Date of Award
6-1-2015
Document Type
Open Access Thesis
Degree Name
Master of Science (MS)
Department
Physics, Applied
First Advisor
Bala Sundaram
Second Advisor
Maxim Olshanii
Third Advisor
Stephen Arnason
Abstract
A one-dimensional Hamiltonian system can be modeled and understood as a two-dimensional incompressible fluid in phase space. In this sense, the chaotic behavior of one-dimensional time dependent Hamiltonians corresponds to the mixing of two-dimensional fluids. Amey (2012) studied the characteristic values of one such system and found a scaling law governing them. We explain this scaling law as a diffusion process occurring in an elliptical region with very low eccentricity. We prove that for such a scaling law to occur, it is necessary for a vorticity field to be present. Furthermore, we show that a conformal mapping of an incompressible fluid in an annular region to an elliptical region explains these results for any positive eccentricity less than one.
Recommended Citation
Jauffred, Francisco J., "Hydrodynamic Analogues of Hamiltonian Systems" (2015). Graduate Masters Theses. 317.
https://scholarworks.umb.edu/masters_theses/317