Physical Sciences and Mathematics Commons^™

Parameter Optimization For Excitable Cell Models, Amrit Parmar

Theses, Dissertations and Culminating Projects

The electrophysiology of nodose ganglia neurons is of great interest in the analysis of cell membrane currents and action potential behavior. This behavior was initially outlined in the Hodgkin-Huxley conductance model [1] using a system of nonlinear differential equations. Later, Schild et al. [2] developed an extension of the Hodgkin-Huxley model to provide a more exhaustive description of ion channels involved in nodose neuronal action potential activity. We consider a variety of methods to fit the parameters of both the Hodgkin-Huxley and Schild et al. models to an empirical stimulus response dataset. Our methods were validated using synthetic datasets, as …

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 …

The Impact Of Social Controls And Vaccination On The Spread Of Covid-19 In New Jersey, Ariel J. Bonneau

Theses, Dissertations and Culminating Projects

The emergence of the novel coronavirus (SARS-CoV-2) in late 2019 has led to a global pandemic (COVID-19) which continues to cause enormous public health and economic challenges around the world. It is therefore important to improve our understanding of the outbreak and spread of COVID-19 as well as to investigate how one might contain or stop the spread of COVID-19 via different control measures. In this thesis, we consider a COVID-19 model based on an SEIR compartmental model. The model includes susceptible, vaccinated, exposed, pre-symptomatic, symptomatic infectious, asymptomatic infectious, hospitalized, recovered, and deceased compartments, each of which is sub-divided into …

Forecasting Electricity Load In New Jersey With Artificial Neural Networks, Erik W. Raab

Theses, Dissertations and Culminating Projects

Load forecasting is an important tool for both the energy and environmental sectors. It has progressed hand-in-hand with machine learning innovation, where recurrent neural networks, a type of artificial neural network, is primarily used. This thesis compares progressively complex, feed-forward artificial neural networks using a mix of weather and temporal data. We demonstrate that electrical load in New Jersey can be reliably predicted using memory-less algorithms with minimal predictors drawn from preexisting public data sources. The methods used in this thesis could be used to build competitive load forecasting models in other states, and if included in diverse model ensembles, …

Modeling The Dynamics Of Excitable Cells, Asja Alić

Theses, Dissertations and Culminating Projects

We consider an electrical parallel conductance membrane model which is an extension of the classical Hodgkin-Huxley neuronal model of excitability. This extended model describes the formation of the resting membrane potential and conductance, and the formation of action potentials in nodose A-type excitable cells. The model consists of a set of nonlinear ordinary differential equations which are numerically solved using the Python programming language. The results show that the model is capable of accurately describing experimental results including resting membrane potential and conductance, duration and form of action potentials, amplitude of the spike, oscillations, and activitydependent changes in [Ca^{2+ …}

Computational Analysis To Study The Efficiency Of Shear Activated Nano-Therapeutics In The Treatment Of Atherosclerosis, Nicholas Jefopoulos

Theses, Dissertations and Culminating Projects

Strokes are the fifth leading cause of death in the United States and can cause long-term disabilities in patients who survive a stroke. The vast majority of these strokes are ischemic, primarily caused by intracranial atherosclerosis. Most therapies to combat intracranial atherosclerosis simply manage it and do not remove the buildup of plaque. Targeted shear-activated nanotherapeutics are currently being developed to remove these plaques. We discuss the roles that aggregate particle density, aggregate particle diameter, vessel geometry, stenosis shape and breakup threshold play in the efficiency of this new technology. Computational studies were performed to test these parameters in three …

Extinction Of Species Due To Deterministic And Stochastic Interactions In Food Webs, Claire M. Burke

Theses, Dissertations and Culminating Projects

Previous research on the extinctions that occur in niche model food webs with deterministic and stochastic dynamics has shown that the structure of the food web can play an important role in extinction cascades. In this thesis, other types of synthetic food web models are considered, namely the cascade and generalized cascade models, and the extinction cascades of these food webs are compared with previous findings on the extinction cascades from the niche model. It was found that there are many similarities in the results for all three models, which prompted a closer analysis using food webs with deterministic dynamics. …

Control Of Secondary Extinctions In Stochastic Food Webs, Dunia M. Fernandez

Theses, Dissertations and Culminating Projects

Studies on both model-based and empirical food webs have shown that per- turbations to an ecological community can cause a species to go extinct, often resulting in the loss of additional species in a cascade of secondary extinctions. These eects can seriously debilitate a food web and threaten the existence of an ecosystem. Here, we consider niche model-based food webs with internal noise and investigate the eects of a control on a secondary extinction cas- cade triggered by a noise-induced extinction. We show that the forced removal of a nonbasal species immediately after a primary extinction can extend the mean …

Stochastic Modeling Of Zoonotic Disease, Sausan Odatalla

Theses, Dissertations and Culminating Projects

We provide an overview of the mathematical modeling of deterministic and stochastic infectious disease models. These models enable one to understand the outbreak, spread, and extinction of disease. We then focus on stochastic models with a disease reservoir to understand outbreak vulnerability for zoonotic diseases such as Ebola Virus Disease (EVD). Numerical results from a more complicated EVD model are compared with the theoretical results of a simplified stochastic SISk model. We also demonstrate the effect that vaccine has on outbreak vulnerability in a population that is connected to a disease reservoir.

Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda

Theses, Dissertations and Culminating Projects

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, …

Least Action Principle Applied To A Non-Linear Damped Pendulum, Katherine Rhodes

Theses, Dissertations and Culminating Projects

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction. However, it can be shown that with large values of damping, the object will no longer …

Understanding The Flow Structure Of Low Reynolds Number Flows, Albert Jarvis

Theses, Dissertations and Culminating Projects

Ocean flows and the mechanisms by which their contents are organized has been a longstanding area of interest in applied mathematics. In recent years, a new theory has been developed to identify the structures responsible for the organization of fluid particles within complex geophysical flows. This theory is known as the theory of Lagrangian Coherent Structures (LCS) and details which structures are responsible for the organization of the flow and how to identify them. Being able to identify these LCS in real time has far reaching implications ranging from developing strategies for search and rescue missions to identifying the best …

Dynamics Of Coupled Particles In A Time-Dependent, Double-Gyre Flow, Manuel Albrizzio

Theses, Dissertations and Culminating Projects

We consider a time-dependent, wind-driven, stochastic double-gyre flow, and investigate the interaction between the flow and coupled particles operating within the flow. It is known that noise can cause individual particles to escape from one gyre to another gyre. By computing the Lagrangian coherent structures (LCS) of the system, one can determine low and high probability regions of particle escape. We adjust the coupling between two particles, and study the effect on particle escape for a variety of initial conditions and noise intensities.

Analysis Of Daily Precipitation Data From Selected Sites In The United States, Sahar Ahmed

Theses, Dissertations and Culminating Projects

Global warming is a contentious topic since modern climate records only exist for the last 100 years in contrast to ice-core analysis that establishes ice ages tens of thousands of years ago. Nevertheless, patterns associated with events such as El Niño Southern Oscillation (ENSO), precipitation, tornadoes, and snowfall amounts over the last century can provide a useful and objective indicator of climate “change”. This project focuses on daily precipitation totals for the state of New Jersey over the last 100 to 150 years from nineteen meteorological recording stations and involves large data sets with a million observations. This research utilizes …

Inertial Particle Transport By Lagrangian Coherent Structures In Geophysical Flows, Alexa Aucoin

Theses, Dissertations and Culminating Projects

Lagrangian Coherent Structures (LCS) provide a skeleton for the underlying structures in geophysical flows. It is known that LCS govern the movement of fluid particles within a flow, but it is not well understood how these same LCS influence the movement of inertial particles within a fluid flow. In this thesis, we consider two geophysical flows, the double-gyre model, and a single-layer quasi-geostrophic PDE model. In particular, we use finite-time Lyapunov exponents (FTLE) to characterize the attracting and repelling LCS for these models and show how inertial particles aggregate with respect to LCS. We numerically investigate the dynamics of inertial …

Seasonal Switching Affects Bacterial-Fungal Dominance In An Ecological System, Kristin Carfora

Theses, Dissertations and Culminating Projects

We consider a model inspired by producer-herbivore-decomposer soil food webs and determine the effect of ecological parameters on the decomposer pool. In particular, we observe how seasonal changes in the stoichiometric quality of the producer coupled with the efficiency of herbivory over the calendar year can induce a shift in the composition of the decomposer pool. Decomposers have a significant effect on the movement of essential nutrients throughout an ecosystem; we further determine how this shift between a bacterially dominated decomposer pool and a fungally dominated pool affects primary production and relative distribution of biomass of the other compartments.

