In this thesis we develop Bragg scattering as a tool for probing and manipulating ultra-cold atoms. Our approach is based on a mean-field treatment of degenerate quantum gases. Bose-Einstein condensates are described by the Gross-Pitaevskii equation and degenerate Fermi gases are described by the Bogoliubov-de-Gennes equations. Our work is presented in three inter-related topics. In Part I we investigate Bose-Einstein condensation in a time-averaged orbiting potential trap by deriving solitary-wave dynamical eigenstates of the system. We invoke the quadratic average approximation in which the dynamic effects of the time-dependent potential can be described simply, even when accounting for atomic collisions. By deriving the transformation to the translating frame, dynamical eigenstates of the system are defined and those states are solitary-wave solutions in the laboratory frame, with a particular circular centre-of-mass motion independent of the strength of the collisional interactions. Our treatment in the translating frame is more general than previous treatments that use the rotating frame to define system eigenstates, as the use of the rotating frame restricts eigenstates to those that are cylindrically symmetric about their centre of mass. In Part II we describe Bragg spectroscopy of a condensate with solitary-wave motion. Our approach is based on a momentum space two-bin approximation, derived by Blakie et al. [Journal of Physics B 33:3961, 2000] to describe Bragg scattering of a stationary condensate. To provide an analytic treatment of Bragg scattering of a solitary-wave condensate we use the translating frame, in which the time dependence of the system is described entirely by a time-dependent optical potential. We derive a simplified treatment of the two-bin approximation that provides a physical interpretation of the Bragg spectrum of a solitary-wave condensate. Our methods are applied to Bragg spectroscopy of a condensate in a time-averaged orbiting potential trap, which accelerates as a solitary wave as derived in Part I. The time-averaged orbiting potential trap system is ideal for testing our approximate analytic methods because the micromotion velocity is large compared to the condensate momentum width. In Part III we present a theoretical treatment of Bragg scattering of an ultra-cold Fermi gas. We give the first non-perturbative numerical calculations of the dynamic behaviour of a degenerate Fermi gas subjected to an optical Bragg grating. We observe first order Bragg scattering, familiar from Bragg scattering of stationary Bose-Einstein condensates, and at lower Bragg frequencies we predict scattering of Cooper pairs into a correlated spherical shell of atoms. Correlated-pair scattering is associated with formation of a grating in the pair potential. We give an analytic treatment of Bragg scattering of a homogeneous Fermi gas, and develop a model that reproduces the key features of the correlated-pair Bragg scattering. We discuss the effect of either a trapping potential or finite temperature on the correlated-pair Bragg scattering.

Synthèse générale des noyaux spiranniques Au cours de ce travail, nous avons développé une méthode générale permettant d'assembler rapidement les noyaux spiro[4,4+n]alcanones (5) et spiro[5,4+n]alcanones (6). Durant l'étape de condensation, les ß-cétocétals (4) et (7) ont été obtenus avec de bons rendements grâce à l'emploi de dichlorure de zinc comme acide de Lewis. Différentes bases ont été testées dans l'étape de spiroannélation. Les meilleurs résultats ont été obtenus en utilisant du tert-butanolate de potassium dans le THF en présence d'un équivalent d'eau. La sélectivité de notre méthodologie a également été examinée lors de la génération des composés spiranniques substitués (10), (11), (13) et (15). Durant cette étude, nous avons notamment montré que la condensation et la cyclisation sont complètement diastéréosélectives au départ des éthers d'énols silylés (12) et des orthoesters (2) et (3). Applications En utilisant notre séquence réactionnelle, nous avons synthétisé la spirocétone (18). La fonctionnalisation de ce dérivé spirannique (18), nous a conduit à l'intermédiaire (19) qui pourrait être ultérieurement utilisé pour la synthèse de produits naturels tel que (20), appartenant à la classe des spirovétivanes La spirodicétone (23) a été employée dans la synthèse total de l'Erythrodiène (24) et du Spirojatamol (25) par Fukumoto. Notre méthodologie nous a permis de générer cet intermédiaire clef (23) en seulement trois étapes.

It is well known that multivalent cations can cause DNA to condense from solution to form high-density nanometer scale particles. However, several fundamental questions concerning the phenomenon of DNA condensation remain unanswered. DNA condensation in vitro has been of interest for many years as a model of naturally occurring DNA packaging (e.g. chromatin, sperm head and virus capsid packing). More recently, DNA condensation has been of interest in optimizing artificial gene delivery, where packaging genes to an optimal size is essential to developing efficient uptake and delivery systems. The research presented in this dissertation provides an in depth biophysical study of the factors that control DNA condensate size and morphology. Millimolar changes in the ionic strength of the solution were found to alter the size of toroidal condensates. Variations in the order of addition of the counterions also significantly changed the size and morphology of the condensates. Studies were also performed to investigate the effects of static curvature and increased DNA flexibility on DNA condensation. These include the addition of static bending by sequence directed curvature, dynamic bending through protein-DNA interactions and reducing DNA persistence length by condensing single-stranded DNA. Several new models of DNA condensation are proposed based on the experimental data presented in this thesis.

This study presents continued development of the Nenes and Seinfeld (2003) cloud droplet activation parameterization. First, we expanded the formulation to i) allow for a lognormal representation of aerosol size distribution, and, ii) include a size-dependant mass transfer coefficient for the growth of water droplets to accommodate the effect of size (and potentially organic films) on the droplet growth rate. The performance of the new scheme is evaluated by comparing the parameterized cloud droplet number concentration with that of a detailed numerical activation cloud parcel model. The resulting modified parameterization robustly and closely tracks the parcel model simulations, even for low values of the accommodation coefficient (average error 4.11.3%). The modifications to include the effect of accommodation coefficient do not increase the computational cost but substantially improves the parameterization performance. This work offers a robust, computationally efficient and first-principles approach for directly linking complex chemical effects (e.g., surface tension depression, changes in water vapor accommodation, solute contribution from partial solubility) on aerosol activation within a global climate modeling framework.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 126-136). Available also in a digital version from Dissertation Abstracts.

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The present thesis is devoted to an analysis of the possibility of Bose condensates supporting persistent currents in the ring geometry. Our analysis is based on an approach developed by F. Bloch which focuses on the ground state energy of the condensate as a function of its angular momentum L. According to this approach, persistent currents are stable if the energy exhibits a local minimum at some nonzero angular momentum. We have used this approach for a single-species gas within a mean- eld approximation to show that persistent currents are stable at integral multiples of N*hbar, where N is the number of atoms in the system, provided a certain interaction parameter exceeds some critical value. These results are extended to a binary mixture of bosonic atoms and we show that the system is still capable of supporting persistent currents under certain conditions. Some of our conclusions contradict those appearing in the earlier literature. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2012-03-27 10:05:21.831