My favorite applied mathematics projects are linked here, mostly conducted in the early years of my Olin education when the introductory curriculum emphasised interdisciplinary activities and strong modelling skills. Application domains range from biology, and medicine to science and sports.  Synchronization of Chaotic Flows using Variable Replacement Nonlinear Dynamics and Chaos, Spring 2010 Remote communications often employ chaotic oscillators as sources of pseudo-randomness for encryption. In this work we discuss one method for achieving synchronized flows and study stability criteria necessary for alignment.  Image Encryption using 1D Chaotic Maps Nonlinear Dynamics and Chaos, Spring 2010 I investigate design considerations necessary for image encryption via chaotic maps, present a simple encryption procedure based on a modified logistic map, and highlight security vulnerabilities of that scheme.  Modelling Memory Recall with piecewise 1D chaotic maps Nonlinear Dynamics and Chaos, Spring 2010 Chaos is often implicated in brain functions like memory. In this work I demonstrate that piecewise 1D chaotic maps can be constructed to perform simple associative recall of information strings like telephone numbers (e.g. 867-5309). Estimating Genetic Mutation Rates Modern Biology, Fall 2007 I investigate different methods used by scientists to infer the rate of spontaneous DNA mutation. This was a bonus project for my biology course and resulted in a poster and a brief paper.  Modeling the U.S. Organ Donation System Interdisciplinary Contest in Modeling, March 2007 Team contest to model U.S. transplant network and diagnose improvements. Our paper won a Meritorious Winner designation.  Focal Length of an Electromagnetic Lens Vector Calculus and Electromagnetic Physics, Spring 2007 A study of physical and geometrical parameters that influence the focal length of an E-M lens, such as those used in electron microscopes.  Numerical Analysis of Stock Option Value using the Black-Scholes PDE Vector Calculus, Spring 2007 Analysis of the Black-Scholes model, including motivation of the theoretical model for stock option valuation, description on numerical implementation, and study of convergence and error against the closed-form solution.  Design and Optimization of an Aluminum Heat Sink with Rectangular Fins Modelling and Control, Spring 2007 Design competition in first-year course had students design and fabricate a heat sink out of a block of aluminum that had lowest possible specific heat conductivity. Our analytical solution scored at the top of the nearly 40 designs entered.  Analysis of Human Dynamics in the Caber Toss Calculus and Mechanics, Fall 2006 Team project developed and analysed governing equations for the act of tossing a caber (a Scottish highland sport). Numerical analysis revealed running speed as the most important factor for achieving a high-scoring toss. |
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