In this paper, two projects have been undertaken. First, Workman's calculations have been checked to a higher degree of approximation to determine the accuracy of his method. Second, a new set of boundary conditions has been developed for obtaining solutions of the neutron diffusion equation which do not depend on the solution of the equation inside the detector.

The name Diploma thesis is "Benedictine Rule for Laymen or Becoming an Oblate". The main goal of this thesis is the presentation of benedictione spirituality as it is lived in common daily life not only among the walls of monastery. It focuses mainly on benedictine oblate laymen. It shows that the Rule created in the sixth centurty is not obsolete and provides guidelines for getting closer to God through everyday labor and prayer. It is divided into three parts which cover historical and spiritual aspects benedictine rule regarding oblates. The first part describes beginnings of monasticism and life of Saint Benedict. The second part describes history of oblates since their formation. The last part focuses on role of oblates in the church, their spirituality and their life in the world.

This dissertation presents several experimental methods that were devised to generate or manipulate quantized vortices in highly oblate dilute-gas Bose-Einstein condensates (BECs). Studies that involve single vortex dynamics, vortex-vortex interactions, and vortex-impurity interactions are essential in developing a deeper understanding of the nature of superfluidity and in particular, superfluid turbulence. In highly oblate systems, vortex dynamics have a two-dimensional (2D) nature and the resulting superfluid characteristics may be substantially different from those in three-dimensional (3D) superfluids. However, there have been remarkably few experimental studies of 2D vortex dynamics in superfluids. Therefore, to study 2D vortex dynamics and interactions, it is necessary to first develop experimental methods that can generate vortices and vortex distributions in nominally 2D systems, such as highly oblate BECs. Four main experiments are discussed in this dissertation. Two of these experiments generate multiple singly quantized vortices in a relatively stochastic manner leading to disordered vortex distributions. From these two vortex methods, the physics of high vorticity and highly disordered systems may be observed and studied in a highly oblate system. These methods may prove useful in studies of 2D quantum turbulence. The other two experiments involve newly developed techniques for controlled generation and manipulation of vortices. One of these methods creates multiply quantized pinned vortices with a control in the generated vorticity. The other method reliably creates a pair of singly quantized vortices of opposite circulation, whose positions can be easily manipulated after creation, such that they can be placed in any location within the BEC. The two techniques may be scalable to higher number of vortices and may prove useful in superfluid dynamics and vortex interactions that require repeatable vortex distributions. Taken together, these tools and methods may be applicable to many further studies of vortex physics in highly oblate BECs.

The generalized data which are presented in this thesis are the culmination of the determination of the foil depression factor using oblate spheroidal coordinates.

The cemeteries of the Stó:lõ of Shxwõwhámél and the Métis of Île-à-la-Crosse manifest aspects of kinship, local memorialisations, and identity. When analysed in reference to oral histories and spatial analysis, these cemeteries tell a story of space and Aboriginal values. Often in conflict with Oblate doctrine, these spaces nonetheless, also represent syncretism and Aboriginal agency. The Île-à-la-Crosse cemetery spatially pronounces stories of kinship, or wahkootowin, as discussed by Brenda Macdougall, as well as local memorialisations highlighting the local Ste. Mary adoration of the area. In Shxwõwhámél, kinship and status are represented in the cemeteries, as well as stories of burnings and hanging trees, underlining these values in the Stó:lõ community. Together these cemeteries tell similar stories of Oblate control, exclusion, and syncretism as well as Aboriginal identity and agency in their respective spaces of the dead.

The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis. We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity. For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case.

The existence of highest proton numbers at which the nuclear landscape cease to ex- ist, the end of the periodic table of elements and the limits of the existence of the nu- clei are some of the difficult questions to answer. To explore those questions, we in- vestigated hyperheavy nuclei (Z ≥ 126) using covariant density functional theory. We demonstrate the existence of three regions of spherical hyperheavy nuclei centered around (Z ∼ 138, N ∼ 230), (Z ∼ 156, N ∼ 310) and (Z ∼ 174, N ∼ 410). Also, we explored other properties of hyperheavy nuclei such as octupole deformation, alpha decay half lives, chemical potential, etc.

La thèse présente une étude numérique des instabilités de trajectoires de sphères, d'ellipsoïdes aplatis et de bulles en mouvement libre sous l'action de la gravité, de la poussée d'Archimède et des forces hydrodynamiques. Le chapitre sur les sphères reprend, complète et étend l'étude numérique de Jenny et al. (2004) en se concentrant sur la transition au chaos et sur les trajectoires chaotiques. Les résultats montrent la différence entre le scénario de transition au chaos de sphères de faible et de grand rapport de densité. Plusieurs grandeurs statistiques sont proposées afin de fournir une caractérisation quantitative des états chaotiques. Elle permettent de mettre en relation les états ordonnées et chaotiques et offrent une possibilité de comparaison objective de données aléatoires d'origine numérique ou expérimentale. L'étude, très extensive, du comportement d'ellipsoïdes aplatis établit le lien entre les disques et les sphères en faisant varier l'aplatissement des objets depuis infiniment plat jusqu'à presque sphérique. Les huit diagrammes d'état présentés permettent de comprendre l'effet de la forme des ellipsoïdes sur le scénario de transition. Le cas d'ellipsoïdes presque sphériques montre que de faibles imperfections de la forme peuvent avoir in impact significatif sur les trajectoires de sphères de très faible rapport de densité. Pour les bulles considérées dans la limite de rapport de densité et viscosité az/liquide nul, l'étude se concentre sur l'analyse de stabilité linéaire et aboutit à la courbe de stabilité marginale dans le plan des paramètres nombre de Bond – nombre de Galilée en tenant compte de la déformation des bulles au moment de la perte de leur axisymétrie. Plus deux décades de nombres de Bond, entre 0,1 et 20, sont couvertes. Les résultats montrent clairement l'effet de la déformation de la bulle sur le seuil de l'instabilité. / The thesis presents a numerical study of path instabilities for spheres, oblate spheroids and bubbles moving freely under the effect of the gravity, buoyancy and hydrodynamic forces. For spheres, the parametric study of Jenny et al. (2004) is revisited, improved end extended with a special focus on the chaotic states. The results reveal that the effect of density ratio responsible for different oblique oscillating states of low and high frequencies has a significant impact both on the onset of chaos and on the behavior of fully chaotic states. Several quantitative statistical quantities are proposed and shown to be relevant for establishing the relation between chaotic and ordered states and for an objective comparison of random data of numerical or experimental origin. The extensive study on freely moving spheroids establishes the link between disks and spheres by varying the aspect ratio of spheroids from infinitely flat to almost spherical. The state diagrams provided for eight different aspect ratios of spheroid show in detail how the transition scenario varies depending of the body shape. The investigation of almost spherical spheroids reveals the specificities of the dynamics of light imperfect spheres.For the deformable gas bubble in the limit of zero gas/liquid density and viscosity ratio, a marginal stability curve is given in the two-parameter plane of the Galileo and the Bond number indicating the critical Galileo numbers for the loss of stability of vertical trajectories. The numerical investigation covers more than two decades of Bond number going from 0.1 to 20. The results clearly show the crucial role of the surface deformation.

Multiple gravity assist (MGA) spacecraft trajectories can be difficult to find, an intractable problem to solve completely. However, these trajectories have enormous benefits for missions to challenging destinations such as outer planets and primitive bodies. Techniques are presented to aid in solving this problem with a global search tool and additional investigation into one particular proximity operations option is discussed. Explore is a global grid-search MGA trajectory pathsolving tool. An efficient sequential tree search eliminates v∞ discontinuities and prunes trajectories. Performance indices may be applied to further prune the search, with multiple objectives handled by allowing these indices to change between trajectory segments and by pruning with a Pareto-optimality ranking. The MGA search is extended to include deep space maneuvers (DSM), v∞ leveraging transfers (VILT) and low-thrust (LT) transfers. In addition, rendezvous or nπ sequences can patch the transfers together, enabling automatic augmentation of the MGA sequence. Details of VILT segments and nπ sequences are presented: A boundaryvalue problem (BVP) VILT formulation using a one-dimensional root-solve enables inclusion of an efficient class of maneuvers with runtime comparable to solving ballistic transfers. Importantly, the BVP VILT also allows the calculation of velocity-aligned apsidal maneuvers (VAM), including inter-body transfers and orbit insertion maneuvers. A method for automated inclusion of nπ transfers such as resonant returns and back-flip trajectories is introduced: a BVP is posed on the v∞ sphere and solved with one or more nπ transfers – which may additionally fulfill specified science objectives. The nπ sequence BVP is implemented within the broader search, combining nπ and other transfers in the same trajectory. To aid proximity operations around small bodies, analytical methods are used to investigate stability regions in the presence of significant solar radiation pressure (SRP) and body oblateness perturbations. The interactions of these perturbations allow for heliotropic orbits, a stable family of low-altitude orbits investigated in detail. A novel constrained double-averaging technique analytically determines inclined heliotropic orbits. This type of knowledge is uniquely valuable for small body missions where SRP and irregular body shape are very important and where target selection is often a part of the mission design.

The physical explanation for the existence of the galactic warp is one of the major research areas in Astronomy. People have proposed various theories but nobody has yet given a convincing explanation. Most of the spiral galaxies are observed to be warped which reveals that the galactic warp is a stable characteristic. In the theory of kinematic bending wave, warp is considered as a wave that is propagated through the galactic disk with a speed called pattern speed. If the pattern initially had straight line of nodes, according to bending wave theory, the warp would tend to wind up rapidly in the gravitational field of galactic disk. But still we observe warped galaxies in the sky. In the literature, it has been claimed that the winding problem of galactic warp may be solved by incorporating the effect of gravitational field of the dark matter halo in which the galactic disk is embedded. Recently some works on the dynamics of galactic disk claim that the shape of the dark matter halo is pro late spheroid. In this thesis, the effect of the gravitational field of a prolate spheroidal dark matter halo with varying eccentricity to the galactic warp is calculated and discussed. Chapter1 gives the general introduction of the topics discussed in the following chapters. The structure of the spiral galaxy, their classifications, and the disk dynamics are discussed in the first few sections. One of the revolutionary concepts that emerged in the previous century was the existence of the dark matter. Presently tracing the mass distribution and the constituent particles of dark matter is one of the major research areas in theoretical and experimental physics. In this thesis, the effect of a particular type of mass distribution in dark matter halo on the warp is discussed in detail. In the next few sections, the following topics are discussed namely; how the concept of dark matter came into astrophysics, how to measure the total mass inside a given radius and what are the different distributions used for various purposes. A new theory called Modified Newtonian Mechanism was also proposed in the previous century as an alternative to the dark matter concept which is also discussed briefly. Kinematic bending wave theory and the winding problem of the galactic warp is also discussed in detail. In the last section a relation between the pattern speed of the warp and the shape of the dark matter halo is obtained. The calculation of the potential of a prolate spheroidal mass distribution with varying eccentricity is not done in any literature as we know. The calculation of the potential and the patten speed of prolate spheroidal mass distributions and of the galactic disk are described in chapter 2. The calculations of oblate spheroidal mass distribution are also discussed in this chapter but that is out of main theme. In chapter 3 we apply the equations obtained in the Chapter 2 to one simple toy model and to the Galaxy. The rotation curve and the pattern speed of a warp in the gravitational field of prolate spheroidal mass distribution of varying eccentricity are described. Usually the Milky Way disk is treated as an in infinitesimally thin disk but for our calculations the three dimensional but thin disk is used. The usually people use some approximation to calculate the potential due to galactic infinitesimal thin disk. The difference of the work from earlier works done by different people(with the approximation mentioned in above line) is also discussed in this Chapter. Chapter 4 discusses the summary of the entire work.