The Mechanics And Thermodynamics Of Amyloid Beta Protein Aggregation In Competing Pathways, Edward Steen

Theses, Dissertations and Culminating Projects

The primary purpose of this paper is to investigate the mechanics of Aβ protein aggregation within the brain through mathematical modeling and simulation. Aggregation of Aβ is the cause of plaques within the brain of Alzheimer’s Disease sufferers. Because the pathways of aggregation from monomer to oligomer to polymer are numerous and complex, we have had to simplify our model to a limited number of species. Of great concern, too, is the process by which Aβ can form as “off-pathway” species, which is when Aβ reacts with fatty acid micelles. It is this species of Aβ, which due to its …

Fluid Dynamics Of Watercolor Painting : Experiments And Modelling, David Edward Baron

Theses, Dissertations and Culminating Projects

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington's experiments has now been clarified. One specific set of such recent studies, which motivates this thesis, concerns the fluid dynamics behind Jackson Pollock's drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and have made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of …

On The 3-Dimensional Fluid-Structure Interaction Of Flexible Fibers In A Flow, Ryan Howard Allaire

Theses, Dissertations and Culminating Projects

We discuss the equilibrium configurations of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s. Experimental results are presented with both two-dimensional and three-dimensional numerical simulations used to model this problem. We present the effects of flow speed and initial configuration angle between the fiber and the direction of the flow. Investigations reveal that both the orientation of the fiber and the fiber length have a significant impact on the deformation of the fiber as well as on the forces it experiences. Specifically, we …

Magnetoviscous Effects Of Magnetized Particle Threads In Magnetized Ferrofluid, Alexander Francis Cali

Theses, Dissertations and Culminating Projects

The magnetoviscous effect of applied fields on ferrofluids has been utilized in many applications in which the ferrofluid must remain in a fixed position while this effect on ferrofluids in motion has yet to be rigorously explored. In light of potential biomedical applications such as drug targeting, experiments were conducted to probe the rheology of ferrofluids on the micrometer scale. A non-conducting glass sphere of diameter 550 μm is dropped into a cylindrical container of magnetized ferrofluid of inner diameter 5.2 mm. This was repeated for two applied field strengths (980 gauss and 480 gauss) and over multiple angles with …

Thermalization And Initial State-Recurrence In Discrete Kdv-Like Lattices, Garrett Taylor Nieddu

Theses, Dissertations and Culminating Projects

Three discretizations of the Korteweg de-Vries equation are studied; convergence rate, initial state-recurrence, and the energy distribution of the three schemes are all considered. For each discrete scheme over 300 lattices with varying grid sizes were investigated, and the solutions were compared with other lattices from the same scheme, as well as solutions from the other two. It is found that the two schemes that are least accurate display the best recurrence at intermediate grid sizes, away from convergence. This is a notable result because the best recurrence is expected to be found in the most accurate, and converged lattices. …

Modeling The Curvature Of A Ferrofluid Interface Using A Height Function Method, Holly Timme

Theses, Dissertations and Culminating Projects

The behavior of an interface embedded in a fluid is central to a wide range of biological, chemical, environmental and physical problems and engineering processes. Modeling the evolution of a fluid interface is thus a critical and important problem. In many instances, including two-phase (e.g. liquid-gas) flows, the interface is an internal boundary within a PDE model. A model of the interface properties and its evolution is then typically performed by numerical computation, within the framework of the PDE solution method, such as finite differences (FD). Volume of Fluid (VOF) is a simple FD based method which exhibits excellent volume …

