Grace aux progrès énormes des techniques de refroidissement, des expériences actuelles avec des atomes fermioniques piégés atteignent des températures extrêmement basses de l'ordre du nanoKelvin. Le but principal de ces expériences est l'étude de la transition nommée "BEC-BCS crossover". Pour cela, on change le champ magnétique autour d'une résonance de Feschbach, ce qui implique que la longueur de diffusion change des valeurs répulsives (a positif), à travers la limite unitaire (a infini) aux valeurs attractives (a négatif). Du côté BEC, où le système forme un condensat de Bose-Einstein de molécules fortement liées, aussi bien que du côté BCS, où les atomes forment des paires de Cooper qui ont une grande extension par rapport à la distance moyenne entre les atomes, on s'attend à ce que le système devienne superfluide, à condition que la température soit inférieure à une certaine température critique. Afin de trouver des signes sans équivoque de la superfluidité, il est nécessaire de regarder des observables dynamiques comme l'expansion du nuage atomique lorsque le piège est éteint ou des oscillations collectives du nuage. Le travail effectué au cours de cette thèse est une étude de la dynamique des modes collectifs dans les gaz de fermions froids. Nous avons développé un modèle basé sur l'évaluation de la matrice T. L'utilisation de l'équation de transport de Boltzmann pour les particules permet ensuite une étude semi-numérique des modes collectifs dans tous les régimes d'interaction. Cette étude a permis de mettre en évidence pour la première fois que la fréquence du mode radial quadrupolaire est supérieure à deux fois la fréquence du piège, comme cela est vérifié expérimentalement et contrairement aux premières théories n'incluant pas les effets de champ moyen. Les résultats obtenus ont aussi mis en évidence la nécessité d'une résolution numérique complète de l'équation de Boltzmann et de l'amélioration des techniques de détermination des observables physiques du gaz. Cette résolution numérique de l'équation de Boltzmann a montré que la détermination du temps de relaxation par la méthode des moments est erronée de 30%, ce qui influe fortement sur la détermination de la fréquence et de l'amortissement du mode collectif. Enfin, l'amélioration de la méthode des moments, considérant l'ordre supérieur, permet d'améliorer sensiblement l'accord avec le résultat numérique. Une telle investigation n'avait jamais été réalisée et montre la nécessité de considérer les moments d'ordre supérieurs pour l'étude des modes collectifs par l'équation de Boltzmann d'un gaz de fermions dans la phase normale.

Les gaz ultrafroids permettent d'étudier sous un angle nouveau des hamiltoniens complexes issus de la matière condensée, tels le modèle de Fermi-Hubbard. Cette thèse présente une nouvelle méthode de mesure de l'équation d'état d'un gaz ultrafroid, autorisant une comparaison directe avec la théorie. Elle repose sur une mesure de la pression à l'intérieur d'un gaz à partir de son image in situ. Nous appliquons cette méthode à l'étude d'un gaz de fermions en interaction résonnante, un gaz de 7Li en interaction faible servant de thermomètre. De manière surprenante, aucune des théories à N corps du gaz unitaire ne rend compte intégralement de l'équation déduite de cette analyse. Le développement du viriel extrait des données à haute température est en accord avec la résolution du problème à trois corps. A basse température nous montrons, contrairement à un certain nombre d'études antérieures, que la phase normale se comporte comme un liquide de Fermi. Enfin, nous obtenons la température critique de superfluidité grâce à une signature claire sur l'équation d'état. Nous avons aussi mesuré la pression de l'état fondamental en fonction du déséquilibre de spin et de la force des interactions - mesure directement utile à la description de la croûte des étoiles à neutrons. Nos données valident les simulations Monte-Carlo et sont en accord avec les corrections Lee-Huang-Yang au champ moyen pour un superfluide fermionique ou bosonique. Nous observons que, dans presque tous les cas, la phase partiellement polarisée peut être décrite comme un liquide de Fermi de polarons. La masse effective du polaron déduite de l'équation d'état est en accord avec une étude de modes collectifs.

Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

Abstract The gap between the revenue generated by division one football players and the value of an athletic scholarship is the marginal revenue product of these athletes. Because of the monopsonistic behavior of the NCAA, division one institutions capture an economic rent from their student athletes. This paper measures the rents generated by NCAA division one football players in the six powerhouse conferences by using linear regressions based on variables such as university revenue, future NFL draft picks, undergraduate population, and weekly AP Top-25 rankings. This paper will inform its readers on how much money these student athletes are generating for the NCAA and their respective schools, and will provide understanding as to why there has been so much controversy regarding the payment of NCAA athletes.

Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

Pharmaceutical cocrystals use principles of crystal engineering for the design of crystalline forms of drugs and can improve their solubility, bioavailability, stability and other important properties without changing the efficacy of the drug. Herein reported are pharmaceutical cocrystals of two API's, caffeine and Pentoxifylline. Research has indicated that caffeine has the ability to reverse AB; plaque deposition in the brain (believed to be the primary cause of Alzheimer's pathogenesis) and thus revert memory and improve cognitive impairment. But owing to the fast absorption rate and short half life, a controlled release formulation of caffeine would be clinically beneficial. Thus, novel cocrystals of caffeine are presented with varying solubilities with respect to caffeine. The pharmaceutical cocrystals of caffeine used herein include: caffeine.cyanuric acid monohydrate, caffeine.syringic acid tetrahydrate, caffeine.chlorogenic acid and caffeine.catechin hydrate. Three caffeine cocrystals were prepared in our lab previously which include caffeine.ferulic acid, caffeine.ethyl gallate dihydrate and caffeine.caffeic acid. In addition, six caffeine cocrystal forms were reproduced from the literature and included in the solubility study: caffeine.quercetin, caffeine.salicylic acid, caffeine.1-hydroxy-2-napthoic acid, caffeine.gallic acid hemihydrate, caffeine.ellagic acid monohydrate and caffeine.coumaric acid. Dissolution studies were performed in aqueous media at room temperature. All of the cocrystals decreased the solubility of caffeine with the highest being a 278 fold decrease in the solubility of caffeine. Analysis of melting point, crystal packing efficiency and solubility of cocrystal former with solubility was also done to determine if they influenced the solubility. Presented herein are the results of the analyses. It was seen that solubility of the cocrystal former had no effect on the decrease in cocrystal solubility. Moreover melting point and solubility of the cocrystal could not be correlated probably due to the variability in the cocrystal formers. Crystal packing efficiency though did not show a high correlation with solubility but it was seen that highest solubility achieved by pure caffeine achieved the lowest crystal packing efficiency and vice versa suggesting its role in cocrystal solubility. Pentoxifylline is contraindicated for its use in autism. But owing to high solubility of the drug, a less soluble form of the drug would help in decreasing the half life and thereby help in forming a sustained form of the drug by modifying the inherent solubility of the API. Here, novel cocrystals of Pentoxifylline are presented with varying solubilities with respect to the API. The pharmaceutical cocrystals used herein include: pentoxifylline.benzoic acid, pentoxifylline.1-hydroxy-2-napthoic acid, pentoxifylline.salicylic acid, pentoxifylline.gallic acid, pentoxifylline. salicylamide, pentoxifylline.coumaric acid, pentoxifylline.caffeic acid and pentoxifylline.catechin hydrate. Dissolution studies were also performed in aqueous media at room temperature. All of the cocrystals decreased the solubility of Pentoxifylline with the highest being a 99 fold decrease in the solubility with pentoxifylline.coumaric acid. On analyzing melting point, crystal packing efficiency and relation of solubility of cocrystal former with solubility of cocrystal, as was done in the case of caffeine, the parameters showed no effect on solubility of the cocrystal.

The cocrystallization of two or more pure compounds by crystal engineering to create a new functional material is of a great academic and industrial interest. Pharmaceutical cocrystallization has allured a lot of attention by means of altering the physicochemical properties of Active Pharmaceutical Ingredient (API) such as solubility, stability and bioavailability. Crystal engineering of nutraceuticals can produce novel compounds such as pharmaceutical cocrystals. To establish the importance of nutraceutical cocrystallization and its use; polyphenols, a major class of nutraceuticals and potential disease preventing agents, are the appropriate targets. The work herein focuses on two polyphenols, protocatechuic acid and quercetin, which are strong antioxidants. The cocrystals of quercetin have been synthesized, aiming to modify its poor water solubility and bioavailability which limits its usage. On the other hand, cocrystals of water soluble protocatechuic acid are also prepared to establish its use as a cocrystal former. Seven novel cocrystals of protocatechuic acid and two novel cocrystals of quercetin are obtained and are characterized by FTIR, DSC (Differential Scanning Calorimetry), PXRD (Powder X-Ray Diffraction), single crystal x-ray diffraction and TGA (Thermo Gravimetric Analysis). The new crystal forms have also been studied via dissolution. Dissolution studies show alteration in solubility of a target molecule by its cocrystal irrespective of solubility of the cocrystal former. Overall, the study helps in understanding the role of crystal engineering and its utility.

