Thesis (M. Sc.)--York University, 1997. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 137-141). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pMQ27373.

The main goal of this project was to write a review about different quantum Hall effects. This review focuses on the integer and relativistic quantum Hall effect in graphene. The quantum Hall effect is a newly discovered phenomena that was experimentally observed in 1980 and relativistic quantum Hall effect in graphene was observed in 2005. This project takes a theoretical approach to describe the quantum Hall effects and graphene itself. Experiments has shown that for very strong magnetic fields applied to 2D systems, the Hall resistance becomes quantized, RH=h/ne2 and only depends on the charge of the electron and Planck's constant, two fundamental constants of nature. This sets a new standard on how to define resistance, and gives a good tool for precise measurements of the fine structure constant.

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Thesis (P.H.D.)--University of Adelaide, Dept. of Physics, 1957. / Typewritten. Includes bibliographical references.

In Part I of this thesis, steady and time-dependent, natural-convection similarity flows with mass transfer are discussed. Similarity flows for natural convection on families of two-dimensional bodies with closed lower ends are enumerated, when both a temperature distribution and a suction velocity distribution are prescribed at the body surface. For steady similarity flow on a heated vertical flat plate, with mass transfer at the surface, a numerical procedure is introduced for determining the velocity and temperature profiles. These results are presented in Figs. 2 and 3. Other similarity flows may be found by the same method. A simplification, valid for “strong” suction, is discussed. An extension of Mangler's transformation [1948] is given which reduces the equations governing axisymmetric flow to those for two-dimensional flow in steady natural convection. In Part II non-linear resonant instability in parallel shear flows is discussed. A.D.D.Craik's (see Usher and Craik [I]) modified version of Bateman's [1956] variational formulation for viscous flows is employed to derive the second-order interaction equations governing the temporal evolution of a resonant wave triad in a sheer flow. (An extension of Craik's variational formulation to free surface flows is presented but is not required in the subsequent analysis for the resonance problem). This problem was treated previously using a ‘direct' approach (employing the Navier-Stokes equations) by Craik [1971]. The major advantage of the present method over the ‘direct' method is the substantial reduction in algebraic complexity. Also, a justification of the validity of Craik's previous analysis is given. For this same resonance problem, third-order interaction equations are derived by the *direct* method since, to this order of approximation, little advantage is to be gained from the variational formulation. The resonance theory is thereby developed to the same order of approximation as the non-resonant third-order theory of Stuart [1960, 1962]. An asymptotic analysis for large Reynolds numbers reveals that the magnitudes of the third-order interaction coefficients – like certain of those at second-order – are remarkably large. Such results lead to a discussion of the regions of validity of the perturbation analysis. Also some light is shed on the roles played by resonance and three-dimensionality in the non-linear instability of shear flows.

