Applied Mathematics Commons^™

Assorted Kerosene-Based Nanofluid Across A Dual-Zone Vertical Annulus With Electroosmosis, Sara I. Abdelsalam, A. M. Alsharif, Y. Abd Elmaboud, A. I. Abdellateef

Basic Science Engineering

The goal of this numerical simulation is to visualize the electroosmotic flow of immiscible fluids through a porous medium in vertical annular microtubes. The inner region (Region I) is filled with an electrically conducting hybrid nanofluid while an electrically conducting Jeffrey fluid is flowing in the second region (Region II). The chosen nanofluid is kerosene-based and the nanoparticles (Fe3O4-TiO2) are of a spherical shape. A strong zeta potential is taken into account and the electroosmotic velocity in the two layers is considered too. The annular microtubes are subjected to an external magnetic field and an electric field. The linked nonlinear …

U-No: U-Shaped Neural Operators, Md Ashiqur Rahman, Zachary E Ross, Kamyar Azizzadenesheli

Department of Computer Science Faculty Publications

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for deeper neural operators. U-NOs exploit the problem structures in function predictions and demonstrate fast training, data …

Monolithic Multiphysics Simulation Of Hypersonic Aerothermoelasticity Using A Hybridized Discontinuous Galerkin Method, William Paul England

Theses and Dissertations

This work presents implementation of a hybridized discontinuous Galerkin (DG) method for robust simulation of the hypersonic aerothermoelastic multiphysics system. Simulation of hypersonic vehicles requires accurate resolution of complex multiphysics interactions including the effects of high-speed turbulent flow, extreme heating, and vehicle deformation due to considerable pressure loads and thermal stresses. However, the state-of-the-art procedures for hypersonic aerothermoelasticity are comprised of low-fidelity approaches and partitioned coupling schemes. These approaches preclude robust design and analysis of hypersonic vehicles for a number of reasons. First, low-fidelity approaches limit their application to simple geometries and lack the ability to capture small scale flow …

Imperfect Immunity And The Stability Of A Modified Kermack-Mckendrick Model, Kaylee Sims

Honors Theses

The classic Kermack-McKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified Kermack-McKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with real-world case data, with its most glaring failure being exponential dampening of the height of each disease case peak due …

Variational And Adaptive Non-Local Image Denoising Using Edge Detection And K − Means Clustering, Shiraz Mujahid

Theses and Dissertations

With the increased presence of image-based data in modern applications, the need for robust methods of image denoising grows greater. The work presented herein considers two of the most ubiquitous approaches towards image denoising: variational and non-local methods. The effectiveness of these methods is assessed using quantitatively using peak signal-to-noise ratio and structural similarity index measure metrics. This study employs ��−means clustering, an unsupervised machine learning algorithm, to isolate the most dominant cluster centroids within the incoming data and propose the introduction of a new adaptive parameter into the non-local means framework. Motivated by the fact that a majority of …

Spectral Multistep Methods For The Scalable Simulation Of Time-Dependent Phenomena, Bailey Rester

Dissertations

Krylov subspace spectral (KSS) methods are high-order accurate, one-step explicit time-stepping methods for partial differential equations (PDEs) that also possess stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE, using techniques developed by Golub and Meurant for approximating bilinear forms involving matrix functions. As a result, KSS methods scale effectively to higher spatial resolution.

This dissertation will present spectral multistep methods, explicit and implicit, designed through the combination of KSS methods and Adams methods. This combination allows spectral multistep methods …

Asymptotic Behavior Of Random Defective Parking Functions, John T. Mann, Zecheng You, Mei Yin

DU Undergraduate Research Journal Archive

Suppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their desired spot and parks there if possible. If the spot is already occupied then the car parks in the first available spot after that; if no such spot is available then the car leaves the street without parking. When m > n, there will always be defects–cars that are not able to park. Building upon the work in Cameron et al. "Counting defective parking functions," we introduce a multi-shuffle construction to defective parking functions and …