Increased BCS at calving due to nutritional manipulation during the prepartum period resulted in greater mobilization of body fat after calving, regardless of plane of nutrition during the last 60 d of gestation. Although fatter cows were shown to have greater mobilization of reserves during the postpartum period, they maintained greater BCS at all points from calving to weaning compared to cows calving with fewer reserves at calving. A unique finding of this experiment was that the variation in BCS at calving was positively associated with BCS loss for cows fed to accrete BC during the prepartum period but was not associated with BCS loss for cows fed at maintenance levels during gestation. This finding suggests a threshold response in which BCS loss postpartum is only related to BCS at calving of 6.5 or greater. Progeny of fatter cows were heavier at d 40 and 84, but no treatment differences existed at weaning. The relationship between BCS at calving and calf BW at d 40 differed by treatment. This suggests a threshold response in which calf BW is positively related to increases in BCS up to 5.75. At BCS ≥ 5.75 calf weights were greater than at lower BCS levels but were unrelated to incremental changes in BCS. Altering dietary energy level during mid and late gestation altered the net lipolytic rate of beef cows and altered the timing of changes in tissue sensitivity and total lipolysis. Basal release of NEFA did not change for cows on a maintenance diet, but increased significantly for fatter cows prior to calving, whereas basal glycerol was unaffected by treatment. The stimulated release of glycerol was also unaffected by treatment, but increased across all periods. The ratio of stimulated glycerol and NEFA release to basal release of glycerol and NEFA indicate that the AT of HI cows has a delayed response to the increase in sensitivity to lipolytic stimulants that is associated with homeorhetic adaptations; however, at 7 d after calving, no differences were observed for net or total lipolytic capacity of the tissue. Providing mature beef cows ad libitum access to a high‐energy diet alters pre‐calving sensitivity of AT, but after calving and when animals are receiving a common diet, no differences in lipolysis were observed. Thus, BCS (4.91 to 6.56), as manipulated by diet, does not appear to impair lipolytic function and regulation in beef cows as observed in dairy cows.

In dieser Dissertation werden das Anregungsspektrum und das Phasendiagramm wechselwirkender Fermi- und Bosegase untersucht. Zu diesem Zweck wird eine neuartige renormierte Kadanoff-Martin-Näherung vorgestellt, die Selbstwechselwirkung von Teilchen vermeidet und somit eine einheitliche Beschreibung sowohl der normalen als auch der kondensierten Phase ermöglicht. Für Fermionen findet man den BCS-Zustand, benannt nach Bardeen, Cooper und Schrieffer, welcher entscheidend ist für das Phänomen der Supraleitung. Charakteristisch für diesen Zustand ist eine Energielücke im Anregungsspektrum an der Fermi-Energie. Weiterhin tritt für Bosonen eine Bose-Einstein-Kondensation (BEC) auf, bei der das Anregungsspektrum für kleine Impulse linear ist. Letzteres führt zum Phänomen der Suprafluidität. Über die bereits bekannten Phänomene hinaus findet man eine dem BCS-Zustand ähnliche Kondensation von Zweiteilchenbindungszuständen, sowohl für Fermionen als auch für Bosonen. Für Fermionen tritt ein Übergang zwischen der Kondensation von Bindungszuständen und dem BCS-Zustand auf, der sogenannte BEC-BCS-Übergang. Die Untersuchung der Zustandsgleichung zeigt, dass im Gegensatz zu Fermi-Gasen und Bose-Gasen mit abstoßender Wechselwirkung Bose-Gase mit anziehender Wechselwirkung zu einer Flüssigkeit kondensieren oder sich verfestigen, bevor es zur Kondensation von Bindungszuständen oder zur Bose-Einstein-Kondensation kommt. Daher können diese Phänomene voraussichtlich nicht in der Gasphase beobachtet werden. Zusammenfassend lässt sich sagen, dass das vorgestellte Näherungsverfahren sehr gut geeignet ist, die erwähnten Phänomene im Zusammenhang mit der Bose-Einstein-Kondensation zu beschreiben.

Recentemente, tem sido questionada a validade do teorema de Migdal nos fuieretos dopados supercondutores. Motivados por esse problema, realizamos nesta dissertação uma revisão das propriedades físicas destes novos e notáveis materiais: os fulerenos e outros representantes desta família de compostos orgânicos que possuem estrutura geométrica de gaiola fechada. Em primeiro lugar abordamos, ainda que de maneira sucinta, alguns fundamentos da teoria microscópica BCS (Bardeen, Cooper e Schrieffer, 1961) da supercondutividade, tais como o problema da instabilidade do líquido de Fermi, a formação de pares de Cooper, o método da transformação canônica para demonstrar o aparecimento da interação efetiva atrativa entre os elétrons do par, as equações de Gor'kov demonstrando o surgimento do gap supercondutor, e a expressão BCS da temperatura crítica no limite de acoplamento fraco. Após, revisamos o trabalho realizado por Grimaldi, Cappelluti e Pietronero (1995), sobre a supercondutividade não adiabática nos fuieretos dopados, no qual são feitas correções de vértice para a interação elétron-fônon, usando o método perturbativo. Naquele trabalho eles utilizam um modelo de fônons de Einstein com uma única freqüência para caracterizar a função espectral de Eliashberg, necessária para obter tais correções de vértice Nossa proposta neste trabalho é generalizar este modelo por um constituído de várias Lorentzianas truncadas, centradas nas freqüências dos principais modos de vibração da rede cristalina: os intermoleculares, os ópticos e os intramoleculares. Encontramos como resultado deste estudo que as correções de vértice, com contribuição multifonônica, introduzem modificações substancias como um aumento da temperatura crítica e variação no coeficiente isotópico, dando resultados mais próximos dos obtidos experimentalmente, em contraste daqueles obtidos na teoria de Migdal-Eliashberg, sem correções de vértice.