Physical Sciences and Mathematics Commons^™

Sperm-Egg Interaction For Fertilization Success, Prajakta P. Bedekar

Biology and Medicine Through Mathematics Conference

No abstract provided.

Incorporating Awareness, Misinformation And Optimal Control In A Model Of Sars-Cov-2, Eric Numfor

Biology and Medicine Through Mathematics Conference

No abstract provided.

Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematically Modeling Stoichiometric Drivers Of Nitrogen Fixation, Rebecca Everett, Corday Selden, Mohamed Hatha Abdulla, Jabir Thajudeen, James Powell, Edwin Cruz-Rivera, Luca Schenone, Renn Schipper, Megan Berberich, Halvor Halvorson, Robinson Fulweiler, Amy Marcarelli, Thad Scott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Constructible Sandwich Cut, Philip A. Son

FIU Undergraduate Research Journal

In mathematical measure theory, the “Ham-Sandwich” theorem states that any n objects in an n-dimensional Euclidean space can be simultaneously divided in half with a single cut by an (n-1)-dimensional hyperplane. While it guarantees its existence, the theorem does not provide a way of finding this halving hyperplane, as it is only an existence result. In this paper, we look at the problem in dimension 2, more in the style of Euclid and the antique Greeks, that is from a constructible point of view, with straight edge and compass. For two arbitrary regions in the plane, there is certainly no …

Effect Of Recommending Users And Opinions On The Network Connectivity And Idea Generation Process, Sriniwas Pandey, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

The growing reliance on online services underscores the crucial role of recommendation systems, especially on social media platforms seeking increased user engagement. This study investigates how recommendation systems influence the impact of personal behavioral traits on social network dynamics. It explores the interplay between homophily, users’ openness to novel ideas, and recommendation-driven exposure to new opinions. Additionally, the research examines the impact of recommendation systems on the diversity of newly generated ideas, shedding light on the challenges and opportunities in designing effective systems that balance the exploration of new ideas with the risk of reinforcing biases or filtering valuable, unconventional …

Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen

Student Research Submissions

Mathematical models in epidemiology describe how diseases affect and spread within a population. By understanding the trends of a disease, more effective public health policies can be made. In this paper, the Susceptible-Infected-Recovered-Susceptible (SIRS) Model was examined analytically and numerically to compare with the data for Coronavirus Disease 2019 (COVID-19). Since the SIRS model is a complex model, analytical techniques were used to solve simplified versions of the SIRS model in order to understand general trends that occur. Then by Euler's Method, the Runge-Kutta Method, and the Predictor-Corrector Method, computational approximations were obtained to solve and plot the SIRS model. …

Entropy Analysis For Three-Dimensional Stretched Flow Of Viscous Fluid Engaging Radiation Effect And Double Diffusion Phenomenon, Syed Tehseen Abbas, Muhammad Sohail, Imran Haider

International Journal of Emerging Multidisciplinaries: Mathematics

A useful technique for comprehending the thermodynamic behavior of fluid flows is entropy analysis. In this paper, we explore the involvement and transfer of entropy in a stretched three-dimensional flow of a viscous fluid. The flow is presumed to be both laminar and incompressible, whereas the properties of the fluid are considered to be unchanged. The governing equations: continuity; momentum; and energy equations; are calculated using the necessary boundary conditions. Considering the acquired velocity and temperature profiles, the entropy generation rate and fluxes are calculated. The results demonstrate that entropy production is significantly influenced by the flow's stretching rate. Through …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations & Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

Non-Contact Wind Turbine Blade Crack Detection Using Laser Doppler Vibrometers, Ali Zabihi, Farhood Aghdasi, Chadi Ellouzi, Nand Kishore Singh, Ratneshwar Jha, Chen Shen

Henry M. Rowan College of Engineering Faculty Scholarship

In response to the growing global demand for both energy and a clean environment, there has been an unprecedented rise in the utilization of renewable energy. Wind energy plays a crucial role in striving for carbon neutrality due to its eco-friendly characteristics. Despite its significance, wind energy infrastructure is susceptible to damage from various factors including wind or sea waves, rapidly changing environmental conditions, delamination, crack formation, and structural deterioration over time. This research focuses on investigating non-destructive testing (NDT) of wind turbine blades (WTBs) using approaches based on the vibration of the structures. To this end, WTBs are first …

Modeling Prices In Limit Order Book Using Univariate Hawkes Point Process, Wenqing Jiang

University of New Orleans Theses and Dissertations

This thesis presents a time-changed geometric Brownian price model with the univariate Hawkes processes to trace the price changes in a limit order book. Limit order books are the core mechanism for trading in modern financial markets, continuously collecting outstanding buy and sell orders from market participants. The arrival of orders causes fluctuations in prices over time. A Hawkes process is a type of point process that exhibits self-exciting behavior, where the occurrence of one event increases the probability of other events happening in the near future. This makes Hawkes processes well-suited for capturing the clustered arrival patterns of orders …

Identifying Transitions In Plasma With Topological Data Analysis Of Noisy Turbulence, Julius Kiewel

Undergraduate Honors Theses

Cross-field transport and heat loss in a magnetically confined plasma is determined by turbulence driven by perpendicular (to the magnetic field) pressure gradients. The heat losses from turbulence can make it difficult to maintain the energy density required to reach and maintain the conditions necessary for fusion. Self-organization of turbulence into intermediate scale so-called zonal flows can reduce the radial heat losses, however identifying when the transition occurs and any precursors to the transition is still a challenge. Topological Data Analysis (TDA) is a mathematical method which is used to extract topological features from point cloud and digital data to …

Mathematical Modeling And Examination Into Existing And Emerging Parkinson’S Disease Treatments: Levodopa And Ketamine, Gabrielle Riddlemoser

Undergraduate Honors Theses

Parkinson’s disease (PD) is the second most common neurodegenerative disease across the world, affecting over 6 million people worldwide. This disorder is characterized by the progressive loss of dopaminergic neurons within the substantia nigra pars compacta (SNpc) due to the aggregation of α-synuclein within the brain. Patients with PD develop motor symptoms such as tremors, bradykinesia, and postural instability, as well as a host of non-motor symptoms such as behavioral changes, sleep difficulties, and fatigue. The reduction of dopamine within the brain is the primary cause of these symptoms. The main form of treatment for PD is levodopa, a precursor …

Modeling Vibration Stiffness: An Analytical Extension Of Hertzian Theory For Angular Contact Bearings With A Thin Viscoelastic Coating, Davis R. Burton

Honors Theses

This thesis considers the novel angular contact rolling-element bearings proposed by NASA’s Glenn Research Center, which are coated with a thin solid lubricant that exhibits viscoelastic behavior. Current analytical models for the dynamic stiffness matrix of angular contact bearings, critical for vibration analysis, lack the ability to model the effects of a solid coating, as well as the time dependencies inherent in viscoelastic theory. The author first presents an overview of the stiffness matrix derivation, followed by a treatment of the underlying Hertzian contact theory. An analytical extension of this theory is proposed which accounts for a thin elastic layer …

Deterministic Global 3d Fractal Cloud Model For Synthetic Scene Generation, Aaron M. Schinder, Shannon R. Young, Bryan J. Steward, Michael L. Dexter, Andrew Kondrath, Stephen Hinton, Ricardo Davila

Faculty Publications

This paper describes the creation of a fast, deterministic, 3D fractal cloud renderer for the AFIT Sensor and Scene Emulation Tool (ASSET). The renderer generates 3D clouds by ray marching through a volume and sampling the level-set of a fractal function. The fractal function is distorted by a displacement map, which is generated using horizontal wind data from a Global Forecast System (GFS) weather file. The vertical windspeed and relative humidity are used to mask the creation of clouds to match realistic large-scale weather patterns over the Earth. Small-scale detail is provided by the fractal functions which are tuned to …

Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace

Electronic Theses, Projects, and Dissertations

Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …

Cost-Risk Analysis Of The Ercot Region Using Modern Portfolio Theory, Megan Sickinger

Master's Theses

In this work, we study the use of modern portfolio theory in a cost-risk analysis of the Electric Reliability Council of Texas (ERCOT). Based upon the risk-return concepts of modern portfolio theory, we develop an n-asset minimization problem to create a risk-cost frontier of portfolios of technologies within the ERCOT electricity region. The levelized cost of electricity for each technology in the region is a step in evaluating the expected cost of the portfolio, and the historical data of cost factors estimate the variance of cost for each technology. In addition, there are several constraints in our minimization problem to …

Convergence Estimate Of Minimal Residual Methods And Random Sketching Of Krylov Subspace Methods, Peter Westerbaan

All Dissertations

This study concerns two main issues in numerical linear algebra: convergence estimate of minimal residual methods based on explicit construction of approximate min-max polynomials for in- definite matrices, and development and analysis of Krylov subspace methods using non-orthonormal basis vectors based on random sketching. For a matrix A with spectrum Λ(A), it is well known that the min-max polynomial problem min max |pk (z)| pk ∈Pk, pk (0)=1, z∈Λ(A) is used to bound the relative error of Krylov subspace minimum residual methods or similar methods. For a symmetric positive definite matrix A, the min-max polynomial for the Conjugate Gradient (CG) …

Domain Decomposition Methods For Fluid-Structure Interaction Problems Involving Elastic, Porous, Or Poroelastic Structures, Hemanta Kunwar

All Dissertations

We introduce two global-in-time domain decomposition methods, namely the Steklov-Poincare method and Schwarz waveform relaxation (SWR) method using Robin transmission conditions (or the Robin method), for solving fluid-structure interaction systems involving elastic, porous, or poroelastic structure. These methods allow us to formulate the coupled system as a space-time interface problem and apply iterative algorithms directly to the evolutionary problem. Each time-dependent fluid and the structure subdomain problem is solved independently, which enables the use of different time discretization schemes and time step sizes in the subsystems. This leads to an efficient way of simulating time-dependent multiphysics phenomena. For the fluid-porous …

Bidding Strategy For A Wind Power Producer In Us Energy And Reserve Markets, Anne Stratman

Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research

Wind power is one of the world's fastest-growing renewable energy resources and has expanded quickly within the US electric grid. Currently, wind power producers (WPPs) may sell energy products in US markets but are not allowed to sell reserve products, due to the uncertain and intermittent nature of wind power. However, as wind’s share of the power supply grows, it may eventually be necessary for WPPs to contribute to system-wide reserves. This paper proposes a stochastic optimization model to determine the optimal offer strategy for a WPP that participates in the day-ahead and real-time energy and spinning reserve markets. The …

Models Of Functional Redundancy In Ecological Communities, Sandra Annie Tsiorintsoa

All Dissertations

Functional redundancy is the number of taxa that perform a given function within a given community. In most systems, high levels of functional redundancy are important, because they contribute to ecosystem stability. However, we currently have very little understanding of why functional redundancy varies among communities. One possible factor that could affect functional redundancy is environmental complexity. Many studies show that simplified ecosystems harbor communities with lower taxon diversity. What is less clear is if this simplicity and lower taxon diversity also affects functional redundancy. To answer this question, we use metacommunity models to explore the connection between environmental complexity …

Interpreting Shift Encoders As State Space Models For Stationary Time Series, Patrick Donkoh

Electronic Theses and Dissertations

Time series analysis is a statistical technique used to analyze sequential data points collected or recorded over time. While traditional models such as autoregressive models and moving average models have performed sufficiently for time series analysis, the advent of artificial neural networks has provided models that have suggested improved performance. In this research, we provide a custom neural network; a shift encoder that can capture the intricate temporal patterns of time series data. We then compare the sparse matrix of the shift encoder to the parameters of the autoregressive model and observe the similarities. We further explore how we can …

