Physical Sciences and Mathematics Commons^™

Geometric Graph Theory And Wireless Sensor Networks, Deniz Sarioz

Dissertations, Theses, and Capstone Projects

In this work, we apply geometric and combinatorial methods to explore a variety of problems motivated by wireless sensor networks. Imagine sensors capable of communicating along straight lines except through obstacles like buildings or barriers, such that the communication network topology of the sensors is their visibility graph. Using a standard distributed algorithm, the sensors can build common knowledge of their network topology.

We first study the following inverse visibility problem: What positions of sensors and obstacles define the computed visibility graph, with fewest obstacles? This is the problem of finding a minimum obstacle representation of a graph. This minimum …

Optomechanics Of Cavity Driven Nanoparticles, Joel T. Rubin

Dissertations, Theses, and Capstone Projects

The subject of this thesis is the opto-mechanical interaction of a spherical high-Q microresonator and a subwavelength particle, which, at optical wavelengths, corresponds to a size on the order of nanometers. After a review of the basic theory of spherical resonators and multi-sphere scattering, the full self-consistent electromagnetic field of the coupled resonator-particle system is derived. The particle-induced frequency shift and broadening is calculated by examining the poles of the scattering coefficients of the resonator. The force exerted on the particle by the field is determined via the Maxwell stress tensor, and is found to be in general non-conservative. From …

Aperture Array Photonic Metamaterials: Theoretical Approaches, Numerical Techniques And A Novel Application, Eli Lansey

Dissertations, Theses, and Capstone Projects

Optical or photonic metamaterials that operate in the infrared and visible frequency regimes show tremendous promise for solving problems in renewable energy, infrared imaging, and telecommunications. However, many of the theoretical and simulation techniques used at lower frequencies are not applicable to this higher-frequency regime. Furthermore, technological and financial limitations of photonic metamaterial fabrication increases the importance of reliable theoretical models and computational techniques for predicting the optical response of photonic metamaterials.

This thesis focuses on aperture array metamaterials. That is, a rectangular, circular, or other shaped cavity or hole embedded in, or penetrating through a metal film. The research …

Reducibility, Degree Spectra, And Lowness In Algebraic Structures, Rebecca M. Steiner

Dissertations, Theses, and Capstone Projects

This dissertation addresses questions in computable structure theory, which is a branch of mathematical logic hybridizing computability theory and the study of familiar mathematical structures. We focus on algebraic structures, which are standard topics of discussion among model theorists. The structures examined here are fields, graphs, trees under a predecessor function, and Boolean algebras.

For a computable field F, the splitting set S_F of F is the set of polynomials in F[X] which factor over F, and the root set R_F of F is the set of polynomials in F[X] which have a root in F …