This thesis presents two-fluid simulations of forced magnetic reconnection with finite electron inertia in two and three dimensional periodic systems. Reconnection in the system is driven by a spatially localized forcing function, added to the ion...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
The auroral zone is a rich source of natural radio emissions that can be observed in space and at ground-level. By studying these waves, scientists can gain insight into the plasma processes that generate them and use the near-Earth space...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
A nocturnal activity pattern is central to almost all hypotheses on the adaptive origins of primates but this view has been challenged recently on the basis of variation in the cone opsin genes of nocturnal primates. The diversity among primates in...
The fluxes of radiation belt electrons are highly variable, due to a competition between various acceleration, loss, and transport processes. Studies of any of the processes are equally important. My study focuses on electron-EMIC (electromagnetic...
In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking n data points at...
The discovery of the Van Allen radiation belts in the 1958 was the first major discovery of the Space Age. There are two belts of energetic particles. The inner belt is very stable, but the outer belt is extremely variable, especially during...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
Whistler-mode chorus waves have recently drawn tremendous attention as an important mechanism for controlling the energetic electron flux in Earthâ€™s radiation belt. This dissertation aims to answer questions about whistler-mode chorus waves, such...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
The ionosphere is the primary source for heavy ions which are ubiquitous in the terrestrial magnetosphere. Low-altitude energization in the auroral ionosphere results in bulk heating and transverse acceleration of ions, which begin to upwell and/or...
The oculomotor system needs up-to-date information about eye position in order to make accurate saccades to stimuli in the environment. This thesis investigated how well the oculomotor system uses information about eye position to make a variety of...
Van Allen radiation belts -- Mathematical models. ; Magnetosphere -- Mathematical models. ; Magnetohydrodynamics -- Mathematical models.
The physics of geomagnetically-trapped radiation has been a topic of interest since the discovery of the Van Allen belts in 1958. As the energetic particles comprising these belts can pose a hazard to human activity in space, considerable effort...
Plasma instabilities. ; Ionospheric electron density. ; Ionosphere.
As a result of an unstable plasma stratification the nighttime equatorial ionosphere is subject to a variety of plasma instabilities known commonly as equatorial spread-F. In its fully developed form spread-F consists of large wedges of depleted...
Van Allen radiation belts -- Mathematical models. Electrons -- Diffusion -- Mathematical models. Magnetohydrodynamic waves -- Mathematical models.
It is becoming increasingly important to understand the dynamics of radiation belt energetic particles given their potentially hazardous effects on satellites and our ever-increasing dependence on those satellites. There is a need to determine...
Flexible fiber scopes are widely used in industry and medicine. Typical scopes are made using conventional optical components and order-packed flexible image bundles. The optical performance of a flexible scope is largely determined by that of the...