In this study I viewed video and corresponding transcripts of two students solving introductory combinatorial problems. Using an adapted version of Harel’s (2008) concepts of Result Pattern Generalization and Process Pattern Generalization, I analyzed the work done by the two students. Both students primarily worked through the problem How many...
In this thesis, we consider Maxwell's Equations and their numerical discretization using finite difference and finite element methods. We first describe Maxwell's equations in linear dielectrics and then present finite difference and finite element methods for this case. We then describe Maxwell's equations in linear metamaterials using the Lorentz and...
In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical...
Understanding the behavior of hydrophobic membranes is important for applications where separating a gas from a liquid-gas mixture is beneficial. For example, in-situ vapor extraction can be used in microscale heat sinks to improve heat transfer and flow stability. In this study, gas is experimentally evaluated flowing through flexible polytetrafluoroethylene...
In the 1954 John Nash [1] showed, through use of an iterative scheme of approximate embedding maps, that the sphere S² could be isometrically embedded into a ball of any radius by a C¹ map. In the 1980's M. Gromov [2] generalized Nash's work to the h-principal and convex integration....
This work presents a novel optimal control strategy for precision motion control of flexible ball-screw feed drives. Typically, ball-screw feed drive control relies on state feedback taken both from motor and the load sides. The controller designed in this thesis is based on the non-collocated framework, where all the feedback...
The importance of local versus distant forcing is studied for the wind driven intra- seasonal (30-120 day) sea level anomaly (SLA) variations along the west coast of India. Three locations on the continental slope are chosen to represent the west coast. Two more locations, one east of Sri-Lanka and another...
Basin-scale superinertial oceanic tides have been observed globally to resonate with the continental shelf (e.g., the Patagonian Shelf) with a clear theoretical framework. However, the response of the shelf to atmospheric tides – another basin-scale forcing – has not been discussed. This study explores this response using a prominent S2...
In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on the unit circle tightly associated with this group. In general, their fundamental domain enjoys what has since been...