Mathematical Sciences 2005 Completed MQPs
Almost Orthogonal Vectors in Euclidean Space
Student:
Cheung, Matthew Gein
Advisor:
MARTIN, W. J. (MA)
This project includes an exposition of the paper "Spherical Codes and Designs" and it's applications to our problem, almost orthogonal vectors. Almost orthogonal vectors can be thought of as lines through the origin that have pair wise angles close to 90 degrees. Growth rates and bounds for the cardinality of sets of almost orthogonal vectors for a tolerance and dimension of the space were investigated. Propagation techniques were developed to fill out a table initially populated by known lower bounds.
Optimization Fractal Antennas
Student:
Cordes, Brian Gregory
Advisor:
YAKOVLEV, V. V. (MA)
Sponsor:
Air Force Research Laboratory
The Sierpinski Carpet fractal antenna is studied in terms of optimality. A 3D full-wave FDTD model of the structure is developed and used in conjunction with a neural network optimization procedure. An original engineering design based on the idea of a broken fractal geometry is suggested. The modified fractal antennas are shown to have the capability of being optimized, in terms of its input impedance, in a narrow frequency band.
Wilson Language Center
Students:
Billings, Justin Mark
Gomes, Egas Matthew
Maglione, Anthony David
Szerlag, Thomas M.
Advisor:
PETRUCCELLI, J. D. (MA)
Sponsor:
Millyard Industrial Properties
This major qualifying project was sponsored by Daniel Prouty of Millyard Industrial Properties of Oxford, Massachusetts. This project aims to provide a comprehensive understanding of the design and construction process by closely following the real development of the world headquarters of the Wilson Language Training Corporation in Oxford, Massachusetts. The project focuses on the initial construction design phases of site procurement, layout and design, and concludes with a comprehensive design of the steel framework and foundation of the forty-six thousand square foot facility.
Modeling glioblastoma Multiforme
Student:
Voutila, David Raymond
Advisor:
WEEKES, S. L. (MA)
Glioblastoma multiforme (GBM), a highly lethal brain cancer, accounts for over 30 percent of brain tumors in adult patients. Patients typically survive only 12-18 months after diagnosis. Our model describes the dynamics of GBM via a system of partial differential equations for tumor cells, nutrients, toxins, and mechanical resistance of brain matter. Using a 2D conservative Alternating Direction Implicit scheme, we numerically approximate the solution to our model and implement it in C for simulation on a parallel computer.
SBV Compactness
Student:
Howard, Thomas T.
Advisor:
LARSEN, C. J. (MA)
A compactness result is proved for SBV, the space of special functions of bounded variation. It is shown that a sequence of functions of SBV on an open, bounded domain with Lipschitz boundary with three quantities bounded will have a subsequence that weakly converges in BV to a function that is also in SBV. This theorem has implications for the existence of desired solutions in problems from the calculus of variations.
Atmospheric Gravity Waves Over Topography
Student:
Fichter, Kevin David
Advisor:
HUMI, M. (MA)
This project examined the theory behind gravity wave analysis and derived methods for detecting the presense of gravity waves from experimental data. To this end we used the Taylor-Goldstein equation and data gathered from the French Alps as part of an international campaign to detect and analyze gravotu waves gemerated by topography. We were able to relate the experimental and expected values of the wavelength and frequency of the gravity waves using a fluid dynamics model.
Volatility Costs in Assigned Risk Plans
Students:
Bui, Vonda Elizabeth
Yu, Ying Fang
Advisor:
HEINRICHER, A. C. (MA)
This project studied the new assigned risk plan for Massachusetts automobile insurance. The current method is a simple lottery in which each company's voluntary market share determines its probability of receiving the next high-risk driver. Results show that a dynamic method that adjusts assignment probabilities according to each company's current residual market share can reduce volatility costs by 50% for all insurance companies in the state.
Computer Modeling of Cell Motility
Students:
Fung, Pui Kwan
Govonlu, David C.
Advisor:
LUI, R. Y. (MA)
The study of amoeboid movement in crawling cells has been a wide topic of interest in the field of cell biology. This project focuses on the development of a computer program that simulates the steps of cell crawling. A statisitical analysis of the variables used in the progrram helps to provide a better understanding of the underlying factors behind amoeboid movement. This provides insight into what accounts for the various shapes and behaviors seen among crawling cells.
Winkler Percolations - A Computational Analysis
Students:
Gronlund, Jason AlanLarsen, John Joseph
Advisor:
SERVATIUS, B. (MA)
Winkler percolations, also known as coordinate percolations, are digraphs generated by random 01-sequences. The percolation's nature is determined by the frequency of 1's in the sequences, governed by a fixed probability p of occurrence. An open question is at what p is the completeness of the percolation no longer ensured. We look into this question using a combinatorial study of small finite examples, and the self-similarity of this model is anaylzed using methods of renormalization group theory.
Math & Phys Analysis of Circuit Jitter
Students:
Coppock, Wayne Ronald
Philbrook, Colin Richard
Advisor:
MARTIN, W. J. (MA)
Sponsor:
General Dynamics C4 Systems
In this paper analysis of jitter is conducted to determine its suitability for use as an entropy source for a true random number generator. Efforts are taken to isolate and quantify jitter in ring oscillator circuits and to understand its relationship to design specifications. The accumulation of jitter via various methods is also investigated to determine whether there is an optimal accumulation technique for sampling the uncertainty of jitter events. Mathematical techniques are used to analyze the accumulation process and an attempt at modeling a signal with jitter is made. The physical properties responsible for the noise that causes jitter are also briefly investigated.
Bifurcations in Rayleigh-Benard Convection
Student:
LeRay, David James
Advisor:
WALKER, H. F. (MA)
Rayleigh-Bernard convection is a particular type of thermal convection problem. The first step in the project was writing computer code to find computational solutions, using algorithms from numerical analysis. Analytical results from the literature were used to verify these computations. Linear stability analysis was then used to get an overview of system behavior. Finally, bifurcations were tracked computationally to develop an understanding of the system as the two main system prameters, Rayleigh number and aspect-ratio, were varied.
Estimating Disability Incidence
Students:
D'Onofrio, Michael David
Lescoe, James Terrence
Simone, Jeffrey Shawn
Twarog, Marek
Advisor:
ABRAHAM, J. P. (MA)
Sponsor:
John Hancock Life Insurance Company
This paper uses data from the 1999 NLTCS and NHIS surveys to compute Long Term Care (LTC) prevalence rates. We develop several triggers, evaluate a test of cognitive ability, and compute prevalence rates for each trigger. We develop a model to compute LTC incidence rates based on the prevalence data. We find that incidence is a strictly increasing function of age and that there is a sharp increase in incidence rates starting at age ninety.
Last modified: December 06, 2006 15:21:32