Du Undergraduate Showcase: Research, Scholarship, And Creative Works, Caitlyn Aldersea, Justin Bravo, Sam Allen, Anna Block, Connor Block, Emma Buechler, Maria De Los Angeles Bustillos, Arianna Carlson, William Christensen, Olivia Kachulis, Noah Craver, Kate Dillon, Muskan Fatima, Angel Fernandes, Emma Finch, Colleen Cassidy, Amy Fishman, Andrea Francis, Stacia Fritz, Simran Gill, Emma Gries, Rylie Hansen, Shannon Powers, Jacqueline Martinez, Zachary Harker, Ashley Hasty, Mykaela Tanino-Springsteen, Kathleen Hopps, Adelaide Kerenick, Colin Kleckner, Ci Koehring, Elijah Kruger, Braden Krumholz, Maddie Leake, Lyneé Alves, Seraphina Loukas, Yatzari Lozano Vazquez, Haley Maki, Emily Martinez, Sierra Mckinney, Audrey Mitchell, Kipling Newman, Audrey Ng, Megan Lucyshyn, Andrew Nguyen, Stevie Ostman, Casandra Pearson, Alexandra Penney, Julia Gielczynski, Tyler Ball, Anna Rini, Christina Rorres, Simon Ruland, Helayna Schafer, Emma Sellers, Sarah Schuller, Claire Shaver, Kevin Summers, Isabella Shaw, Madison Sinar, Claudia Pena, Apshara Siwakoti, Carter Sorensen, Madi Sousa, Anna Sparling, Alexandra Revier, Brandon Thierry, Dylan Tyree, Maggie Williams, Lauren Wols

DU Undergraduate Research Journal Archive

DU Undergraduate Showcase: Research, Scholarship, and Creative Works

Adaptive Multirate Infinitesimal Time Integration, Alex Fish

Mathematics Theses and Dissertations

As multiphysics simulations grow in complexity and application scientists desire more accurate results, computational costs increase greatly. Time integrators typically cater to the most restrictive physical processes of a given simulation\add{,} which can be unnecessarily computationally expensive for the less restrictive physical processes. Multirate time integrators are a way to combat this increase in computational costs by efficiently solving systems of ordinary differential equations that contain physical processes which evolve at different rates by assigning different time step sizes to the different processes. Adaptivity is a technique for further increasing efficiency in time integration by automatically growing and shrinking the …

Machine Learning In Finances, Elma Kastrat, Akinyemi Apampa, Satyanand Singh

Publications and Research

In our study we work on an optimization of an appropriate stock portfolio base on available information. Our work takes into consideration the average return and any associated risk. We produce an investment strategy that predictively allows a portfolio to grow with high yields.

Brief Review: Low Frequency Event Charts (G-Charts) In Healthcare, James Espinosa, David Ho, Alan Lucerna, Henry Schuitema

Rowan-Virtua Research Day

The ability to determine if a change in a system is actually an improvement—or worsening in function—is one of the essential desiderata of quality improvement efforts. There are many ways to look at the issue. A special problem occurs when the event being studied is low frequency by nature. By way of example, patient falls in a given hospital or division of a hospital may occur in a way that is low frequency—yet each event is important. Process engineering has developed an approach to low frequency events. Part of this approach may involve specialized charts that look at the “time-between-events”—as …

Effects Of Factors On The Market Price Of The Shares Using Design Of Experiment, Amir Ahmad Dar, Mohammad Shahfaraz Khan, Imran Azad, Tanveer Ahmad Tarray, N. Anuradha, Qaiser Farroq Dar

Applied Mathematics & Information Sciences

When the cost of capital, dividends and the price of the share at the beginning is known, Modigliani and Miller’s model can be used to estimate the price of the share at the end of the period. A design of experiment (Taguchi’s orthogonal array) is used in order to investigate the impact of three parameters on the price of the share at the end of the period. The main aim of this research article is to find which parameter is more significant on the price of the share at the end of the period. Taguchi’s methodology of design of the …

Volatility Modeling Of Time Series Using Fractal And Self-Similarity Models, William Kubin

Open Access Theses & Dissertations

The study uses various methods to compare financial and geophysical time series scaling parameters and long-term memory behavior. The Cantor Detrended Fluctuation Analysis (CDFA) method is proposed to provide more accurate estimates of Hurst exponents. The CDFA method is applied to real-time series and the results are verified. The study also analyzes the memory behavior of daily Covid-19 cases before and after the announcement of effective vaccines. Low and high-frequency dataâ??s influence on the Hurst Index estimation is investigated, and a new PCDFA method is proposed. The stability of the Dow Jones Industrial Average is analyzed using a multi-scale normalized …

Recursive Forms For Determinant Of K-Tridiagonal Toeplitz Matrices, Eugene Agyei-Kodie

Open Access Theses & Dissertations

Toeplitz matrices have garnered renewed interest in recent years due to their practical applications in engineering and computational sciences. Additionally, research has shown their connection to other matrices and their significance in matrix theory. For example, one study demonstrated that any matrix can be expressed as the product of Toeplitz matrices \citep{ye2016every}, while another showed that any square matrix is similar to a Toeplitz matrix \citep{mackey1999every}.

