Physical Sciences and Mathematics Commons^™

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 …

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 …

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 …

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 …

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 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 …

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 …

Mathematical Equations And System Identification Models For A Portable Pneumatic Bladder System Designed To Reduce Human Exposure To Whole Body Shock And Vibration, Ezzat Aziz Ayyad

UNLV Theses, Dissertations, Professional Papers, and Capstones

A mathematical representation is sought to model the behavior of a portable pneumatic foam bladder designed to mitigate the effects of human exposure to shock and whole body random vibration. Fluid Dynamics principles are used to derive the analytic differential equations used for the physical equations Model. Additionally, combination of Wiener and Hammerstein block oriented representation techniques have been selected to create system identification (SID) block oriented models. A number of algorithms have been iterated to obtain numerical solutions for the system of equations which was found to be coupled and non-linear, with no analytic closed form solution. The purpose …

Mathematical Modeling Of T Cell Clustering Following Malaria Infection In Mice, Reka Katalin Kelemen

Masters Theses

Malaria is the result of the immune system's unsuccessful clearance of hepatocytes (liver cells) infected by the eukaryotic pathogen of the Plasmodium genus. It has been shown that CD8 T cells are required and sufficient for protective immunity against malaria in mice [29, 36], but the mechanisms by which they find and eliminate infected hepatocytes are not known yet. Recently we reported the formation of CD8 T cell clusters consisting of up to 25 cells around infected cells [8]. Our mathematical modeling and data analysis revealed that malaria-specific T cells likely recruit each other and also non-malaria-specific T cells to …

Study Of Virus Dynamics By Mathematical Models, Xiulan Lai

Electronic Thesis and Dissertation Repository

This thesis studies virus dynamics within host by mathematical models, and topics discussed include viral release strategies, viral spreading mechanism, and interaction of virus with the immune system.

Firstly, we propose a delay differential equation model with distributed delay to investigate the evolutionary competition between budding and lytic viral release strategies. We find that when antibody is not established, the dynamics of competition depends on the respective basic reproduction numbers of the two viruses. If the basic reproductive ratio of budding virus is greater than that of lytic virus and one, budding virus can survive. When antibody is established for …

Airborne Wireless Communication Modeling And Analysis With Matlab, Matthew J. Vincie

Theses and Dissertations

Over the past decade, there has been a dramatic increase in the use of unmanned aerial vehicles (UAV) for military, commercial, and private applications. Critical to maintaining control and a use for these systems is the development of wireless networking systems [1]. Computer simulation has increasingly become a key player in airborne networking developments though the accuracy and credibility of network simulations has become a topic of increasing scrutiny [2-5]. Much of the inaccuracies seen in simulation are due to inaccurate modeling of the physical layer of the communication system. This research develops a physical layer model that combines antenna …

Mathematical Modeling Of Fluid Spills In Hydraulically Fractured Well Sites, Oluwafemi Michael Taiwo

Graduate Theses and Dissertations

Improved drilling technology and favorable energy prices have contributed to the rapid pace at which the exploitation of unconventional natural gas is taking place across the United States. As a natural gas well is being drilled, reserve pits are constructed to hold the drilling fluids and other materials returned from the drilling process. These reserve pits can fail, and when they do, plant and animal life of the surrounding area may be adversely affected. This project develops a screening tool for a suitable location for a reserve pit. This work will be a critical piece of the Infrastructure Placement Analysis …

Study Of Malaria Transmission Dynamics By Mathematical Models, Yanyu Xiao

Electronic Thesis and Dissertation Repository

This Ph.D thesis focuses on modeling transmission and dispersal of one of the most common infectious disease, Malaria. Firstly, an integro-differential equation system is derived, based on the classical Ross-Macdonald model, toemphasize the impacts of latencies on disease dynamics. The novelty lies in the fact that different distributionfunctions are used to describe the variance of individual latencies. The theoretical results of this projectindicate that latencies reduce the basic reproduction number. Secondly, a patch model is derived to examine how travels of human beings affects the transmission and spread of Malaria. Due to coexistence of latency and dispersal, the model turns …

Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena

All Theses

Over the past decades, a number of mathematical models and solution techniques have been developed to preserve reserve sites for species and their natural habitats. Two optimization models for designing spatially compact ecological reserve systems are addressed here as zero-one integer programming problems. These formulations have a bicriteria objective function that is a combination of both boundary length and distance. The two formulations cluster the sites into a relatively small number of compact groups while preserving a required number of sites that contain a certain species using a given amount of resources. Two general types of approaches have been developed …

Mathematical Aids Epidemic Model: Preferential Anti-Retroviral Therapy Distribution In Resource Constrained Countries, Nadia Abuelezam

HMC Senior Theses

HIV/AIDS is one of the largest health problems the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. ART-distribution methods need to be created that prevent the largest number of future HIV infections. We have developed a compartment model that tracks the spread of HIV in multiple two-sex populations over time in the presence of limited treatment. The model has been fit to represent the HIV epidemic in rural and urban areas in Uganda. With the model we examine the spread of HIV among urban and …