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Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
In Memory of an Emily is a piece of creative nonfiction and a short film that together detail the author’s experience with mental illness in the collegiate environment. In its 45 pages, Jackman begins to detail the realities of living with depression, anxiety, and anorexia nervosa. The piece includes five sections of writing, including a preface and four portions describing freshman to senior year. Each section endeavors to explore simplistic and purposefully cliché events common in young adult/collegiate life and juxtapose the banal nature of these events with the experience of the mentally ill. Her story endeavors to explore the emotional truths of pain and suffering, revealing that beneath her tender façade lies a very different existence, one tangled in eating disorders, panic attacks, and overwhelming sadness. While maintaining a story-like quality traditional to creative non-fiction, Jackman ventures to warn with a cautionary tale of pathologizing abnormality and exploring the long lasting effects of childhood trauma. Weaving careful storytelling into an exploration of the mentally ill mind, Jackman keeps the reader both terrifyingly close and far away, whispering painful secrets and then desperately running away with the truth. She speaks frankly of all aspects of life, ranging from far more mundane events, such as break ups and college rejection letters, to complicated issues, such as the suicide of her grandfather and her admission into an eating disorder facility. The author attempts to establish a balanced rapport with the reader, recognizing the need to maintain distance and elicit emotion simultaneously. Jackman writes In Memory of an Emily as a heartbreaking but authentic tale, playing with stream of consciousness and paralyzing emotional description. She opens the door and invites the reader into her mind so as to share in the physical and emotional discomfort of the storyteller, but then promptly slams the door once inside.
ContributorsJackman, Emily Deprey (Author) / Soares, Rebecca (Thesis director) / Barca, Lisa (Committee member) / Economics Program in CLAS (Contributor) / Department of Psychology (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
The following creative project defends that, whether intentionally or not, mental illness and substance abuse are inevitably romanticized in young adult media and discusses the dangers of this romanticization. This project is divided into three parts. The first part consists of psychological evaluations of the main characters of two popular, contemporary forms of young adult media, Catcher in the Rye by J.D Salinger and Euphoria by Sam Levinson. These evaluations use textual evidence and the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) to determine what symptoms of psychopathology the characters appear to display. The second part consists of a self-written short story that is meant to accurately depict the life of a young adult struggling with mental illness and substance abuse. This story contains various aesthetic techniques borrowed from the two young adult media forms. The final part consists of an aesthetic statement which discusses in depth the aesthetic techniques employed within the short story, Quicksand by Anisha Mehra.
ContributorsMehra, Anisha (Author) / Cryer, Michael (Thesis director) / Cavanaugh Toft, Carolyn (Committee member) / Department of Psychology (Contributor) / Dean, The College of Liberal Arts and Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
In this study I hope to begin evaluating contemporary young adult literature that focuses on the bereavement of adolescents to see if the novels portray psychologically proven productive coping methods. I hope to initiate a conversation around how complicated bereavement is depicted within young adult literature that will establish a body of research that can be expanded into a further exploration into the young adult literature market. Within my study, I will conduct a psychological literature review on young adult complicated grief and coping mechanisms. Then I will create an instrument of analysis, a rubric/model to evaluate the fidelity of novels based on the research within the literature review. Finally, I will evaluate the depiction of productive adolescent grief coping mechanisms in the recently published novel All My Rage by Saaba Tahir based upon my literary model. Finally, I will write my own short story based upon my research and findings in analyzing the model, seeking to represent methods not seen in the literature or not discussed within research.
ContributorsBeadle, Ruth (Author) / Blasingame, James (Thesis director) / Irish, Jenny (Committee member) / Barrett, The Honors College (Contributor) / Department of English (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Art (Contributor) / School of International Letters and Cultures (Contributor)
Created2023-05
Description
This Creative Project was carried out in coordination with the capstone project, Around the Corner Imaging with Terahertz Waves. This capstone project deals with a system designed to implement Around the Corner, or Non Line-of-Sight (NLoS) Imaging. This document discusses the creation of a GUI using MATLAB to control the Terahertz Imaging system. The GUI was developed in response to a need for synchronization, ease of operation, easy parameter modification, and data management. Along the way, many design decisions were made ranging from choosing a software platform to determining how variables should be passed. These decisions and considerations are discussed in this document. The resulting GUI has measured up to the design criteria and will be able to be used by anyone wishing to use the Terahertz Imaging System for further research in the field of Around the Corner or NLoS Imaging.
ContributorsWood, Jacob Cannon (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This honors thesis explores and models the flow of air around a cylindrical arrow that is rotating as it moves through the air. This model represents the airflow around an archery arrow after it is released from the bow and rotates while it flies through the air. This situation is important in archery because an understanding of the airflow allows archers to predict the flight of the arrow. As a result, archers can improve their accuracy and ability to hit targets. However, not many computational fluid dynamic simulations modeling the airflow around a rotating archery arrow exist. This thesis attempts to further the understanding of the airflow around a rotating archery arrow by creating a mathematical model to numerically simulate the airflow around the arrow in the presence of this rotation. This thesis uses a linearized approximation of the Navier Stokes equations to model the airflow around the arrow and explains the reasoning for using this simplification of the fully nonlinear Navier Stokes equations. This thesis continues to describe the discretization of these linearized equations using the finite difference method and the boundary conditions used for these equations. A MATLAB code solves the resulting system of equations in order to obtain a numerical simulation of this airflow around the rotating arrow. The results of the simulation for each velocity component and the pressure distribution are displayed. This thesis then discusses the results of the simulation, and the MATLAB code is analyzed to verify the convergence of the solution. Appendix A includes the full MATLAB code used for the flow simulation. Finally, this thesis explains potential future research topics, ideas, and improvements to the code that can help further the understanding and create more realistic simulations of the airflow around a flying archery arrow.
ContributorsCholinski, Christopher John (Author) / Tang, Wenbo (Thesis director) / Herrmann, Marcus (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05