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In this dissertation, we study the existence and multiplicity of positive solutions to classes of one-dimensional singular p-Laplacian problems with nonlinear and intergral boundary conditions when the reaction termis p-superlinear or p-sublinear at infinity. In the p-superlinear case, we prove the existence of a large positive solution when a parameter is small and if, in addition, the reaction term satisfies a concavity-like condition at the origin, the existence of two positive solutions for a certain range of the parameter. In the p-sublinear case, we establish the existence of a large positive solution when a parameter is large. We also investigate the number of positive solutions for the general PHI-Laplacian with nonlinear boundary conditions when the reaction term is positive. Our results can be applied to the challenging infinite semipositone case and complement or extend previous work in the literature.Our approach depends on Amann's fixed point in a Banach space, degree theory, and comparison principles.

To assess the long-term performance of a solar thermal system, mathematical models that accurately capture the effects of heat transfer within and interactions between individual components are required. For solar domestic hot water systems, the components can include the solar collectors, storage tanks, heat exchangers, pumps, and associated piping. In addition, weather data and demand profiles are also required. Simplified models for each component are needed to reduce the computational time required to run long-term simulations. The simplified models, however, must also be sufficiently accurate in order to provide meaningful system-level results. Accurate prediction of the temperature profiles in the storage tanks of these systems is important since the temperature within the tank has a large impact on the efficiency of the entire system. TRNSYS, which is a commercial code commonly used for such simulations, contains a variety of different one-dimensional storage tank models. Previous research has indicated that these models have deficiencies in predicting experimental data. Therefore, this thesis is focussed on the analysis of the tank modelling used in TRNSYS. Results of this thesis show that the poor predictions are a result of numerical diffusion due to insufficient grid resolution. The correct theoretical profiles could be obtained by using a large number of nodes. However, this would lead to a significant increase in computational time. Alternative modelling strategies were also developed using analytical techniques to more accurately predict the temperature profiles within a storage tank while keeping a relatively low computational cost. Different models were created which considered the different mixing mechanisms present in a storage tank, such as increasing inlet temperatures with time, heat losses to the surroundings, tank wall heat conduction, and inlet jet mixing. / Thesis / Master of Applied Science (MASc)

This thesis presents theoretical investigations of triplet superfluidity (triplet superconductivity) in quasi-one-dimensional organic conductors and ultra-cold Fermi gases. Triplet superfluidity is different from its s-wave singlet counterpart since the order parameter is a complex vector and the interaction between fermions is in general anisotropic. Because of these distinctions, triplet superfluids have different physical properties in comparison to the s-wave case. The author discusses in this thesis the interplay between triplet superconductivity and spin density waves in quasi-one-dimensional organic conductors, and proposes a coexistence region of the two orders. Within the coexistence region, the interaction between the two order parameters acquires a vector structure, and induces an anomalous magnetic field effect. Furthermore, the author analyzes the matter-wave interference between two p-wave Fermi condensates, and proposes a polarization effect. For a single harmonically trapped p-wave Fermi condensate, the author also shows that the expansion upon release from the trap can be anisotropic, which reflects the anisotropy of the p-wave interaction.

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Selectively-transparent and conducting photonic crystals (STCPCs) made of alternating layers of sputtered indium-tin oxide (ITO) and spin-coated silica (SiO2) nanoparticle films have potential applications in micromorph solar cells and building integrated photovoltaics (BIPVs). In this work, theoretical calculations have been performed to show performance enhancement of the micromorph solar cell upon integration of the STCPC an intermediate reflector. Thin semi-transparent hydrogenated amorphous silicon (a-Si:H) solar cells with STCPC rear contacts are demonstrated in proof-of-concept devices. A 10% efficiency increase in a 135nm thick a-Si:H cell on an STCPC reflector with Bragg peak at 620nm was observed, while the transmitted solar irradiance and illuminance are determined to be 295W/m2 and 3480 lux, respectively. The STCPC with proper Bragg peak positioning can boost the a-Si:H cell performance while transmitting photons that can be used as heat and lighting sources in building integrated photovoltaic applications.

Ferromagnetismo itinerante permanece um problema elusivo em Física. O fenômeno resulta da competição entre interação eletrônica e efeitos de muitos corpos e não pode ser tratado perturbativamente. Particularmente em uma dimensão, teoremas proíbem fases ferromagnéticas em T = 0 para modelos de rede com hopping de primeiros vizinhos. Nos últimos vinte anos, entretanto, apareceram modelos na literatura que estendem o hopping para além de primeiros vizinhos e para os quais ordem ferromagnética foi rigorosamente estabelecida. Praticamente todas as demonstrações da existência de ferromagnetos unidimensionais são feitas em fase isolante (com exceção de casos patológicos, como repulsão infinita). Isto nos levou a investigar o acoplamento entre os setores de spin e carga no regime fortemente interagente quando se dopa o sistema, o que introduz pontos de Fermi pF e -pF. Encontramos, com teoria de perturbação, singularidades logarítmicas na autoenergia do mágnon quando seu momentum é pF ou -pF. Derivamos uma teoria de campo efetiva para o espalhamento em torno desses pontos entre os mágnons e férmions sem spin (que representam o setor de carga). O modelo efetivo é similar ao modelo Kondo, que consiste de uma impureza magnética localizada acoplada localmente com um mar fermiônico por uma interação de troca entre spins. Em nosso modelo, há, na realidade, um pseudospin que indica se o momentum de uma partícula é próximo de pF ou de -pF e o mágnon se comporta como uma impureza móvel. A mobilidade da impureza leva a uma relação de dispersão para os férmions dependente do pseudospin da impureza. / Itinerant ferromagnetism remains an elusive problem in Physics. The phenomenon arises from a competition between electronic interaction and many-body effects and cannot be treated perturbatively. Particularly in 1D, there are rigorous proofs that forbid ferromagnetic phase for lattice models with nearest-neighbours hopping only. In the last twenty years, however, models with hopping beyond nearest-neighbours were proposed in the literature and for which ferromagnetic phase was rigorously established. Virtually every proof of the existence of one-dimensional ferromagnets is done in an insulator phase (disregarding some pathological cases, such as infinite electronic repulsion). That motivated us to investigate the coupling between spin and charge sectors in the strongly interacting regime when we dope the system, introducing two Fermi points, pF and -pF. We found out, through perturbation theory, logarithmic singularities in the magnon selfenergy when its momentum is pF or -pF. To understand them, we derived an effective field theory for the scattering between magnons and spinless fermions (which represent the charge sector) close to these points. The effective model resembles the Kondo model, which describes a magnetic impurity locally coupled to a fermionic sea through spin exchange interaction. In our model, there is actually a pseudospin that indicates if a particle momentum is closest to pF or -pF and the magnon behaves as a mobile impurity. The impurity mobility leads to a fermionic dispersion relation that depends on the impurity pseudospin.

Molibdatos têm atraído grande atenção devido à existência de compostos com caráter elétrico unidimensional como conseqüência da presença de cadeias contendo ligações de Mo-O ou Mo-Mo em suas estruturas cristalinas. Com o objetivo de estudar molibdatos com esta característica, amostras policristalinas do sistema K-Mo-O foram preparadas pelo método de reação de difusão no estado sólido e caracterizadas por difratometria de raios x, propriedades elétricas e magnéticas. Estes resultados demonstram a existência de uma nova fase neste sistema com estequiometria KxMoO2-&#948;. Medidas da resistência elétrica em função da temperatura deste material mostram comportamento metálico anômalo que está relacionado a um ordenamento antiferromagnético. Foi observado ainda que a anomalia na resistência elétrica em baixas temperaturas (T < TM) comporta-se segundo uma lei de potência com expoente próximo de 0,5, o que sugere que o comportamento elétrico do KxMoO2-&#948; pode ser descrito por um mecanismo de condutividade unidimensional. / Molybdates have attracted great attention due to the existence of compounds which show one-dimensional electrical behavior as consequence of the channel containing Mo-O or Mo-Mo bonds in their crystalline structure. In order to study molybdates exhibiting onedimensional conductivity, polycrystalline samples of the K-Mo-O system were prepared using the solid state diffusion reaction method and characterized by X-ray powder diffractometry, electrical and magnetic properties. These results demonstrate the existence of a new phase in this system with KxMoO2-&#948; stoichiometry. Electrical resistance as a function of temperature measurements for this compound have shown anomalous metallic behavior which is related to an antiferromagnetic ordering. It has been also observed that the anomaly in the electrical resistance at low temperatures (T < TM) is fitted by power law temperature dependence with an exponent near 0.5 which suggests that the electrical behavior of the KxMoO2-&#948; can be well described by the one-dimensional conducting mechanism.