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dc.contributor.authorKumar, Pankajen_US
dc.date.accessioned2016-08-24T20:00:20Z
dc.date.available2016-08-24T20:00:20Z
dc.date.created2016en_US
dc.date.issued2016en_US
dc.identifier.urihttps://repository.tcu.edu/handle/116099117/11279
dc.descriptionPh. D.Texas Christian University2016en_US
dc.descriptionDepartment of Physics and Astronomy; advisor, Bruce N. Miller.en_US
dc.descriptionIncludes bibliographical references.en_US
dc.descriptionGravitational 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.en_US
dc.descriptionDescription based on online resource; title from PDF title page (viewed February 20, 2017).en_US
dc.format.extent1 online resource (xx, 225 pages) :en_US
dc.format.mediumFormat: Onlineen_US
dc.language.isoengen_US
dc.relation.ispartofTexas Christian University dissertationen_US
dc.relation.ispartofUMI thesis.en_US
dc.relation.ispartofTexas Christian University dissertation.en_US
dc.subject.lcshChaotic behavior in systems.en_US
dc.subject.lcshDynamics.en_US
dc.subject.lcshLyapunov exponents.en_US
dc.titleChaotic dynamics and thermodynamics of periodic systems with long-range forces /en_US
dc.typeTexten_US
local.academicunitDepartment of Physics and Astronomy
local.subjectareaPhysics and Astronomy


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