The Persistence Of Infectious Diseases In Metapopulations, Jonathan Calvin Hayes

Theses, Dissertations and Culminating Projects

Mathematical models provide a great deal of information about the dynamics of disease spread. In this paper, we use stochastic simulation to investigate spontaneous disease extinction and réintroduction in a SIR model. We begin by investigating path to extinction and time to extinction in single population models, and then expand to a multipopulation model linked with linear migration. We have found that in a single population model, it is more effective to use random pulse vaccinations less per year at a higher removal rate. We have expanded this result by developing a vaccination strategy giving one large, well timed pulse …

An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses, Karin Weule

Theses, Dissertations and Culminating Projects

We analyze real data sets from two e-mail viruses, the Magistr.b and the Sircam.a to explore how we can use mathematical models to predict the behavior described by the data. Analysis of the data is conducted primarily with computer programming in MatLab. We focus mainly on the use of two continuous models commonly used in the study of biological diseases, the SIS and the SIR models. A discrete modeling approach using agent-based simulations is also explored and revealed to be potentially useful in developing a compartmentalized model that incorporates both SIS and SIR model behavior. The theory behind the continuous …

A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data, Steven Spero

Theses, Dissertations and Culminating Projects

This research applies time series methods to determine relationships among a set of weather variables which are continually monitored in the Hackensack Meadowlands region of northern New Jersey. Weather data includes chemical and atmospheric factors. Chemical factors are Nitrogen Oxide, atmospheric Ozone, Carbon Monoxide, and Carbon Dioxide. Weather factors are wind speed, barometric pressure, air temperature, humidity, and solar radiation. Additionally, traffic density and time of week are brought in as categorical factors. This research attempts to (a) introduce the reader to various time series methodologies, (b) find a significant and efficient model for forecasting Nitrogen Oxide levels, and (c) …

Patch Models And Applications On The Spread Of Avian Influenza, Kimberly Rude

Theses, Dissertations and Culminating Projects

The avian influenza virus (AIV) is an infectious disease that predominantly affects birds. Economic losses due to large-scale deaths of domestic poultry as a result of past outbreaks have been devastating. Additionally, there is major concern about the spread of the virus to humans. The virus has spread to humans in the past, but has not yet been known to spread beyond one human. Since influenza viruses are known to mutate easily, there is serious concern that the virus could mutate into a strain that can be transmitted easily to and among humans.

There has been much speculation that migratory …

Migration And Mixing Between Populations In Disease Models, David Burger

Theses, Dissertations and Culminating Projects

The goal of this thesis is to model the spread of disease between populations and find ways to prevent its continued epidemic. This thesis studies disease spread as a function of migration in epidemiological models. The models are constructed using the compartmental approach, and we compare discrete and continuous time approximations. In the discrete model, we will look at ways that induced migration can cause an epidemic case to turn into a dieout case. It will be shown that migration can only effect the size of an outbreak, but cannot create or destroy one. For the continuous cases, we will …

Dynamics Of A Two Serotype Disease With Antibody Dependent Enhancement, Amy Fiorillo

Theses, Dissertations and Culminating Projects

The dengue virus is a serious infectious disease that can be found in many regions of Southeast Asia. There exist four serotypes of the virus. Recovery from one serotype produces a natural immunity from that serotype. However, it also creates complexes with a second infection and will increase viral production. This process is know as antibody dependent enhancement (ADE). As a result, it is very difficult to vaccinate against the disease. An optimal vaccination would have to cover all four serotypes at once. To understand the dynamics of the disease, we will study a mathematical model for two coexisting serotypes …

Disease Outbreaks In Coupled Populations : An Application To Measles Spread In Cameroon, Kirsten Maggie Viz

Theses, Dissertations and Culminating Projects

Many childhood diseases can be modeled mathematically using a system of differential equations that group the overall population into compartments. Much research has been done to understand and control the spread of these diseases within a single population and between coupled populations with constant parameters. In this thesis, we are concerned with how a disease is spread through and between coupled populations using models with time-varying parameters and asymmetric coupling.

Measles outbreaks in the West African country of Cameroon present a good example of disease spread with seasonality. By dividing Cameroon into two subpopulations and using parameters that reflect recent …