Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Entire DC Network
Nonlinear Dispersive Partial Differential Equations Of Physical Relevance With Applications To Vortex Dynamics, Robert Vangorder
Nonlinear Dispersive Partial Differential Equations Of Physical Relevance With Applications To Vortex Dynamics, Robert Vangorder
Electronic Theses and Dissertations
Nonlinear dispersive partial differential equations occur in a variety of areas within mathematical physics and engineering. We study several classes of such equations, including scalar complex partial differential equations, vector partial differential equations, and finally non-local integro-differential equations. For physically interesting families of these equations, we demonstrate the existence (and, when possible, stability) of specific solutions which are relevant for applications. While multiple application areas are considered, the primary application that runs through the work would be the nonlinear dynamics of vortex filaments under a variety of physical models. For instance, we are able to determine the structure and time …
On Hall Magnetohydrodynamics: X-Type Neutral Point And Parker Problem, Kyle Reger
On Hall Magnetohydrodynamics: X-Type Neutral Point And Parker Problem, Kyle Reger
Electronic Theses and Dissertations
The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, …
Solitary Wave Families In Two Non-Integrable Models Using Reversible Systems Theory, Jonathan Leto
Solitary Wave Families In Two Non-Integrable Models Using Reversible Systems Theory, Jonathan Leto
Electronic Theses and Dissertations
In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal …