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Les travaux présentés dans cette thèse portent sur la classification et l'analyse des manipulateurs 3R à axes orthogonaux. Le but final est de proposer une classification exhaustive de ces manipulateurs selon leur topologie d'espace de travail. On définit une topologie d'espace de travail par un couple (nombre de points cusps, nombre de nœuds). Ces points particuliers apparaissent sur les surfaces de singularités. Notre étude se décompose en 4 parties. La première partie de ce travail est consacrée à une étude bibliographique de quelques notions liées à la cinématique et à la conception des manipulateurs sériels et plus particulièrement leurs singularités. Dans la deuxième partie de ce travail, nous établissons une classification exhaustive de toutes les topologies d'espace de travail d'une famille de manipulateurs 3R à axes orthogonaux telle que r3 = 0 en fonction des paramètres de DHm. Pour chaque topologie d'espace de travail, nous donnons toutes les propriétés cinématiques décrites dans la première partie. Une nouvelle condition nécessaire et suffisante pour qu'un manipulateur soit cuspidal (peut changer de posture sans franchir une singularité) a été établie sous forme d'une relation entre les paramètres de DHm. La troisième partie a été consacrée à étendre la classification réalisée dans la partie précédente à une famille de manipulateurs orthogonaux plus large (r3 <> 0). La quatrième partie a été consacrée à l'analyse des manipulateurs selon deux critères de performance. Le premier est relatif aux conditionnements maximum et moyen. Le second permet de calculer les proportions des régions à 2 et 4 solutions au MGI ainsi que tout le domaine accessible par rapport à une sphère centrée sur l'origine et englobant l'espace de travail. Les résultats proposés dans ce travail constituent une aide intéressante pour la conception de mécanismes innovants. En effet, en utilisant ce travail, nous pouvons choisir la topologie d'espace de travail la mieux adaptée à la tâche souhaitée. Nous venons ensuite ajuster les paramètres de DHm du manipulateur satisfaisant les critères proposés.

The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.

In this study we investigate the flow of a Boussinesq fluid contained in a rotating, differentially heated spherical shell. Previous work, on the spherical shell of Boussinesq fluid, differentially heated the shell by prescribing temperature on the inner boundary of the shell, setting the temperature deviation from the reference temperature to vary proportionally with -cos 20, from the equator to the pole. We change the model to include an energy balance equation at the earth's surface, which incorporates latitudinal solar radiation distribution and ice-albedo feedback mechanism with moving ice boundary. For the fluid velocity, on the inner boundary, two conditions are considered: stress-free and no-slip. However, the model under consideration contains only simple representations of a small number of climate variables and thus is not a climate model per se but rather a tool to aid in understanding how changes in these variables may affect our planet's climate. The solution of the model is followed as the differential heating is changed, using the pseudo arc-length continuation method, which is a reliable method that can successfully follow a solution curve even at a turning point. Our main result is in regards to hysteresis phenomenon that is associated with transition from one to multiple convective cells, in a dfferentially heated, co-rotating spherical shell. In particular, we find that hysteresis can be observed without transition from one to multiple convective cells. Another important observation is that the transition to multiple convective cells is significantly suppressed altogether, in the case of stress-free boundary conditions on the fluid velocity. Also, the results of this study will be related to our present-day climate. / UOIT

The present study investigates longshore sediment transport for a variety of bathymetric and wave conditions using the National Oceanic Partnership Program (NOPP) NearCoM Model. The model is used to determine the effects of wave shape and bathymetry changes on the resulting longshore sediment transport. The wave drivers, REF/DIF 1 and REF/DIF S, are used to assess the effects of monochromatic and spectral waves on longshore sediment transport, respectively. SHORECIRC is used as the circulation module and four different sediment transport models are used. Longshore transport comparisons are made with and without skewed orbital velocities in the shear stress and current velocities. It is found that the addition of skewed orbital velocities in shear stress and transport formulations increases longshore sediment transport by increasing time-varying effective shear stress. The addition of skewed orbital velocities greatly increases the transport due to advection by waves. The localized longshore sediment transport is calculated using a generic physics based method and formulas by Bagnold, Bailard, and Bowen, Watanabe, and Ribberink. The transport results for each scenario are compared to the total transport CERC, Kamphuis, and GENESIS formulas. The bathymetries tested include an equilibrium beach profile, cusped beach profiles, and barred beach profiles with different bar locations. The longshore transport on an equilibrium beach profile is modeled for a 0.2 mm and 0.4 mm grain size and transport is compared to the CERC formula. The longshore sediment transport for d=0.2 mm is larger than d=0.4 mm when wave power is small, but as wave power increases the transport for the larger grain size dominates. The transport is also affected by the addition of cusps and bars on an equilibrium beach profile. The barred beach is modified to compare transport between waves breaking at the bar, before the bar, and after the bar. The features affect the transport when the wave powers are small, but as wave heights increase the cusp and bar features induce little change on the longshore sediment transport.

In this work, we have implemented an orbital-free density functional theory (OF-DFT) solver using the finite element method. In OF-DFT, the total ground state energy is minimized directly with respect to the electron density, rather than via orbitals like in the standard Kohn-Sham approach. For this to be possible, one needs an approximation of a universal density functional of the non-interacting kinetic energy. Presently available approximations allow for computation with very low computational expense, but which gives inaccurate energies. A stable OF-DFT code can be used as a testbed for new kinetic energy functionals and provide the necessary tool for investigating the accuracy of OF-DFT calculations for complex systems. We have implemented Thomas-Fermi theory with and without nuclear cusp condition, as well as additional exchange terms of Dirac and Amaldi. The program uses an extended version of the steepest descent in order to find the minimizing density in the variational principle. Our results include convergence tests for the hydrogen atom, weak bonding in the H2 molecule, and accurate results for the lightest noble gases (He, Ne, Ar). For heavier atoms (Kr, Xe, Rn), the results are less accurate. In addition, we consider hydrogen in the simple cubic structure without the cusp condition, which is a first attempt to use the code for periodic systems. Lastly, we discuss some possible improvements for the iterative process towards the minimizing density, as well as other possible directions for future development.

Hypersonic vehicles generate shocks that can heat the air sufficiently to partially ionize the air and create an electrically conducting plasma that can be studied using the equations of single fluid magnetohydrodynamics (MHD). Introducing strong applied magnetic and electric fields into the flow could have beneficial effects such as reducing heat damage, providing a sort of MHD parachute, and generating electric power or thrust in the vehicle. The Low Diffusion E-CUSP (LDE) scheme with a fifth order WENO scheme has recently been developed by Zha et al. [1, 2]. The purpose of this work is to incorporate the low magnetic Reynolds number MHD model and the thermodynamics of high temperature air to the above CFD algorithm so that it can be used to simulate hypersonic flows with MHD effects. In this work we compare results treating air as chemically frozen, neglecting all high temperature real gas effects with results obtained treating the air as a real gas in thermodynamic equilibrium, whose thermodynamic properties are changed by the high temperature. The hypersonic flows at high altitudes considered in this study have low Reynolds numbers. The Reynolds numbers range from about 2000 to 5000 for Mach 6 flows and reach up to 1200000 for Mach 15 flows. Thus, the flows are treated as laminar for the former cases and as turbulent for the latter using the Baldwin-Lomax turbulence model.

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No description available.