Neste trabalho consideramos o problema de enumerar G-fibrados sobre variedades de dimensão baixa (menor ou igual a 3), em particular fibrados vetoriais sobre as ?spherical space forms? tridimensionais. É dada uma resposta completa para estas questões e na seção 5.1 são colocadas tabelas que explicitam os possíveis fibrados vetoriais sobre as ?spherical space forms?. Este tipo de problema é recorrente em topologia algébrica e por motivos dados pela teoria de homotopia, é preciso calcular certos invariantes algébricos com sistemas de coeficientes locais, o que torna o problema mais interessante. Mostramos ainda que sobre condições consideravelmente abrangentes no grupo estrutural G, os G-fibrados sobre variedades de dimensão menor ou igual a três podem ser enumerados de maneira efetiva / In this work we consider the problem of enumerating G-bundles over low dimensional manifolds (dimension · 3) and in particular vector bundles over the three dimensional ?spherical space forms?. We give a complete answer to these questions and in section 5.1 we give tables for the possible vector bundles over the ?spherical space forms?. We deal with the problem of enumerating vector bundles over a class of manifolds. This is a long standing classical problem in algebraic topology, and because of homotopy theoretical reasons, it implies calculations of algebraic invariants with local system of coefficients, and thus becomes a cumbersome target away from the trivial occurrences. Although, we show that, under reasonably wide assumptions on the structure group G, G-bundles over low (lower or equal to three) dimensional manifolds can be counted effectively

Neste trabalho consideramos o problema de enumerar G-fibrados sobre variedades de dimensão baixa (menor ou igual a 3), em particular fibrados vetoriais sobre as ?spherical space forms? tridimensionais. É dada uma resposta completa para estas questões e na seção 5.1 são colocadas tabelas que explicitam os possíveis fibrados vetoriais sobre as ?spherical space forms?. Este tipo de problema é recorrente em topologia algébrica e por motivos dados pela teoria de homotopia, é preciso calcular certos invariantes algébricos com sistemas de coeficientes locais, o que torna o problema mais interessante. Mostramos ainda que sobre condições consideravelmente abrangentes no grupo estrutural G, os G-fibrados sobre variedades de dimensão menor ou igual a três podem ser enumerados de maneira efetiva / In this work we consider the problem of enumerating G-bundles over low dimensional manifolds (dimension · 3) and in particular vector bundles over the three dimensional ?spherical space forms?. We give a complete answer to these questions and in section 5.1 we give tables for the possible vector bundles over the ?spherical space forms?. We deal with the problem of enumerating vector bundles over a class of manifolds. This is a long standing classical problem in algebraic topology, and because of homotopy theoretical reasons, it implies calculations of algebraic invariants with local system of coefficients, and thus becomes a cumbersome target away from the trivial occurrences. Although, we show that, under reasonably wide assumptions on the structure group G, G-bundles over low (lower or equal to three) dimensional manifolds can be counted effectively

I have developed a tiling interpretation of the q-binomial coefficients. The aim of this thesis is to apply this combinatorial interpretation to a variety of q-identities to provide straightforward combinatorial proofs. The range of identities I present include q-multinomial identities, alternating sum identities and congruences.

Ce travail de thèse est lié concerne l’étude de composants optoélectroniques à base de nouveaux matériaux semi-conducteurs, les nitrures de gallium (GaN) déposés sur silicium. Les défis qui nous attendent concernent essentiellement la qualité microstructurale des couches et la fabrication de composants fonctionnant à hautes fréquences avec des faibles pertes optiques. Durant ces recherches, il a été nécessaire d’évaluer les propriétés optiques et électro-optiques par la technique du couplage prisme, sur des configurations GaN/Si. Il a été démontré que les indices de réfraction du GaN restent relativement élevés (n0=2.285 à la longueur d’onde λ=1.5µm), assez comparables à ceux obtenus sur le substrat de référence, le saphir. Des analyses en température ont également permis de vérifier la stabilité des indices. Par contre, nous avons pu observer une augmentation des pertes de propagation optique, liées à la forte densité de dislocations dans la couche GaN. Une première démonstration des effets électro-optiques de type Pockels a pu être réalisée au cours de cette thèse. Pour une structure d’épaisseur 1µm, nous avons relevé des coefficients r13 de l’ordre de +1pm/V et r33 de +1.67 pm/V, soit 50% supérieurs à ceux du GaAs. L’ensemble de ces travaux doit permettre la conception de composants de type modulateurs et commutateurs optiques. / This research is related to the study of optoelectronic devices based on new gallium nitride semi-conductors (GaN) deposited on silicon. The aim concerns essentially the microstructural quality of the materials and the fabrication of components operating at high frequency with limited optical propagation loss. During this study, we have evaluated the optical properties as well as the electro-optic ones by prism coupling into GaN on Si. We have demonstrated that the refractive index of GaN remains relatively constant to a value of 2.285 at λ=1.5µm, comparable to the index reported for the reference structure, GaN/sapphire. The influence of temperature has been also investigated, showing a relative stability of the index. The increase of optical loss is observed as a consequence of the higher dislocation density in GaN deposited on Si. The investigation of electro-optic effect is proposed here: we report Pockels coefficients r13=+1pm/V and r33=+1.67pm/V: they are higher to 50% than those obtained in well-known GaAs semiconductors. This study will allows us to design and fabricate optical components as modulators and switches.

This thesis presents the static and dynamic performance data for a 5 pad tilting pad bearing in both the load-on-pad (LOP) and the load-between-pad (LBP) configurations over a variety of different loads and speeds. The bearing tested was an Orion Advantage with direct lubrication exhibiting these specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametrical clearance, 60.325 mm (2.375 in) pad length. Dynamic tests were performed over a range of frequencies to observe any frequency effects on the dynamic stfffnesses. It was found that under most test conditions the direct real part of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency. This frequency dependency is caused by pad inertia, pad flexibility, and fluid inertia. The observed frequency dependency can be accounted for with the addition of an added mass matrix to the conventional [K][C] matrix model to produce a frequency independent [K][C][M] model. This method eliminates the often debated question over whether a stability analysis should be performed at the running speed or at the first natural frequency. Substantially large added mass terms in the loaded direction were found that approached 60 kg. Some conditions for the LBP bearing exhibited unloaded direct mass coefficients that were at or near zero, which would lead to a frequency dependent [K][C] model to be used instead. The whirl frequency ratio was found to be zero at all test conditions. Static data were also recorded which included pad temperatures, attitude angle, eccentricity, static stiffness and power loss. Some cross coupling in the form of deviation from the loaded axis was evident from the locus plots; however, the cross coupled stiffness coefficients were found to be very small relative to the direct stiffness coefficients. Both static and dynamic experimental results were compared to theoretical predictions via a bulk flow analysis. Most parameters were modeled well including the static eccentricity e dynamic direct stiffness coefficients Kxx and Kyy, which were slightly over predicted. However, the direct damping coefficients Cxx and Cyy were significantly over predicted.

This thesis presents the static and dynamic performance data for a 5 pad tilting pad bearing in both the load-on-pad (LOP) and the load-between-pad (LBP) configurations over a variety of different loads and speeds. The bearing tested was an Orion Advantage with direct lubrication exhibiting these specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametrical clearance, 60.325 mm (2.375 in) pad length. Dynamic tests were performed over a range of frequencies to observe any frequency effects on the dynamic stfffnesses. It was found that under most test conditions the direct real part of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency. This frequency dependency is caused by pad inertia, pad flexibility, and fluid inertia. The observed frequency dependency can be accounted for with the addition of an added mass matrix to the conventional [K][C] matrix model to produce a frequency independent [K][C][M] model. This method eliminates the often debated question over whether a stability analysis should be performed at the running speed or at the first natural frequency. Substantially large added mass terms in the loaded direction were found that approached 60 kg. Some conditions for the LBP bearing exhibited unloaded direct mass coefficients that were at or near zero, which would lead to a frequency dependent [K][C] model to be used instead. The whirl frequency ratio was found to be zero at all test conditions. Static data were also recorded which included pad temperatures, attitude angle, eccentricity, static stiffness and power loss. Some cross coupling in the form of deviation from the loaded axis was evident from the locus plots; however, the cross coupled stiffness coefficients were found to be very small relative to the direct stiffness coefficients. Both static and dynamic experimental results were compared to theoretical predictions via a bulk flow analysis. Most parameters were modeled well including the static eccentricity e dynamic direct stiffness coefficients Kxx and Kyy, which were slightly over predicted. However, the direct damping coefficients Cxx and Cyy were significantly over predicted.

Rotor-bearing system characteristics, such as natural frequencies, mode shapes, stiffness and damping coefficients, are essential to diagnose and correct vibration problems during system operation. Of the above characteristics, accurate identification of bearing force parameters, i.e. stiffness and damping coefficients, is one of the most difficult to achieve. Field identification by imbalance response measurements is a simple and often reliable way to determine synchronous speed force coefficients. An enhanced method to estimate bearing support force coefficients in flexible rotor-bearing systems is detailed. The estimation is carried out from measurements obtained near bearing locations from two linearly independent imbalance tests. An earlier approach assumed rotordynamic measurements at the bearing locations, which is very difficult to realize in practice. The enhanced method relaxes this constraint and develops the procedure to estimate bearing coefficients from measurements near the bearing locations. An application of the method is presented for a test rotor mounted on two-lobe hydrodynamic bearings. Imbalance response measurements for various imbalance magnitudes are obtained near bearing locations and also at rotor mid-span. At shaft speeds around the bending critical speed, the displacements at the rotor mid-span are an order of magnitude larger than the shaft displacements at the bearing locations. The enhanced identification procedure renders satisfactory force coefficients in the rotational speed range between 1,000 rpm and 4,000 rpm. The amount of imbalance mass needed to conduct the tests and to obtain reliable shaft displacement measurements influences slightly the magnitude of the identified force coefficients. The effect of increasing the number of rotor sub-elements in the finite-element modeling of the shaft is noted. Sensitivity of the method and derived parameters to noise in the measurements is also quantified.

No description available.

This thesis provides experimental frequency dependent stiffness and damping coefficient results for a high-speed, lightly loaded, flexible-pivot tilting-pad bearing, with a load-on-pad configuration. Test conditions include four shaft speeds (6000, 9000, 13000 and 16000 rpm), and bearing unit loads from 172 kPa to 690 kPa. The results show that the bearing stiffness is a quadratic function of the frequency of vibration; hence their frequency dependency can be modeled by added-mass terms. The additional degrees of freedom introduced by the pads and the influence of the inertial forces generated in the fluid film account for this frequency dependency. The conventional frequency-dependent stiffness and damping model for tilting-pad bearings is extended with an added-mass matrix to account for the frequency dependency. This approach allows the description of the bearing dynamic characteristics with frequency-independent stiffness, damping and added-mass matrices. Experimental results are compared with predictions from the Reynolds equation and from a bulk-flow Navier-Stokes model. Both models produce good predictions of the stiffness and damping coefficients. However, results show that the bulk-flow model is more adequate for predicting the direct added-mass terms because it accounts for the fluid inertial forces. A bulk-flow solution of the Navier-Stokes equations that includes the effects of fluid inertia should be used to calculate the rotordynamic coefficients of a flexible-pivot tilting-bearing. Static performance measurement results are also detailed. Results include pad metal temperatures, eccentricity-ratios and attitude-angle as a function of bearing load, and estimated power losses.

No description available.