Academic literature on the topic 'Two Dimensional Confined Geometry'

This thesis explores a variety of topics in two-dimensional arithmetic geometry, including the further development of I. Fesenko's adelic analysis and its relations with ramification theory, model-theoretic integration on valued fields, and Grothendieck duality on arithmetic surfaces. I. Fesenko's theories of integration and harmonic analysis for higher dimensional local fields are extended to an arbitrary valuation field F whose residue field is a local field; applications to local zeta integrals are considered. The integral is extended to F^n, where a linear change of variables formula is proved, yielding a translation-invariant integral on GL_n(F). Non-linear changes of variables and Fubini's theorem are then examined. An interesting example is presented in which imperfectness of a positive characteristic local field causes Fubini's theorem to unexpectedly fail. It is explained how the motivic integration theory of E. Hrushovski and D. Kazhdan can be modified to provide a model-theoretic approach to integration on two-dimensional local fields. The possible unification of this work with A. Abbes and T. Saito's ramification theory is explored. Relationships between Fubini's theorem, ramification theory, and Riemann-Hurwitz formulae are established in the setting of curves and surfaces over an algebraically closed field. A theory of residues for arithmetic surfaces is developed, and the reciprocity law around a point is established. The residue maps are used to explicitly construct the dualising sheaf of the surface.

Supersonic micronozzles operate in the unique viscosupersonic flow regime, characterized by large Mach numbers (M>1) and low Reynolds numbers (Re<1000). Past research has primarily focused on the design and analysis of converging-diverging de Laval nozzles; however, plug (i.e. centerbody) designs also have some promising characteristics that might make them amenable to microscale operation. In this study, the effects of plug geometry on plug micronozzle performance are examined for the Reynolds number range Re = 80-640 using 2D Navier-Stokes-based simulations. Nozzle plugs are shortened to reduce viscous losses via three techniques: one - truncation, two - the use of parabolic contours, and three - a geometric process involving scaling. Shortened nozzle are derived from a full length geometry designed for optimal isentropic performance. Expansion ratio (ε = 3.19 and 6.22) and shortened plug length (%L = 10-100%) are varied for the full Reynolds number range. The performance of plug nozzles is then compared to that of linear-walled nozzles for equal pressure ratios, Reynolds numbers, and expansion ratios. Linear-walled nozzle half-angle is optimized to to ensure plug nozzles are compared against the best-case linear-walled design. Results indicate that the full length plug nozzle delivers poor performance on the microscale, incurring excessive viscous losses. Plug performance is increased by shortening the nozzle plug, with the scaling technique providing the best performance. The benefit derived from reducing plug length depends upon the Reynolds number, with a 1-2% increase for high Reynolds numbers an up to 14% increase at the lowest Reynolds number examined. In comparison to Linear-walled nozzle, plug nozzles deliver superior performance when under-expanded, however, this trend reverses at low pressure ratios when the nozzles become over-expanded.

Since the discovery of conductance quantization within a nanostnucture, investigations have sought out causes to conductance fluctuations beyond the established plateaus. The focus of this work is to show the fundamental effects upon conductance due to longitudinal potentials and double quantum boxes when confined by hardwall boundaries. A theoretical model based upon a tight-binding recursive tureen's function methodology was modified to incorporate potential barrier variations. A qualitative evaluation, as well as, explanation of the model's results and limitations is discussed.<br>Department of Physics and Astronomy

This thesis presents numerical investigations of two-dimensional single-phase turbulent jets and bubbly mixing layers using Reynolds-Averaged Navier-Stokes (RANS) equations. The behavior of a turbulent jet confined in a channel depends on the Reynolds number and geometry of the channel which is given by the expansion ratio (channel width to jet thickness) and offset ratio (eccentricity of the jet entrance). Steady solutions to the RANS equations for a two-dimensional turbulent jet injected in the middle of a channel have been obtained. When no entrainment from the channel base is allowed, the flow is asymmetric for a wide range of expansion ratio at high Reynolds number. The jet attaches to one of the channel side walls. The attachment length increases linearly with the channel width for fixed value of Reynolds number. The attachment length is also found to be independent of the (turbulent) jet Reynolds number for fixed expansion ratio. By simulating half of the channel and imposing symmetry, we can construct a steady symmetric solution to the RANS equations. This implies that there are possibly two solutions to the steady RANS equations, one is symmetric but unstable, and the other solution is asymmetric (the jet attaches to one of the side walls) but stable. A symmetric solution is also obtained if entrainment from jet exit plane is permitted. Fearn et al. (Journal of Fluid Mechanics, vol. 121, 1990) studied the laminar problem, and showed that the flow asymmetry of a symmetric expansion arises at a symmetry-breaking bifurcation as the jet Reynolds number is increased from zero. In the present study the Reynolds number is high and the jet is turbulent. Therefore, a symmetry-breaking bifurcation parameter might be the level of entrainment or expansion ratio. The two-dimensional turbulent bubbly mixing layer, which is a multiphase problem, is investigated using RANS based models. Available experimental data show that the spreading rate of turbulent bubbly mixing layers is greater than that of the corresponding single phase flow. The presence of bubbles also increases the turbulence level. The global structure of the flow proved to be sensitive to the void fraction. The present RANS simulations predict this behavior, but different turbulence models give different spreading rates. There is a significant difference in turbulence kinetic energy between numerical predictions and experimental data. The models tested include k-ε, shear-stress transport (SST), and Reynolds stress transport (SSG) models. All tested turbulence models under predict the spreading rate of the bubbly mixing layer, even though they accurately predict the spreading rate for single phase flow. The best predictions are obtained by using SST model.<br>Master of Science

