dc.contributor.advisor | Miller, Bruce N. | |
dc.contributor.author | Kumar, Pankaj | en_US |
dc.date.accessioned | 2016-08-24T20:00:20Z | |
dc.date.available | 2016-08-24T20:00:20Z | |
dc.date.created | 2016 | en_US |
dc.date.issued | 2016 | en_US |
dc.identifier | cat-002934912 | |
dc.identifier.uri | https://repository.tcu.edu/handle/116099117/11279 | |
dc.description.abstract | Gravitational and electromagnetic interactions form the backbone of our theoretical understanding of the universe. While, in general, such interactions are analytically inexpressible for three-dimensional infinite systems, one-dimensional modeling allows one to treat the long-range forces exactly. Not only are one-dimensional systems of profound intrinsic interest, physicists often rely on one-dimensional models as a starting point in the analysis of their more complicated higher-dimensional counterparts. In the analysis of large systems considered in cosmology and plasma physics, periodic boundary conditions are a natural choice and have been utilized in the study of one dimensional Coulombic and gravitational systems.^Such studies often employ numerical simulations to validate the theoretical predictions, and in cases where theoretical relations have not been mathematically formulated, numerical simulations serve as a powerful method in characterizing the systems physical properties. In this dissertation, analytic techniques are formulated to express the exact phase-space dynamics of spatially-periodic one-dimensional Coulombic and gravitational systems. Closed-form versions of the Hamiltonian and the electric field are derived for single-component and two-component Coulombic systems, placing the two on the same footing as the gravitational counterpart. Furthermore, it is demonstrated that a three-body variant of the spatially-periodic Coulombic or gravitational system may be reduced isomorphically to a periodic system of a single particle in a two-dimensional rhombic potential.^^The analytic results are utilized for developing and implementing efficient computational tools to study the dynamical and the thermodynamic properties of the systems without resorting to numerical approximations. Event-driven algorithms are devised to obtain Lyapunov spectra, radial distribution function, pressure, caloric curve, and Poincare surface of section through an N-body molecular-dynamics approach. The simulation results for the three-body systems show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. The results for the large versions of the single-component and two-component Coulombic systems show no clear-cut indication of a phase transition.^However, as predicted by the theoretical treatment, the simulated temperature dependencies of energy, pressure as well as Lyapunov exponent for the gravitational system indicate a phase transition and the critical temperature obtained in simulation agrees well with that from the theory. | |
dc.format.extent | 1 online resource (xx, 225 pages) : | en_US |
dc.format.medium | Format: Online | en_US |
dc.language.iso | eng | en_US |
dc.relation.ispartof | Texas Christian University dissertation | en_US |
dc.relation.ispartof | UMI thesis. | en_US |
dc.relation.ispartof | Texas Christian University dissertation. | en_US |
dc.subject.lcsh | Chaotic behavior in systems. | en_US |
dc.subject.lcsh | Dynamics. | en_US |
dc.subject.lcsh | Lyapunov exponents. | en_US |
dc.title | Chaotic dynamics and thermodynamics of periodic systems with long-range forces | en_US |
dc.type | Text | en_US |
etd.degree.department | Department of Physics and Astronomy | |
etd.degree.level | Doctoral | |
local.college | College of Science and Engineering | |
local.department | Physics and Astronomy | |
local.academicunit | Department of Physics and Astronomy | |
dc.type.genre | Dissertation | |
local.subjectarea | Physics and Astronomy | |
etd.degree.name | Doctor of Philosophy | |
etd.degree.grantor | Texas Christian University | |