dc.contributor.advisor Miller, Bruce N. dc.contributor.author Reidl, Charles J. en_US dc.date.accessioned 2019-10-11T15:11:14Z dc.date.available 2019-10-11T15:11:14Z dc.date.created 1991 en_US dc.date.issued 1991 en_US dc.identifier aleph-533450 en_US dc.identifier Microfilm Diss. 571. en_US dc.identifier.uri https://repository.tcu.edu/handle/116099117/34212 dc.description.abstract The search for relaxation to equilibrium (thermalization) of one-dimensional, self-gravitating systems has been investigated via theory and computer simulation for the past three decades. The casual reader of these investigations may be easily confused by the abundance of contradictory conjectures that have appeared in the recent literature. These conjectures have been examined in this research and new statistical tools and procedures to test for equilibrium have been developed. This research examines the problem by simulating the evolution of large and small N systems, where N is the system population. For large N systems (N = 100) procedures including correlations in time, chi-square and central limit theorem statistics applied to Rybicki's (1971) equilibrium density functions, and ensemble averaging have been employed. For small N systems (3 $\leq$ N $\leq$ 20) the stability of selected periodic modes has been examined by calculating their Lyapunov characteristic numbers. For large N systems it may be concluded from this research that thermalization has never really been observed. A system may enter a state that mimics equilibrium but slowly drifts away from it. This state is referred to as "quasi-equilibrium" and has been shown to have long-term, weak correlations in positions and velocities. Systems with N $\leq$ 10 are definitely not ergodic as shown by the stability of selected periodic orbits. Stability appeared to decrease logarithmically with increasing N $\leq$ 10. For N $\geq$ 11 any perturbation caused instability in the periodic orbits. However, the failure of the Lyapunov characteristic numbers to converge to a single positive value from different modes for a given N suggests that the energy surface in phase space may be segmented. Thus, one-dimensional, self-gravitating systems may only be merely ergodic which would require a time t $\to$ $\infty$ for a system to explore its entire energy surface on the phase space. This would account for the fact that relaxation to equilibrium has never been seen. dc.format.extent ix, 123 leaves : illustrations en_US dc.format.medium Format: Print en_US dc.language.iso eng en_US dc.relation.ispartof Texas Christian University dissertation en_US dc.relation.ispartof AS38.R435 en_US dc.subject.lcsh Gravitation en_US dc.title Gravity in one dimension: the evolution of large and small N systems en_US dc.type Text en_US etd.degree.department Department of Physics etd.degree.level Doctoral local.college College of Science and Engineering local.department Physics and Astronomy local.academicunit Department of Physics dc.type.genre Dissertation local.subjectarea Physics and Astronomy dc.identifier.callnumber Main Stacks: AS38 .R435 (Regular Loan) dc.identifier.callnumber Special Collections: AS38 .R435 (Non-Circulating) etd.degree.name Doctor of Philosophy etd.degree.grantor Texas Christian University
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