Multi-Objective Radiological Analysis In Real Environments, David Raji

Doctoral Dissertations

Designing systems to solve problems arising in real-world radiological scenarios is a highly challenging task due to the contextual complexities that arise. Among these are emergency response, environmental exploration, and radiological threat detection. An approach to handling problems for these applications with explicitly multi-objective formulations is advanced. This is brought into focus with investigation of a number of case studies in both natural and urban environments. These include node placement in and path planning through radioactivity-contaminated areas, radiation detection sensor network measurement update sensitivity, control schemes for multi-robot radioactive exploration in unknown environments, and adversarial analysis for an urban nuclear …

Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens

Doctoral Dissertations

Mathematical modeling can achieve otherwise inaccessible insights into bio-logical questions. We use ODE (ordinary differential equations) and Game Theory models to demonstrate the breadth and power of these models by studying three very different biological questions, involving socio-behavioral and socio-economic systems, conservation biology, policy and decision making, and organismal homeostasis.

We adapt techniques from Susceptible-Infected-Recovered (SIR) epidemiological models to examine the mental well-being of a community facing the collapse of the industry on which it’s economically dependent. We consider the case study of a fishing community facing the extinction of its primary harvest species. Using an ODE framework with a …

Analysis Of Nonsmooth Neural Mass Models, Cadi Howell

Honors College

Neural activity in the brain involves a series of action potentials that represent “all or nothing” impulses. This implies the action potential will only “fire” if the mem- brane potential is at or above a specific threshold. The Wilson-Cowan neural mass model [6, 28] is a popular mathematical model in neuroscience that groups excita- tory and inhibitory neural populations and models their communication. Within the model, the on/off behavior of the firing rate is typically modeled by a smooth sigmoid curve. However, a piecewise-linear (PWL) firing rate function has been considered in the Wilson-Cowan model in the literature (e.g., see …

The Mathematical And Historical Significance Of The Four-Color Theorem, Brock Bivens

Scholars Day Conference

Computers becoming more readily used in mathematics.

Mathematical Modeling For Dental Decay Prevention In Children And Adolescents, Mahdiyeh Soltaninejad

Dissertations

The high prevalence of dental caries among children and adolescents, especially those from lower socio-economic backgrounds, is a significant nationwide health concern. Early prevention, such as dental sealants and fluoride varnish (FV), is essential, but access to this care remains limited and disparate. In this research, a national dataset is utilized to assess sealants' reach and effectiveness in preventing tooth decay, particularly focusing on 2nd molars that emerge during early adolescence, a current gap in the knowledge base. FV is recommended to be delivered during medical well-child visits to children who are not seeing a dentist. Challenges and facilitators in …

Rsa Algorithm, Evalisbeth Garcia Diazbarriga

ATU Research Symposium

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

Bioheat Equation Analysis, Johnathan Makar

Mathematics Student Work

In our research, we are investigating Pennes Bioheat equation, which is used for simulating the propagation of heat energy in human tissues. This equation was proposed by Pennes in 1948 based on his experiments of measuring the radial temperature distribution in the forearm of nine subjects. Pennes' equation provides the theoretical basis for studying heat transfer in perfused tissue and has been widely studied since then. However, Pennes' equation has been criticized for various reasons, including the fact that his experimental data did not seem to match the model. One of the objectives of our work is to find the …

An Augmented Matched Interface And Boundary (Amib) Method For Solving Problems On Irregular 2d Domains, Benjamin Pentecost

Mathematics Student Work

A new method called Augmented Matched Interface and Boundary (AMIB) has been developed to solve partial differential equation models, such as the heat equation, over irregular two-dimensional domains. The original AMIB method features unique numerical treatments to solve problems with various boundary conditions and shapes, resulting in highly accurate and efficient numerical solutions. However, recent numerical experiments have revealed that the original AMIB method can fail when dealing with sharply curved boundaries. To address this issue, new numerical techniques have been introduced in our latest work to enhance the robustness of the AMIB method. These techniques have been numerically verified …