L’étude du déplacement par le courant électrique des parois de domaine magnétique a généré beaucoup d’intérêt depuis l’observation de leurs importantes vitesses de déplacement dans des multicouches ayant une asymétrie d’inversion verticale (SIA). Cet intérêt se justifie par leur fort potentiel pour de nouvelles applications à basse consommation d’énergie en mémoire cache ou mémoires centrale. L’inversion de symétrie (SIA) induit deux mécanismes dont l’action conjointe permet de déplacer efficacement les parois de domaines. Il s’agit d’une contribution énergétique chirale, appelée l’interaction Dzyaloshinskii-Moriya (DMI), et des couples de spin-orbite (SOT). Ce modèle reste incomplet vu qu’il n’explique pas plusieurs résultats expérimentaux. De plus, une contribution dissipative chirale appelée l’amortissement anisotrope, également induite par la SIA, a été proposée récemment et dont le rôle, sous courant, n’as pas encore été étudié.Le but de ce travail a été d’amener une connaissance détaillée des différentes interactions en jeu dans la dynamique des parois de domaine. Pour cela, j’ai étudié la propagation de parois sous courant dans une géométrie non colinéaire. Cette étude a été réalisée dans des systèmes ayant des SIA différentes (Pt/Co/Pt et Pt/Co/AlOx). Dans cette géométrie, j’ai observé l’asymétrie du déplacement qui illustre la compétition entre les contributions chirales d’énergie et d’amortissement dans des multicouches à faible SIA. Quant aux multicouches à forte SIA, l’asymétrie ne peut être expliquée par l’action conjointe de DMI et SOT même dans le régime à forte mobilité. Une des conséquences de ce type de déplacement est de contribuer à la déviation des bulles de skyrmion en mouvement. Nous avons appelé cet effet l’effet Hall extrinsèque des skyrmions.En mettant en évidence de nouveaux effets induits par SIA, les résultats de cette thèse contribuent à une meilleur compréhension des mécanismes intervenant dans les déplacements des parois et des skyrmions sous courant dans les multicouches magnétiques<br>The study of the current-induced magnetic domain walls motion has attracted a lot of interest since the report of their large velocities of motion in thin layers with structural inversion asymmetry (SIA). This interest comes from their high potential for low power consumption functionalities in cache and main memories applications. The SIA induces two mechanisms whose combined action allows to drive efficiently the domain walls. The two mechanisms are the chiral energy term, called the Dzyaloshinskii-Moriya interaction (DMI), and the spin-orbit torques (SOT). This model is still incomplete since it does not explain several experimental results. In addition, a chiral dissipation term called the chiral damping, also induced by SIA, has recently been proposed. However, its effect on current-induced domain wall motion has not been studied.The objective of this work was to bring a more detailed understanding of the interactions involved in the domain wall motion. To that end, I have studied the domain wall motion in a non-collinear geometry with respect to the current, in materials with different SIA (Pt/Co/Pt and Pt/Co/AlOx). This motion has been found to be asymmetric. It illustrates the interplay between chiral energy and chiral dissipation in current-induced domain wall motion in weak SIA materials. In large SIA materials, the DMI and SOT model, even in the flow regime of motion, cannot explain this asymmetry. I have also evidenced that the asymmetric non-collinear domain wall motion induces a well-defined deflection of the skyrmion bubbles. This is the first observation of the extrinsic skyrmion Hall effect.The results of this thesis contribute to the understanding of the physical mechanisms behind domain wall and skyrmion motion in ultrathin layers by evidencing supplementary effects from SIA

Convective heat transfer in a steady developing laminar flow in domains of complex geometry is investigated numerically using the finite difference method and orthogonal boundary-fitted coordinates. A Fortran code was developed and validated. The following cases involving complex flow domains were examined in detail; (1) The flow and heat transfer characteristics of Newtonian and power-law fluids in a two-dimensional duct fitted with transverse fins of triangular, semi-circular, and rectangular sections. The calculated velocity distribution is compared with experimental measurements made with a laser-Doppler anemometer. (2) The flow and heat transfer in a two-dimensional 90$ sp circ$ bend formed between two corrugated walls with variable corrugation angles. The results are compared with those obtained for a plain bend and a straight corrugated duct. (3) The flow and heat transfer under a submerged, confined slot jet impinging on planar, wavy, and semi-circular target surfaces. The containment surface was either perpendicular to the jet axis or inclined at a different angle to it.<br>The Nusselt number and friction factor dependence on the appropriately defined Reynolds number and domain geometry was examined; a number of correlations based on extensive numerical experiments are proposed for design calculations. The physical domains chosen in this study have potential applications in heat transfer augmentation and novel compact heat exchanger designs.