Thesis (Ph.D.) - University of Queensland, 2004. / Includes bibliography.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 93-98).

Dissertation (Ph.D.) -- Worcester Polytechnic Institute. / Keywords: ladder approximation; inelastic process; Bethe-Salpeter; BSE; nucleon; scalar field; pion. Includes bibliographical references (p.161-163).

This thesis investigates some of the properties of a variational approximation to scalar field theories: a trial wavefunctional which has a gaussian form is used as a ground state ansatz for an interacting scalar field theory - the expectation value of the Hamiltonian in this state is then minimized. This we call the Gaussian Approximation; the resulting effective potential we follow others by calling the Gaussian Effective Potential (GEP). An equivalent but more general finite temperature formalism is then reviewed and used for the calculations of the GEP in this thesis. Two scalar field theories are described: ϕ⁴ theory in four dimensions (ϕ⁴₄) and ϕ⁶ theory in three dimensions (ϕ⁶₃). After showing what the Gaussian Approximation does in terms of Feynman diagrams, renormalized GEP's are calculated for both theories. Dimensional Regularization is used in the renormalization and this this is especially convenient for the GEP in ϕ⁶₃ theory because it becomes trivially renor-malizable. It is noted that ϕ⁶₃ loses its infrared asymptotic freedom in the Gaussian Approximation. Finally, it is shown how a finite temperature GEP can be calculated by finding low and high temperature expansions of the temperature terms in ϕ⁶₃ theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In the first part of the thesis, we carried out direct two-dimensional (2D) multipoint measurements of the velocity fields in a turbulent Rayleigh-Benard convection cell to study the properties of small-scale convective turbulence. The local homogeneity and isotropy of the velocity field are tested using a number of criteria and are found to hold to an excellent degree. The properties of velocity circulation Gammar are also studied. The results show that the circulation appears to be more effective to capture the effect of local anisotropy than the velocity field itself. The distribution of Gammar is found to depend on the scale r, reflecting strong intermittency. It is further found that velocity circulation has the same anomalous scaling exponents as the longitudinal and transverse structure functions for low-order moments (p ≲ 5). Whereas, for high-order moments (p ≳ 5), the anomalous scaling exponents for circulation are found to be systematically smaller than the scaling exponents of the longitudinal and transverse structure functions. / In the second part of the thesis, the simultaneous visualization of the temperature and velocity fields was used to study the properties of thermal plumes. Our visualization reveals the process of the morphological evolution between sheetlike and mushroomlike plumes, which were also quantified by the height dependence of plume numbers and of vorticity fluctuations. A direct connection between the heat transport and coherent structures, i.e. thermal plumes, was established, which shows that it is plume number that primarily determines the Nu-Ra scaling relation. Individual plumes were extracted and their statistical and geometric properties were studied. It is found that the log-normal distribution is universal for thermal plumes and the log-normal statistics may be used to model them. In addition, both our quantitative characteristic and direct 3D spatial visualizations indicate that the previously-believed sheetlike plumes should be reconsidered to be only one-dimensional structures. / In the third part of the thesis, the planar laser-induced fluorescence technique was induced to study the 2D passive scalar mixing in high-Schmidt-number buoyancy-driven turbulence. The passive scalar mixing evolution was studied and various geometric properties, such as shape complexity, fractal dimension and local curvature, were used to characterize the isoconcentration contours of the 2D passive scalar fields. It is found that when the flow gets more turbulent the shape of passive scalar packets becomes closer to a circular shape and the passive scalar mixing becomes more isotropic, indicating the increased mixing and stirring of the turbulent flow. / The objective of this thesis is to address the following three key issues in turbulent thermal convection, i.e. turbulent fluctuations in small scales, coherent structures and passive scalar mixing in buoyancy-driven turbulence. / Zhou, Quan = 對流熱湍流中能量級串, 相干結構和標量場混合的实验研究 / 周全. / Adviser: Ke-Qing Xia. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3576. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 103-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Zhou, Quan = Dui liu re tuan liu zhong neng liang ji chuan, xiang gan jie gou he biao liang chang hun he de shi yan yan jiu / Zhou Quan.

This thesis develops novel analytic models of scalar-tensor theories with quadratic coupling. In this framework, the coupling strength between scalar and matter is regulated in a way that allows the vacuum expectation value to vanish for low matter densities while becoming non-vanishingly large in the high-density regime. This results in significant deviations from the predictions of General Relativity in the strong-gravity regime. In astrophysics, we addressed the core-collapse supernova problem to account for the apparently missing energy required to explain the observed powerful explosions. We assumed a small, massless scalar gravitational field, thus allowing General Relativity to be recovered in the weak-gravity asymptotic limit. The non-trivial effects coming from the coupling function in the presence of a high-density field were analyzed at the instant of neutron star formation. Our results show that the scalar gravitational field evolves from a cosmological value to a new equilibrium via a Higgs-like mechanism. Additionally, the calculations associated with the gravitational binding energy shift and relevant relaxation timescale are explicitly shown. The full theory space of the model was also investigated for positive values of the coupling parameter. We studied a mechanism to address the stalled shock issue in core-collapse scenarios, which involved the application of sufficiently large positive values to the coupling parameter. Our results show that pulsating neutron stars act like optical cavities in which resonant scalar waves are parametrically amplified. It implies that the surface of a neutron star acts like an anti-phase reflector, releasing traveling scalar gravitational waves similar to an optical laser. In cosmology, the same framework was applied to a generic Friedman-Robertson-Walker universe involving general metric coupling and scalar potential functions. In cosmology, the same framework was applied to a generic Friedman-Robertson-Walker universe involving general metric coupling and scalar potential functions. We developed a mechanism which allowed the scalar field to be dynamically trapped, thus generating a potential capable of driving primordial inflation. Our results show that a trapped scalar field produces non-trivial dynamical consequences when applied to standard cosmology. Additionally, our analytic solutions for the generic inflationary behaviour, produce acceptable duration and e-foldings, thus recovering the Hubble parameter which is consistent with the present-day value. A feature of our cosmological model is that the universe can undergo several accelerating or decelerating phases, even though the scalar potential and metric coupling are monotonic functions overall. As this is important for the current dark energy problem, the quasi-static motion of the gravitational field induced by the scalar potential in the early universe, is investigated for a small value of the scalar field with normalized metric at the present time. Our results show that a variable Lambda Cold Dark Matter universe emerges naturally from the quadratic model.

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Errata inserted opposite p.177. / Bibliography: p. 173-177. / x, 177 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / The classical dynamical structure of cosomological models in which the matter content of the universe consists of a scalar field with arbitrary non-negative potential is analyzed in full. (abstract) / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1996?

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 72-77).