Physical Sciences and Mathematics Commons^™

Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist

CODEE Journal

In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.

An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …

Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu

Dissertations

Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …

A New Sir Model With Mobility., Ciana Applegate

Electronic Theses and Dissertations

In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Modeling The Effect Of Human Behavior On Disease Transmission, Katie Yan

Mathematics and Statistics Theses

Many infectious disease models build upon the classical Susceptible-Infected-Recovered (SIR) model. The SIR model is a compartmental model that is used to model disease transmission throughout a population. The SIR model and its variations often focus on the transmission of disease but rarely include behavioral or informational components that explore how the perception of a disease influences transmission. In this thesis we propose a six compartment SIR model that segments the classical SIR model based on knowledge of information to explore the sharing of information and its ability to increase and decrease transmission. We designate these two model states as …

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 …

Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev

Scientific-technical journal

Centrifugal cyclones have been developing for 100 years, while the efficiency of all cyclones for fine dust does not increase by 80%. The widespread use of cyclones in all branches of industrial production is determined by the simplicity of the design and sufficient reliability in operation. Along with this, the process carried out in a cyclone presents a complex scientific problem that has not been solved from the standpoint of aerohydromechanics. This is confirmed by various cyclone designs. Currently, the efficiency of cyclone cleaning of technological flows does not meet the requirements of sanitary standards and largely determines the level …

Mathematical Models Of Infection Prevention Programs In Hospital Settings, Kelly A. Reagan

Theses and Dissertations

Hospitals play a vital role in providing for the healthcare needs of a community. Patients can develop hospital-acquired infections (HAIs) during their hospitalization due to exposure to foreign bacteria, viruses, and fungi. Infection prevention programs target and reduce HAIs, but implementing the infection prevention programs often comes with a cost. The goal of my research is to use mathematical models to quantify the impact of infection prevention programs on cases of HAIs and total healthcare costs. First, I use a Markov chain model to quantify how one infection prevention program reduces general HAIs in the hospital. Then, I calculate the …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

A Computational Investigation Of The Biophysical Mechanisms Underlying Thermotaxis In The Afd Neurons Of Caenorhabditis Elegans, Zachary Mobille

Theses and Dissertations

Thermotaxis in the nematode Caenorhabditis elegans (C. elegans) is studied at the cellular scale of the amphid finger-like ciliated (AFD) neurons, which have previously been shown to be essential for thermoreception. The voltage and calcium signals of AFD during temperature stimuli are described with ordinary differential equations. The primary calcium model is a modified version of that published by Kuramochi and Doi in 2017 to explain the calcium responses of the chemosensitive amphid single-ciliated right (ASER) neuron to fluctuations in extracellular salt concentration. To account for the effects of temperature, changes to the stimuli conditions under which inactivation takes place …

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva

Acta of Turin Polytechnic University in Tashkent

В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.

Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher

Mahurin Honors College Capstone Experience/Thesis Projects

A mathematical model for the healing response of diabetic foot ulcers was developed using averaged data (Krishna et al., 2015). The model contains four major factors in the healing of wounds using four separate differential equations with 12 parameters. The four differential equations describe the interactions between matrix metalloproteinases (MMP-1), tissue inhibitors of matrix metalloproteinases (TIMP-1), the extracellular matrix (ECM) of the skin, and the fibroblasts, which produce these proteins. Recently, our research group obtained the individual patient data that comprised the averaged data. The research group has since taken several approaches to analyze the model with the individual …

Dimension-Breaking For Traveling Waves In Interfacial Flows, Matthew W. Seiders

Theses and Dissertations

Fluid flow models in two spatial dimensions with a one-dimensional interface are known to support overturned traveling solutions. Computational methods of solving the two-dimensional problem are well developed, even in the case of overturned waves. The three-dimensional problem is harder for three prominent reasons. First, some formulations of the two-dimensional problem do not extend to three-dimensions. The technique of conformal mapping is a prime example, as it is very efficient in two dimensions but does not have a three-dimensional equivalent. Second, some three-dimensional models, such as the Transformed Field Expansion method, do not allow for overturned waves. Third, computational time …

Mathematical Model Investigating The Effects Of Neurostimulation Therapies On Neural Functioning: Comparing The Effects Of Neuromodulation Techniques On Ion Channel Gating And Ionic Flux Using Finite Element Analysis, Kaia Lindberg

Mathematics Theses

Neurostimulation therapies demonstrate success as a medical intervention for individuals with neurodegenerative diseases, such as Parkinson’s and Alzheimer’s disease. Despite promising results from these treatments, the influence of an electric current on ion concentrations and subsequent transmembrane voltage is unclear. This project focuses on developing a unique cellular-level mathematical model of neurostimulation to better understand its e↵ects on neuronal electrodynamics. The mathematical model presented here integrates the Poisson-Nernst-Planck system of PDEs and Hodgkin-Huxley based ODEs to model the e↵ects of this neurotherapy on transmembrane voltage, ion channel gating, and ionic mobility. This system is decoupled using the Gauss-Seidel method and …

The Mathematical Modeling Of Ballet, Kendall Gibson

Mathematics Senior Capstone Papers

This project aims to analyze the connections between ballet and mathematics. Specifically, this project focuses on analyzing the three-dimensional surfaces created as a dancer performs ballet choreography. The primary goal is to use a Vicon motion capture system in conjunction with MATLAB to model the three-dimensional lines and surfaces created by a dancer’s legs as she performs specific ballet movements. The movements used for this experiment were a pique turn and a rond de jambe. The data was collected using sensors to create objects in Vicon to record the position of the ankle, knee, and hip of the working leg …

Mathematical Models Of Mosquito Populations, Hanna Reed

Honors Undergraduate Theses

The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquito-borne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting …

Modeling Public Opinion, Arden Baxter

Honors Program Theses

The population dynamics of public opinion have many similarities to those of epidemics. For example, models of epidemics and public opinion share characteristics like contact rates, incubation times, and recruitment rates. Generally, epidemic dynamics have been presented through epidemiological models. In this paper we adapt an epidemiological model to demonstrate the population dynamics of public opinion given two opposing viewpoints. We find equilibrium solutions for various cases of the system and examine the local stability. Overall, our system provides sociological insight on the spread and transition of a public opinion.

On Honey Bee Colony Dynamics And Disease Transmission, Matthew I. Betti

Electronic Thesis and Dissertation Repository

The work herein falls under the umbrella of mathematical modeling of disease transmission. The majority of this document focuses on the extent to which infection undermines the strength of a honey bee colony. These studies extend from simple mass-action ordinary differential equations models, to continuous age-structured partial differential equation models and finally a detailed agent-based model which accounts for vector transmission of infection between bees as well as a host of other influences and stressors on honey bee colony dynamics. These models offer a series of predictions relevant to the fate of honey bee colonies in the presence of disease …

Comparison Of The Regulatory Dynamics Of Related Small Gene Regulatory Networks That Control The Response To Cold Shock In Saccharomyces Cerevisiae, Natalie Williams

Honors Thesis

The Dahlquist Lab investigates the global, transcriptional response of Sacchromyces cerevisiae, baker’s yeast, to the environmental stress of cold shock, using DNA microarrays for the wild type strain and strains deleted for a particular regulatory transcription factor. Gene regulatory networks (GRNs) consist of transcription factors (TF), genes, and the regulatory connections between them that control the resulting mRNA and protein expression levels. We use mathematical modeling to determine the dynamics of the GRN controlling the cold shock response to determine the relative influence of each transcription factor in the network. A family of GRNs has been derived from the …

From Random To Organized: The Architecture Of Neural Networks During Development, Avery Isabella Morris

