Full Record

New Search | Similar Records

Author
Title Transport in higher dimensional phase spaces
URL
Publication Date
Date Accessioned
Degree PhD
Discipline/Department Physics
Degree Level doctoral
University/Publisher University of Texas – Austin
Abstract 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.
Subjects/Keywords Nonlinear dynamics; Symplectic mappings; Plasma physics; Hamiltonian; Computational; GPU; OpenCL; Data
Contributors Morrison, Philip J. (advisor); Horton, Jr., Claude W (committee member); Hazeltine, Richard (committee member); Matzner, Richard (committee member); Gamba, Irene (committee member)
Country of Publication us
Record ID handle:2152/46396
Repository texas
Date Indexed 2020-10-15
Grantor The University of Texas at Austin
Note [department] Physics;

Sample Search Hits | Sample Images | Cited Works

…Chapter 5. Visualizing Tori in Higher Dimensions 105 5.1 Canonical Transformations and Higher Dimensional Symplectic Mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2 Projections of Higher Dimensional Data: Unwinding the…

…115 5.4 Discussion: Tori or Not Tori? . . . . . . . . . . . . . . . . . . . 119 Chapter 6. Numerical Explorations of Symplectic Mappings 124 6.1 Escape Times for the Coupled Cubic-Quadratic Mapping . . . 124 6.2 The Escape Mapping: A Fast Tool for…

…it is not uncommon to refer to any motion of a trajectory around existing tori in higher dimensional phase spaces as such, and di↵erent types of di↵usion [134, 135, 82] can occur. 1.5 Symplectic Mappings 1.5.1 Symplectic Maps and the…

…flow, and we may easily construct symplectic mappings by means of a generating function. In Chap. 3 we shall do just this. 1.5.2 The Standard Map The standard map, also known as the Chirikov-Taylor map, is one of the most important models in modern…

…the perturbation. Hence, the description is apt. 1.5.3 Higher Dimensional Symplectic Mappings Examples of higher dimensional symplectic mappings exist in the literature [29, 33, 30, 63, 139]. Here we introduce some phenomena of a higher…

…Escape Mappings . . . . . . . . 132 Chapter 7. Conclusion and Summary of Results Bibliography 140 145 viii List of Tables 1.1 Initial conditions for Figure 1.8 . . . . . . . . . . . . . . . . . 30 3.1 3.2 Initial conditions for Figure 3.8…

…analysis of a possible torus (II) . . . . . . . . . . . 89 A regular orbit for Form1 of the coupled map . . . . . . . . . 90 Shadowing plots for the uncoupled cubic and quadratic mappings 93 Shadowing plot for the coupled cubic and quadratic…

…mapping . 94 Shadowing of orbits . . . . . . . . . . . . . . . . . . . . . . . . 95 Shadowing plot for a regular orbit . . . . . . . . . . . . . . . . 96 Frequency shadowing for the coupled cubic-quadratic mappings (I)…

.