

We formulated and analyzed a set of partial integro-differential equations that capture the dynamics of our adaptive network model of social fragmentation involving behavioral diversity of agents. Previous results showed that, if the agents’ cultural tolerance levels were diversified, the social network could remain connected while maintaining cultural diversity. Here we converted the original agent-based model into a continuous equation-based one so we can gain more theoretical insight into the model dynamics. We restricted the node states to 1-D continuous values and assumed the network size was very large. As a result, we represented the whole system as a set …

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …

Toward Suicidal Ideation Detection With Lexical Network Features And Machine Learning, Ulya Bayram, William Lee, Daniel Santel, Ali Minai, Peggy Clark, Tracy Glauser, John Pestian

Northeast Journal of Complex Systems (NEJCS)

In this study, we introduce a new network feature for detecting suicidal ideation from clinical texts and conduct various additional experiments to enrich the state of knowledge. We evaluate statistical features with and without stopwords, use lexical networks for feature extraction and classification, and compare the results with standard machine learning methods using a logistic classifier, a neural network, and a deep learning method. We utilize three text collections. The first two contain transcriptions of interviews conducted by experts with suicidal (n=161 patients that experienced severe ideation) and control subjects (n=153). The third collection consists of interviews conducted by experts …

Active Polar Liquid Crystal Channel Flows: Analyzing The Roles Of Nematic Strength And Activation Parameter, Lacey Schenk, Ruhai Zhou

College of Sciences Posters

Suspensions of active polar liquid crystalline polymers (APLC) exhibit complex phenomena such as spontaneous flows, pattern formations and defects. Using the Kinetic Model, which couples the Smoluchowski Equation and the Navier-Stokes Equations, we conduct numerical simulations of APLC in a microfluidic channel to investigate the competitive effect among different material constants, such as the nematic concentration (the strength of the potential for nematic order) and active strength (the individual nano-rods strength of their individual movement) with and without a pressure gradient. Both Dirichlet and Neumann boundary conditions on the mathematical model are employed. Steady states, including isotropic and nematic states, …

A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng

College of Sciences Posters

Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.

Factors That Relate To Academic Excellence, Matthew Lemoine

Mathematics Senior Capstone Papers

The American College Testing (ACT) provides university admissions offices a look into a student’s academic ability so that the university can determine admittance and scholarships. The premise of this study is to see whether this is the most effective way to determine academic ability, using the Logistic Regression Model. The data was collected from October 21, 2021 to December 31, 2021 at Louisiana Tech University. Using the Logistic Regression Model, predictions of academic excellence are obtained based on the parameters outlined in this paper. After the parameters for the Logistic Regression Model are calculated, conclusions can be drawn that the …

Predicting Box Office Revenues Using Differential Equation Models, Brenden David

Mathematics Senior Capstone Papers

The growing popularity of the internet has increased exponentially in the past few decades. This sudden increase in popularity allows for users to gain access to more information than was thought possible in the past, including access to box-office movie revenues of previously released movies. Since we now have access to thousands of movie’s box office revenues, we can analyze some sort of trend within specific genres of movies. With these trends we develop a differential equations model that will predict the box office revenues of a movie that is in its early stages of the box office. This model …