# Papers & Projects

## Student Research Showcase: S.I.R. Measles Model for Wilmington, NC

The resurgence of previously controlled diseases, such as measles, is on the rise. The dynamics of a measles outbreak is affected by several important factors centering upon the risk of exposure and immunity to the disease. As Wilmington, NC is a tourist destination and port city, there exists a possibility of exposure to the measles virus. Through mathematical analysis and numerical simulation, we manipulated a system of three differential equations to demonstrate the effects of varied immunity rates on outbreak severity for Wilmington NC. Download button below.

Full Credits: Christine McCraib, Michael Ruff, Zachary G. Wolfe

## ODE Modeling: Resonance Frequency Effects of Earthquakes on Buildings

Earthquakes can bring down buildings in an interesting way, through resonance frequency. This phenomenon is where the vibration of the group matches the resonance frequency of a building and causes it to start vibrating like a spring. In this presentation, we outline how this might occur, the laws involved, and develop a mathematical model detailing the phenomenon. Download button below.

Full Credits: Mark Decatur, Duane Moree, Zachary Wolfe

## Analysis: Bifurcations in Interstellar Gas Clouds

Chaos theory, or popularly known as the "Butterfly Effect", details the effects of tiny variations in large systems, such as the weather (Blog post on chaos theory and weather prediction HERE). However, such phenomena occurs in many systems. One amazing example is how it occurs in the darkest, coldest regions of space - Gas Clouds. Depending on small variations in radiation flux, a gas cloud may diverge into highly or lowly ionized species. A FORTRAN model based on the UMIST database was explored to demonstrate these bifurcations. Download button below.

## Review: Fundamental Structure of Water

Water is the most pervasive compound in liquid form on our earth and composes over half of the molecular composition of human beings. The structure has been studied extensively and currently is accepted that a water molecule will interact with its neighbors in a tetrahedral fashion which develops into a hexagonal matrix once frozen. Wernet, using x-ray absorption spectroscopy (XAS) and x-ray Raman scattering data, developed his new model based on the similarities between surface ice, and typical liquid water at ambient conditions. With this finding coupled with molecular dynamics (MD) simulations, Wernet’s analysis concluded that the molecules in liquid form are not predominantly four-coordinated. He has proposed that there are only two strong H-bond interactions, one accepting and one donating, in which they develop into chains. A counter paper was published by Dr. J.D Smith. Smith’s paper outlines flaws in the model proposed by Wernet under two main discrepancies. First, Smith introduces a criterion to characterize the degree of how H- bond distortion affects XAS spectra; with it, he shows that XAS has a large sensitivity to changes in H-bond structure. Smith’s main argument is that the cluster model that Wernet employed to describe his criteria for H-bond structure is not adequate to represent liquid water. Smith’s new criterion of H-bond restructuring, once used in Wernet’s model, shows excellent agreement between the new structure and the experimentally verified XAS data. Download button below.

Full Credits: Erick Holguin, Zachary Wolfe

## Review: Two State Vector Formalism

In this paper we reflect on a debate that has existed in quantum mechanics for nearly as long as the

topic itself has been around. This debate concerns time-symmetry in quantum mechanics, more

specifically, where quantum states can evolve forwards in time and backwards in time. This paper is a

review of two-state vector formalism, the most prominent theory, and an experiment that details one

such phenomena probing the heart of this theory. Download button below.

## Statistical Analysis: Officer Involved Shootings (LA vs CLT)

Crime is an event which takes place at any time. One such crime which can have many factors to consider that leads to that event are officer involved shootings. After a search using the Police Data Initiative website, we were able to obtain historical data (2006-2016) native to the Los Angeles, California and the Charlotte, North Carolina metropolitan areas to perform an analyses of this particular issue. Each police department records crime data and provides variables tied to an individual incident. The purpose of this project is to use various statistical methods to identify any possible trends within the historical data, and evaluate the results. An initial calculation of incidents per 100,000 people for each city will be used to help summarize our conclusions.

Los Angeles: (284/(3,976,322/100,000)) = 7.14 incidents per 100,000 people (sample size=284 observations)

Charlotte: (65/(842,051/100,000)) = 7.72 incidents per 100,000 people (sample size=65 observations)

Full Credits: Virginia Wolfe, Zachary Wolfe

## Versatility of the Wolfram Language

University of North Carolina Wilmington supports Maple over Mathematica, as I discovered my freshman year. However, being the ever-curious and stubborn student coupled with the fact that I'm not terrible with a PC, I decided to investigate multiple CAS packages. Enter my discovery of the wonderous Mathematica software. I can honestly say I have never looked back. I've used it in research projects and other scenarios as well as my own personal studies. I fully believe in this package and felt that if I could voice my opinion in hopes to persuade someone to check it out, that I should -- so here is my point of view on the Wolfram Language, the mainstay of Mathematica as seen from a Science Student. Download button below.

## The Putzer Algorithm

The Putzer Algorithm, coded. This was further outlined in my blog post HERE While the intrinsic functions work awesome, certainly some better than this, I simply thought it was a good idea to get a feel for exactly how this works. The code is rather simple.

## The Mind Palace Program

This was further outlined in my blog post HERE but the basic idea is you associate images with an idea you want to remember, imprint the idea on a picture if you will. Head over to the blog if you don't understand.

Upcoming: Digitizing the book *Elementary Calculus* by Woods & Bailey