Senior Projects Fall 2017

The brain is constantly changing during development as a result of various stimuli: memories, language, visual patterns and other sensory information. As a result, networks need to have specific learning rules to function being both plastic and stable. In this project, I’ve constructed a mathematical model based on a biological neural network during development. I’ve written differential equations to describe these specific learning rules as well as methods of visual input to the network. I’ve changed my model, using Euler’s method, to create a discrete-time version of this biological phenomenon to implement on the computer. I’ve successfully coded this, using …

Convergence To Consensus In Heterogeneous Groups And The Emergence Of Informal Leadership, Sergey Gavrilets, Jeremy David Auerbach, Mark Van Vugt

Faculty Publications and Other Works -- Ecology and Evolutionary Biology

When group cohesion is essential, groups must have efficient strategies in place for consensus decisionmaking. Recent theoretical work suggests that shared decision-making is often the most efficient way for dealing with both information uncertainty and individual variation in preferences. However, some animal and most human groups make collective decisions through particular individuals, leaders, that have a disproportionate influence on group decision-making. To address this discrepancy between theory and data, we study a simple, but general, model that explicitly focuses on the dynamics of consensus building in groups composed by individuals who are heterogeneous in preferences, certain personality traits (agreeability and …

The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares

Department of Math & Statistics Faculty Publications

Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and sub-optimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …

Roles Of A Teacher And Researcher During In Situ Professional Development Around The Implementation Of Mathematical Modeling Tasks, Hyunyi Jung, Corey Brady

University Faculty Publications and Creative Works

Partnership with teachers for professional development has been considered beneficial because of the potential of collaborative work in the teacher’s own classroom to be relevant to practice. From this perspective, both teachers and researchers can draw on their own expertise and work as authentic partners. In this study, we address the need for such collaboration and focus on how a teacher and a researcher performed their roles when collaboratively implementing mathematical modeling tasks within a context of in situ professional development. Using multi-tier design-based research, as a framework, a researcher worked in a teacher’s classroom to implement a series of …

Modeling Of Piezoelectric Traveling Wave Rotary Ultrasonic Motors With The Finite Volume Method, Ivan Arturo Renteria Marquez

Open Access Theses & Dissertations

In 1983 Toshiiku Sashida developed a new motor concept called Piezoelectric Traveling Wave Rotary Ultrasonic Motor (PTRUSM). The advantages of these motors include high torque at low speed, absence of a generated magnetic field, and high potential for miniaturization. Unfortunately PTRUSMs have some disadvantages that limit the areas of applications for these types of motors. The disadvantages are a short operating life (about 1000 hours), small output power, and the need of a complex motor controller.

On one hand, these motors have been used in satellites, mobile phones, photocopiers, robotic arms, telescopes, automobiles, and camera autofocusing. On the other hand, …

Mechanisms For Social Influence, Jeremy David Auerbach

Masters Theses

Throughout the thesis, I study mathematical models that can help explain the dependency of social phenomena in animals and humans on individual traits. The first chapter investigates consensus building in human groups through communication of individual preferences for a course of action. Individuals share and modify these preferences through speaker listener interactions. Personality traits, reputations, and social networks structures effect these modifications and eventually the group will reach a consensus. If there is variation in personality traits, the time to reach consensus is delayed. Reputation models are introduced and explored, finding that those who can best estimate the average initial …

Mathematical Modeling Of Emiliania Huxleyi And A Host-Specific Virus, Julia Middleton

Honors Theses

The world’s oceans provide the basis for life on the planet. One microscopic algae, the coccolithophores, and Emiliania huxleyi in particular, is a major source of carbon drawdown in the context of the global carbon cycle and account for a significant amount of the primary production in oceanic ecosystems. We know that the oceans are packed with marine viruses and they have an important role in the rise and fall of plankton populations but current mathematical models do not accurately account for virus-host interactions when predicting plankton blooms. Therefore I am using model optimization and comparison techniques to evaluate current …

Multistrain Infections In Metapopulations, Sydney Garmer, Rachel Lynn, Dan Rossi, Alex Capaldi

Alex Capaldi