Thesis (M.S.)--University of Wisconsin--Madison, 1984. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 59-60).

Thesis (Ph.D.)--University of Tulsa, 1973. / Bibliography: leaves 67-68.

Thesis (Ph.D.)--University of Tulsa, 1971. / Bibliography: leaves 34-36.

Understanding complex population dynamics is critical for both basic and applied ecology. Analysis of genetic data has been promoted as a way to reconstruct recent non-equilibrium processes that influence the apportioning of genetic diversity among populations of organisms. In a structured-deme context, where individual populations exist as geographically distinct units, island biogeography theory and metapopulation genetics predict that the demographic processes of extinction, colonization, and migration will affect the magnitude and rate of genetic divergence between demes. New methods have been developed to attempt to detect the influence of non-equilibrium dynamics in structured populations. I challenged two of these methods: decomposed pairwise regression and allele frequency analyses, using simulations of genetic data from structured demes. I found that these methods suffer from a high type II error rate, or failure to reject the null hypothesis of mutation-migration-drift equilibrium for demes experiencing historical demographic events. In addition, island biogeography and metapopulation ecology predict that at equilibrium, some species in a patch will be recent colonists, as equilibrium indicates a balance between colonization of the patch and extinction from the patch. Recent colonists are unlikely to have reached population mutation-migration-drift equilibrium; hence a paradox exists between population and community level equilibrium. I used nuclear and mitochondrial genetic data from populations of two species of reptiles from the Turks and Caicos Islands, British West Indies to test for patterns of equilibrium vs. non-equilibrium. I found unexpected shallow genetic divergence in the Turks Island boa (Epicrates chrysogaster), indicating that this species likely existed as a panmictic population prior to the inundation of the Turks and Caicos Banks during the last glaciation. As the initial methods I tested using simulations proved unreliable, I used methods from phylogeography, landscape genetics, and island biogeography to detect significant non-equilibrium dynamics in the Turks and Caicos curly-tailed lizard (Leiocephalus psammodromus), finding evidence for high levels of biased gene flow. I propose that studies of genetic diversity on island archipelagos use tools from all three of these methods to evaluate empirical data in the context of equilibrium and the null hypotheses offered by island biogeography and population genetics theory. I frame the results both in the context of conservation and an understanding of equilibrium and non-equilibrium dynamics.

No description available.

In this thesis we examine methodologies for determining free energy differences (FEDs) of phases via Monte Carlo simulation. We identify and address three generic issues that arise in FED calculations; the choice of representation, the choice of estimator, and the choice of sampling strategy. In addition we discuss how the classical framework may be extended to take into account quantum effects. Key words: Phase Mapping, Phase Switch, Lattice Switch, Simulated Tempering, Multi-stage, Weighted Histogram Analysis Method, Fast Growth, Jarzynski method, Umbrella, Multicanonical, Path Integral Monte Carlo, Path Sampling, Multihamiltonian, fluctuation theorem.

We study non-equilibrium and strongly-correlated dynamics in two contexts. We begin by analysing quantum many-body systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highly-imbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a many-body quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highly-localised impurity interacting with a weakly-interacting trapped quasi low-dimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the self-trapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodically-trapped impurity through a quasi one-dimensional Bose gas. We show that placing the weakly-interacting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurity-Bose gas system exhibits phonon-induced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different strongly-correlated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a strongly-correlated system we use the powerful and near-exact time-evolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate non-equilibrium classical stochastic processes. We study its efficacy for a well-understood model of transport, the totally-asymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of sampling-based numerical methods for high variance observables we adapt and apply TEBD to simulate a path-dependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a one-dimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlo-based simulators of non-equilibrium stochastic processes.