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Rotordynamic and thermal analyses of compliant flexure pivot tilting pad gas bearings were performed. First, compliant flexure pivot tilting pad gas bearings with pad radial compliance (CFTPBs) were introduced and designed for high-speed oil-free micro turbomachinery. The pad radial compliance was for accommodation of large rotor growth at high speeds. Parametric studies on pivot offset, preload, and tilting stiffness were performed using non-linear orbit simulations and coast-down simulations for an optimum design. Second, coast-down tests for imbalance response and stability of typical rotor-bearing system with a rigid rotor and two CFTPBs designed from the above design studies were conducted over operating speeds up to 55 krpm. Prediction of synchronous rotordynamic responses was made in terms of critical speed for various imbalance modes by using a rotordynamic analysis software (XLTRC), combined with dynamic force coefficients from the perturbation analysis. For stability analyses, a generalized orbit simulation program was developed considering both the translational and angular rotor motions with two different bearings. Linear stability analyses for the conical vibration mode were also performed by using XLTRC and the perturbation analysis based on the Lund method. Predictions of whirl speed showed good agreement to the tests, but the estimated onset speed of instability appeared lower than the measured instability. Finally, a new thermo-hydrodynamic analysis model of a typical rotor-bearing system with CFTPBs was presented, accompanying linear perturbation analyses to investigate thermal effects on the rotordynamic performance. A numerical procedure was established for solving the generalized Reynolds equation, the 3-D energy equation, and the associated boundary conditions at the pad inlet flow and solid walls (rotor and pad) simultaneously. Parametric studies were conducted on nominal clearance and external load. Nominal clearance showed significant influence on temperature fields, and external load had uneven thermal effects among pads. Case studies with heat flux and temperature boundary conditions on the rotor end surface were performed to simulate various working conditions of the bearing. Large rotor thermal growth due to the high rotor temperature showed noticeable influence on rotordynamic performance by increasing direct stiffness and damping coefficients.

Four problems in non-equilibrium statistical physics are investigated: 1. The thermodynamics of single-photon gas; 2. Energy of the ground state in Multi-electron atoms; 3. Energy state of the H2 molecule; and 4. The Condensation behavior in N weakly interacting Boson gas. In the single-photon heat engine, we have derived the equation of state similar to that in classical ideal gas and applied it to construct the Carnot cycle with a single photon, and showed the Carnot efficiency in this single-photon heat engine. The energies of the ground state of multi-electron atoms are calculated using the modi ed Bohr model with a shell structure of the bound electrons. The di erential Schrodinger equation is simpli ed into the minimization problem of a simple energy functional, similar to the problem in dimensional scaling in the H-atom. For the C-atom, we got the ground state energy -37:82 eV with a relative error less than 6 %. The simplest molecular ion, H+ 2 , has been investigated by the quasi-classical method and two-center molecular orbit. Using the two-center molecular orbit derived from the exact treatment of the H+ 2 molecular ion problem, we can reduce the number of terms in wavefunction to get the binding energy of the H2 molecule, without using the conventional wavefunction with over-thousand terms. We get the binding energy for the H2 with Hylleraas correlation factor 1 + kr12 as 4:7eV, which is comparable to the experimental value of 4:74 eV. Condensation in the ground state of a weakly interacting Bose gas in equilibrium is investigated using a partial partition function in canonical ensemble. The recursive relation for the partition function developed for an ideal gas has been modi ed to be applicable in the interacting case, and the statistics of the occupation number in condensate states was examined. The well-known behavior of the Bose-Einstein Condensate for a weakly interacting Bose Gas are shown: Depletion of the condensate state, even at zero temperature, and a maximum uctuation near transition temperature. Furthermore, the use of the partition function in canonical ensemble leads to the smooth cross-over between low temperatures and higher temperatures, which has enlarged the applicable range of the Bogoliubov transformation. During the calculation, we also developed the formula to calculate the correlations among the excited states.

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Στην συγκεκριμένη διπλωματική εργασία ασχολήθηκα με το φωτοβαρυτικό περιορισμένο πρόβλημα των τριών σωμάτων.Εστίασα στις τρισδιάστατες περιοδικές κινήσεις και περιέγραψα αναλυτικά οικογένειες τρισδιάστατων περιοδικών τροχιών. / At this master I work on the photogravitational restricted 3-orbit problem. Espesially I focus on the 3-dimensional orbits solutions and I describe families of 3-dimensional orbits.

There is no apparent, dominant interaction in heavy transition metal oxides (TMO), especially in 5d-TMO, where all relevant interactions are of comparable energy scales, and therefore strongly compete. In particular, the spin-orbit interaction (SOI) strongly competes with the electron-lattice and on-site Coulomb interaction (U). Therefore, any tool that allows one to tune the relative strengths of SOI and U is expected to offer an opportunity for the discovery and study of novel materials. BaIrO3 is a magnetic insulator driven by SOI whereas the isostructural BaRuO3 is a paramagnetic metal. The contrasting ground states have been shown to result from the critical role of the strong SOI in the iridate. This dissertation thoroughly examines a wide array of newly observed novel phenomena induced by adjusting the relative strengths of SOI and U via a systematic chemical substitution of the Ru4+(4d4) ions for Ir4+(5d5) ions in BaIrO3, i.e., in high quality single crystals of BaIr1-xRuxO3(0.0 < x < 1.0) . Our investigation of structural, magnetic, transport and thermal properties reveals that Ru substitution directly rebalances the competing energies so profoundly that it generates a rich phase diagram for BaIr1-xRuxO3 featuring two major effects: (1) Light Ru doping (0 < x < 0.15) prompts a simultaneous and precipitous drop in both the magnetic ordering temperature TC and the electrical resistivity, which exhibits metal-insulator transition at around TC. (2) Heavier Ru doping (0.41 < x < 0.82) induces a robust metallic and spin frustration state. For comparison and contrast, we also substituted Rh4+(4d5) ions for Ir4+(5d5) ions in BaIrO3, i.e. BaIr1-xRhxO3(0.0 < x < 0.10), where Rh only reduces the SOI, but without altering the band filling. Hence, this system remains tuned at the Mott instability and is very susceptible to disorder scattering which gives rise to Anderson localization.

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Plusieurs familles de fonctions spéciales de plusieurs variables, appelées fonctions d'orbites, sont définies dans le contexte des groupes de Weyl de groupes de Lie simples compacts/d'algèbres de Lie simples. Ces fonctions sont étudiées depuis près d'un siècle en raison de leur lien avec les caractères des représentations irréductibles des algèbres de Lie simples, mais également de par leurs symétries et orthogonalités. Nous sommes principalement intéressés par la description des relations d'orthogonalité discrète et des transformations discrètes correspondantes, transformations qui permettent l'utilisation des fonctions d'orbites dans le traitement de données multidimensionnelles. Cette description est donnée pour les groupes de Weyl dont les racines ont deux longueurs différentes, en particulier pour les groupes de rang $2$ dans le cas des fonctions d'orbites du type $E$ et pour les groupes de rang $3$ dans le cas de toutes les autres fonctions d'orbites. / Several families of multivariable special functions, called orbit functions, are defined in the context of Weyl groups of compact simple Lie groups/Lie algebras. These functions have been studied for almost a century now because of their relation to characters of irreducible representations of Lie algebras, their symmetries and orthogonalities. Our main interest is the description of discrete orthogonality relations and their corresponding discrete transforms which allow the applications of orbit functions in the processing of multidimensional data. This description is provided for the Weyl group of different lengths of root, in particular groups of rank 2 for so-called $E-$orbit functions and of rank 3 for all the other families of special functions.