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O emprego da química computacional fornece subsídios para a interpretação dos estudos experimentais e permite fazer previsões sobre as propriedades de sistemas ainda não sintetizados. Devido aos avanços computacionais, métodos de química quântica com diferentes níveis de tratamento de estrutura eletrônica são mais facilmente encontrados. Entretanto, certas aproximações ainda são necessárias devido à grande demanda por recursos computacionais dos métodos mais avançados. Desta forma, os resultados obtidos podem não representar adequadamente as propriedades dos sistemas estudados. Para compostos contendo elementos pesados, como é o caso de muitos catalisadores, seriam necessários estudos que levem em conta os efeitos relativísticos. Desta forma, foi realizado um estudo cinético de quatro tipos de reações envolvendo sistemas contendo átomos pesados. Na determinação das geometrias otimizadas verificou-se que os efeitos relativísticos escalares são geralmente predominantes e que não há diferença significativa entre os resultados do método de dois componentes ZORA em relação ao tradicional tratamento RECP. No entanto, cálculos DKH2 não conseguiram descrever os parâmetros geométricos de compostos de platina com a mesma eficácia. Por outro lado, foi possível observar que os efeitos relativísticos são muito mais importantes para uma determinação confiável de outras propriedades relacionadas à cinética química, como as energias relativas ao longo do mecanismo de reação. Neste caso, além dos efeitos relativísticos escalares, o acoplamento spin-órbita também se torna crucial para uma descrição acurada das barreiras de ativação em compostos com elementos do sexto período em diante. Assim, recomenda-se o uso de um tratamento combinado em duas etapas para uma correta descrição dos sistemas. Em geral, a etapa de otimização de geometrias pode ser realizada em nível RECP. Entretanto, para a obtenção de valores acurados de energia por métodos relativísticos, sugere-se a utilização dos tratamentos de quatro componentes, como Dirac-Coulomb (DC), e dos formalismos exatos de dois componentes, como X2C-MMF. / The use of computational chemistry provides support for the interpretation of experimental studies and allows making predictions about the properties of systems not yet synthesized. Quantum chemistry methods with different levels of electronic structure treatments are more easily found due to computational advances. However, some approximations are still required because of the significant demand for computational resources associated to more advanced methods. Thus, the results obtained may not adequately represent the properties of the systems studied. In the case of compounds containing heavy elements, such as many catalysts, studies that take into account the relativistic effects would be need. Thus, a kinetic study of four reaction categories involving systems containing heavy atoms was conducted. It was noticed that the scalar relativistic effects are generally predominant and that there is not significant differences between the results from the ZORA method in relation to the traditional RECP treatment during the determination of optimized geometries. Nevertheless, the DKH2 calculations failed to describe the geometric parameters of platinum compounds with the same efficiency. On the other hand, it was possible to observe that relativistic effects are very important for a reliable determination of other properties related to chemical kinetics, such as the relative energies along the reaction mechanism. In this case, in addition to scalar relativistic effects, the spin-orbit coupling also becomes crucial for an accurate description of the activation barriers in compounds with elements from the sixth period and beyond. Therefore, a two-step combined treatment is recommended for a correct description of the systems. In general, the geometry optimization step can be performed at the RECP level. However, in order to obtain accurate energy values by relativistic methods, we suggest the use of four-component treatments such as Dirac-Coulomb (DC) and exact two-component formalisms like X2C-MMF.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: We consider the ferromagnetic phase in pure neutron matter as well as charge neutral, betaequilibrated nuclear matter. We employ Quantum Hadrodynamics, a relativistic field theory description of nuclear matter with meson degrees of freedom, and include couplings between the baryon (proton and neutron) magnetic dipole moment as well as between their charge and the magnetic field in the Lagrangian density describing such a system. We vary the strength of the baryon magnetic dipole moment till a non-zero value of the magnetic field, for which the total energy density of the magnetised system is at a minimum, is found. The system is then assumed to be in the ferromagnetic state. The ferromagnetic equation of state is employed to study matter in the neutron star interior. We find that as the density increases the ferromagnetic field does not increase continuously, but exhibit sudden rapid increases. These sudden increases in the magnetic field correspond to shifts between different configurations of the charged particle’s Landau levels and can have significant observational consequences for neutron stars. We also found that although the ferromagnetic phase softens the neutron star equation of state it does not significantly alter the star’s massradius relationship. The properties of magnetised symmetric nuclear matter were also studied. We confirm that magnetised matter tends to be more proton-rich but become more weakly bound for stronger magnetic fields. We show that the behaviour of the compressibility of nuclear matter is influenced by the Landau quantisation and tends to have an oscillatory character as it increases with the magnetic field. The symmetry energy also exhibits similar behaviour. / AFRIKAANSE OPSOMMING: In hierdie studie het ons die ferromagnetiese fase in suiwer neutronmaterie, sowel as in ladingsneutrale, beta-ge¨ekwilibreerde neutronstermaterie, ondersoek. Vir die doeleindes het ons die Kwantum Hadrodinamika-model van kernmaterie gebruik. Dit is ’n relatiwistiese, veldteoretiese model wat mesone inspan om die interaksies tussen die protone en neutrone te bemiddel. Om die impak van die magneetveld te bestudeer, sluit ons ’n koppeling tussen die barioonlading en die magneetveld, asook barioondipoolmoment en die magneetveld, in by die Lagrange digtheid wat ons sisteem beskryf. Om die ferromagnetiese fase te ondersoek, varieer ons die sterkte van die barioondipoolmoment om ’n nie-nul waarde van die magneetveld wat energie digtheid sal minimeer te vind. Die ferromagnetiese toestandsvergelyking word toegepas op materie aan die binnekant van die neutronster en die impak hiervan op die waarneembare eienskappe van die ster word ondersoek. Ons vind dat die ferromagnetiese magneetveld nie kontinu toeneem soos die digtheid verhoog nie. Die skielike toenames in die magneetveld is die gevolg van die sisteem wat die konfigurasie van die gelaaide deeltjies se Landau-vlakke skielik verander en dit kan beduidende waarneembare gevolge vir die ster inhou. Ons vind ook dat die ferromagnetiese fase die toestandsvergelyking versag, maar dat die versagting die massa-radius verhouding van die ster nie grootliks beïnvloed nie. Die eienskappe van gemagnetiseerde kernmaterie word ook ondersoek. Ons bevestig dat gemagnetiseerde materie meer proton-ryk, maar minder sterk gebind word. Ons wys dat die saampersbaarheid van kernmaterie deur die teenwoordigheid van Landau-vlakke beïnvloed word en ossilerend saam met die magneetveld toeneem. Die simmetrie-energie manifesteer ook soortgelyke gedrag.