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You searched for +publisher:"University of Texas – Austin" +contributor:("Horton, Jr., Claude W"). One record found.

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1. Curry, Christopher Timothy. Transport in higher dimensional phase spaces.

Degree: PhD, Physics, 2016, University of Texas – Austin

We use a four dimensional symplectic mapping, the coupled cubic-quadratic map, to provide evidence of Arnol’d Diffusion in phase space. We use the method of frequency analysis for dynamical systems to demonstrate the existence of regular orbits, and show that these orbits enclose weakly chaotic orbits which escape in finite time around the tori. A new collocation method for frequency analysis is employed by adapting it to allow for higher precision results. Arbitrary precision numerics are used to obtain highly accurate orbits for long timescales, and the adapted frequency method is used to obtain highly accurate frequencies of the mapping. We review the method of frequency analysis, demonstrate its effectiveness and accuracy in determining frequencies and finding tori in simple systems and low-dimensional mappings, and extend the results to higher dimensions. In the four dimensional mapping, we find several regular orbits with irrational frequency ratios, indicating the existence of tori in the phase space, as well as interior orbits that escape around these tori. Advisors/Committee Members: Morrison, Philip J. (advisor), Horton, Jr., Claude W (committee member), Hazeltine, Richard (committee member), Matzner, Richard (committee member), Gamba, Irene (committee member).

Subjects/Keywords: Nonlinear dynamics; Symplectic mappings; Plasma physics; Hamiltonian; Computational; GPU; OpenCL; Data

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APA (6th Edition):

Curry, C. T. (2016). Transport in higher dimensional phase spaces. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/46396

Chicago Manual of Style (16th Edition):

Curry, Christopher Timothy. “Transport in higher dimensional phase spaces.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed November 29, 2020. http://hdl.handle.net/2152/46396.

MLA Handbook (7th Edition):

Curry, Christopher Timothy. “Transport in higher dimensional phase spaces.” 2016. Web. 29 Nov 2020.

Vancouver:

Curry CT. Transport in higher dimensional phase spaces. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2020 Nov 29]. Available from: http://hdl.handle.net/2152/46396.

Council of Science Editors:

Curry CT. Transport in higher dimensional phase spaces. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/46396

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