Numerous studies have examined various properties of Toeplitz matrices, including ideals of lower triangular Toeplitz matrices \citep{dogan9some}, matrix power computation with band Toeplitz structures \citep{dogan2017matrix}, and norms of Toeplitz matrices. Moreover, the use of …

Numerical Evaluation Of Wavenumbers Of The Acoustic Waves Propagating In An Ice-Covered Ocean, Mohammad Khan

Masters Theses and Doctoral Dissertations

We consider acoustic wave propagation in a layered ocean waveguide covered by thick ice. The standard method of separation of variables leads to a Sturm-Liouville problem in the crosssection of the waveguide. We are specifically interested in the two leading modes, the separated solutions for the maximal eigenvalues. We first consider the homogeneous waveguide. We prove the differentiability of the eigenvalues with respect to the frequency, the monotonicity of the eigenvalues with respect to the frequency, and the existence of the cut-off frequency. We compare these eigenvalues with the eigenvalues for the case of a waveguide with a free surface. …

Dynamics Of Inertial And Non-Inertial Particles In Geophysical Flows, Nishanta Baral

Theses, Dissertations and Culminating Projects

We consider the dynamics of inertial and non-inertial particles in various flows. We investigate the underlying structures of the flow field by examining their Lagrangian coherent structures (LCS), which are found by computing finitetime Lyapunov exponents (FTLE). We compare the behavior of massless noninertial particles using the velocity fields from four models, the Duffing oscillator, the Bickley jet, the double-gyre flow, and a quasi-geostrophic geophysical flow model, with that of inertial particles. For inertial particles with finite size and mass, we use the Maxey-Riley equation to describe the particle’s motion. We explore the preferential aggregation of inertial particles and demonstrate …

Creating The Optimal Wedding Seating Chart, Madison Lane

Theses/Capstones/Creative Projects

The purpose of this project is to develop an effective seating arrangement for a wedding reception that enhances the comfort of guests. The ultimate aim is to create a harmonious and enjoyable atmosphere for all attendees. To achieve this, an integer program was designed to optimize the seating arrangement for the author’s upcoming wedding on May 27th, 2023. To ensure accuracy and feasibility, actual feedback was gathered from the guests to evaluate their compatibility and preferences. The proposed seating chart optimization not only addresses the placement of guests but also determines the number of tables required for the reception. The …

Analysis And Application Of Finite Element And High-Order Finite Difference Methods For Maxwell’S Equations In Complex Media, Li Zhu

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Perfectly Matched Layer (PML) technique is an effective tool introduced by B´erenger [13] to reduce the unbounded wave propagation problem to a bounded domain problem. This dissertation focuses on two different PML models and their applications to wave propagation problems with Maxwell’s equation in complex media. We investigate these models using two popular numerical methods: the Finite Difference Method (FDM) in Chapters 2 and 3, and the Finite Element Method (FEM) in Chapters 4 and 5.In Chapter 2, we focus on analyzing the stability of a PML developed by B’ecache et al. [10] for simulating wave propagation in the …

Trajectory Analysis For Driving Safety Quantification, Michael I. Chang

UNLV Theses, Dissertations, Professional Papers, and Capstones

In order to evaluate the efficacy of the skid recovery exercise in the Driver’s Edge teenage driving program, a process is established to determine the trajectories of vehicles from recorded videos, compare them in terms of similarity through dynamic time warping (DTW), and then analyze the similarity measurements to assess whether the program has a significant effect on driving ability by repeated measures analysis of variance (rANOVA). The video is analyzed by Harris corner detection and Lucas-Kanade optical flow method to ascertain the vehicle trajectories. A homography is then estimated to translate coordinates from video into real-world. The instructor and …

Mathematical Modeling: Finite Element Analysis And Computations Arising In Fluid Dynamics And Biological Applications, Jorge Reyes

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is often the case when attempting to capture real word phenomena that the resulting mathematical model is too difficult and even not feasible to be solved analytically. As a result, a computational approach is required and there exists many different methods to numerically solve models described by systems of partial differential equations. The Finite Element Method is one of them and it was pursued herein.This dissertation focuses on the finite element analysis and corresponding numerical computations of several different models. The first part consists of a study on two different fluid flow models: the main governing model of fluid …