Other Applied Mathematics Commons^™

Mathematical Model Of Graphene, Douglas M. Sanor

Williams Honors College, Honors Research Projects

Graphene, a single-atom-thick layer of carbon arranged in a hexagonal lattice, exhibits exceptional mechanical, electrical, and thermal properties that make it a promising material for a wide range of engineering applications. This paper presents a mathematical framework for modeling the mechanical behavior of graphene, with a focus on atomistic-to-continuum approaches. We begin with a onedimensional Frenkel-Kontorova model that represents graphene as a discrete chain of particles interacting with both their nearest neighbors through harmonic spring potentials and an underlying substrate through van der Waals forces. Numerical simulations of this discrete model demonstrate the commensurate-toincommensurate phase transition, revealing how geometric mismatch …

Characterizing Probabilities Of Outbreaks Of Dengue In Central Argentina Using A Temperature-Dependent Stochastic Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue virus (DENV) causes over 390 million infections and around 40,000 deaths worldwide each year. DENV is primarily transmitted by the mosquito Aedes aegypti, and both the life cycle of these mosquitoes and dengue transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks of dengue can only occur due to new introductions of DENV from other regions. Due to the relationships between temperature and dengue, the risk of outbreak changes throughout the year.

We develop a stochastic model including temperature-dependent mosquito life history traits and transmission-related parameters. …

From Branches To Fibers - Investigating F-Actin Networks With Biochemistry And Mathematical Modeling, Melissa A. Riddle

Senior Honors Projects, 2020-current

F-actin networks have different structures throughout the cell depending on their location or mechanical role. For example, at the leading edge of a migrating cell, F-actin is organized in a region called the lamellipodia as a branched network responsible for pushing the membrane outwards. Behind the lamellipodia is a lamellar actin network where focal adhesions and stress fibers originate, and then within the cell cortex, actin is arranged in a gel-like network. Stress fibers are an important organization of F-actin and how they arise from either the branched lamellipodia network or the gel-like cortex network is poorly understood. Our approach …

A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez

Honors Program: Senior Projects (Public)

Crime is often regarded as nonsensical, impulsive, and irrational. These conjectures are pointed, though conversation about the pros and cons of crime does not happen often. People point to harsh fines, jail times, and life restrictions as their reason for judgement, stating that the trade-offs are far too unbalanced to participate in illicit activity. Yet, everyday people commit small crimes, sometimes based on hedonistic desires, other times based on a rational thought process.

Speeding seems to be one of those that almost all people commit at least once during their life. Our work hopes to make an incremental improvement on …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty

Honors College Theses

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete …