Die vorliegende Arbeit widmet sich der, vorwiegend experimentellen, Untersuchung der Wirkung wandparalleler Lorentzkräfte in Strömungsrichtung auf Grenzschichtprofile und Körperumströmungen. Die Themen - Beeinflussung der Grenzschicht an ebenen Platten mit stationären Lorentzkräften - Kontrolle von Strömungsablösungen an Zylindern und symmetrischen Profilen mit stationären Lorentzkräften - Beeinflussung von Zylindernachläufen und abgelösten Tragflügelumströmungen mit zeitlich periodischen Lorentzkräften werden behandelt.

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Symmetry has played a crucial role in our understanding of physical systems. In this thesis, we review several works based on investigating the symmetry properties of theories. We examine and improve the Noether's theorem and the coset construction, both powerful tools when studying the symmetry aspects of a physical system. We manipulate the intrinsic ambiguities in the derivation of the stress-energy tensor using Noether's theorem to systematically compute, without any guesswork, the necessary ``improvement terms'' which make the tensor satisfy certain algebraic properties such as symmetry and tracelessness, even off-shell. We then construct a new type of coset construction, which can accommodate relativistic particles with arbitrary spins. This is the first work we know of to incorporate arbitrary spin degrees of freedom into coset construction. We then present two interesting examples of condensed matter systems described by effective field theories that come from spontaneous symmetry breaking. For the so-called framid, we present the peculiar behavior of its stress-energy tensor that it is Lorentz-invariant even though the system breaks Lorentz boosts spontaneously. An analogy is drawn to the cosmological constant problem since the vacuum energy there and the Lorentz-breaking terms here are all surprisingly zero. Lastly, we describe how the inflation of the universe can be driven by a solid. We focus on the icosahedral inflation model, where the isotropies of background evolution and scalar power spectrum are guaranteed although the system is anisotropic. We discuss some observational signatures of this model.

We solve a one-sided Cauchy problem with zero right hand side modulo smooth errors for the wave operator associated to a smooth symmetric 2-tensor which is Lorentz on the interior and degenerate at the boundary. The degeneracy of the metric at the boundary gives rise to singularities in the wave operator. The initial data prescribed at the boundary must be modified from the classical Cauchy problem to suit the problem at hand. The problem is posed on the interior and the local solution is constructed using microlocal analysis and the techniques of Fourier Integral Operators. / Mathematics

The use of high-powered electrical energy systems requires an efficient and capable means to move electrical energy from one location to another while reducing energy losses. This paper describes the design and construction process of a high-powered busbar system that is to be implemented in pulsed-power applications. In order to obtain a robust system capable of handling in excess of 25kJ, both mechanical and electrical analyses were performed to verify a capable design. The following methodology describes how the Lorentz force was balanced with mechanical forces during the design process and then validated after construction was completed using the fundamental Maxwell equations and computer simulations. Main focuses include handling of EMF, high current density concentrations, and overall mechanical stability of the system and how these effects determine the physical design and implementation. In the end, a repeatable methodology is presented in the form of a design process that can be implemented in any system given the design criteria. / Master of Science

Dans cette thèse, nous étudions plusieurs aspects de la radiation de Hawking en présence de violations de l'invariance locale de Lorentz. Ces violations sont introduites par une modification de la relation de dispersion, devenant non-linéaire aux courtes longueurs d’onde. Les principales motivations de ces travaux ont une double origine. Il y a d’une part le développement en matière condensée de trous noirs analogues, ou l’écoulement d’un fluide est perçu comme une métrique d’espace-temps pour les ondes de perturbations et ou la radiation de Hawking pourrait être détectée expérimentalement. D’autre part, il se pourrait que des effets de gravité quantique puissent être modélisés par une modification de la relation de dispersion. En premier lieu, nous avons obtenu des caractérisations précises des conditions nécessaires au maintien de l’effet Hawking en présence de violation de l’invariance de Lorentz. De plus, nous avons étudié l’apparition d’une onde macroscopique de fréquence nulle, dans des écoulements de type trous blancs et également pour des champs massifs. Une autre partie de ce travail a consisté à analyser une instabilité engendrée par les effets dispersifs, ou la radiation de Hawking est auto-amplifiée, générant ainsi un flux sortant exponentiellement croissant dans le temps. / In this thesis, we study several features of Hawking radiation in the presence of ultraviolet Lorentz violations. These violations are implemented by a modified dispersion relation that becomes nonlinear at short wavelengths. The motivations of this work arise on the one hand from the developing field of analog gravity, where we aim at measuring the Hawking effect in fluid flows that mimic black hole space-times, and on the other hand from the possibility that quantum gravity effects might be approximately modeled by a modified dispersion relation. We develop several studies on various aspects of the prob- lem. First we obtain precise characterizations about the deviations from the Hawking result of black hole radiation, which are induced by dispersion. Second, we study the emergence, both in white hole flows or for massive fields, of a macroscopic standing wave, spontaneously produced from the Hawking effect, and known as ‘undulation’. Third, we describe in detail an instability named black hole laser, which arises in the presence of two horizons, where Hawking radiation is self-amplified and induces an exponentially growing in time emitted flux.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo deste trabalho à aplicar o modelo de bumblebee, um modelo de quebra de simetria espontÃnea de Lorentz gerada por um quadri-vetor de valor esperado de vÃcuo nÃo-nulo, a um espaÃo de vÃcuo. Apresentamos resultados para quebra de simetria de Lorentz radial/temporal em um espaÃo de Schwarzschild. AlÃm disso, à verificada uma incompatibilidade entre a hipÃtese de o universo ser homogÃneo quando nÃo hà presenÃa de matÃria massiva ordinÃria e a imposiÃÃo de um campo de bumblebee paralelamente transportado na direÃÃo radial. / The objective of this work is apply bumblebee model, a spontaneously Lorentz symmetry breaking model due to a non-vanishing vacuum expectation value vector field, to a vacuum space. Results are presented for a radial/temporal Lorentz symmetry breaking in a Schwarzschild space. Also, it is verified an incompatibility between the hypothese of the universe to be homogenous in the absence of massive ordinary matter and the imposition of a parallelly transported bumblebee field in radial direction.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-07T18:20:05Z No. of bitstreams: 1 PauloPinheiro.pdf: 740954 bytes, checksum: 7a586404eb9969daad1f2c29dbbf0b42 (MD5) / Made available in DSpace on 2017-06-07T18:20:05Z (GMT). No. of bitstreams: 1 PauloPinheiro.pdf: 740954 bytes, checksum: 7a586404eb9969daad1f2c29dbbf0b42 (MD5) Previous issue date: 2009-07-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / The possibility of spontaneous breaking of Lorentz symmetry in the context of string theory appeared in 1990´s as an element capable to direct new ways for developing physics at Planck scale. Possible breaking of Lorentz invariance is seen as a characteristic of the physics beyond the usual Model Standard, that forbids such breaking in its structure. The observation of Lorentz breaking (LV) at lower energies can be seen as an evidence of occurrence of Lorentz spontaneous breaking at Planck scale, with important consequence for the development of the quantum gravitation theory. This work aims at studying the LV effects in a regime of low energies, more necessarily in the context of the Maxwell electrodynamics, in the presence of the CPT-even term (W∝υρφF∝υFρφ) of the standard model extension. In the first part of the work, we deal with the electrodynamics stemming from the parity-odd sector of the tensor W∝υρφ, where the electric and magnetic sectors are connected by the breaking parameter (violating vector k). The method of Green is then used to yield the classic solutions for this electrodynamics. It is observed that Lorentz-violating coefficients contribute in first order for the electric and magnetic sectors. An experiment of feasible accomplishment in laboratory is considered for stipulating an upper bound for the background magnitude (k < 10−16). In the sequel we deal with the electrodynamics stemming from the parity-even sector of the tensor W∝υρφ. The solutions for the electric and magnetic sector are attained similarly by the Green method. With such solutions, we are able to impose an upper bound on the parameters: (eκe−)ib < 2.9 × 10−20. Finally, we evaluate the gauge propagator of this theory, both for the parity-even and the parity-odd sectors. We then use it to analyze the stability, causality and unitary of this model. Keywords: Maxwell electrodynamics, Lorentz symmetry, Classical solutions, / A possibilidade de violação espontanea da simetria de Lorentz no contexto da teoria das cordas surgiu nos anos 90 como um elemento capaz de direcionar novos caminhos para a fısica na escala de Planck. Possíveis violações da invariância de Lorentz são vistas como uma caracterıstica da fısica além do Modelo Padrão usual, que proíbe tal violação em sua estrutura. A observação da violação de Lorentz (VL) em mais baixas energias pode ser vista como uma evidência da ocorrência do mecanismo de quebra espontanea na escala de Planck, com importantes consequências para o desenvolvimento da teoria da gravitação quantica. Este trabalho propõe-se a estudar efeitos da VL em um regime de baixas energias, mais precisamente no contexto da eletrodinâmica de Maxwell modificada pelo termo CPT-par (W∝υρφF∝υFρφ) do Modelo Padrão Estendido. Na primeira parte do trabalho, tratamos a eletrodinamica resultante do setor de paridade ímpar do tensor W∝υρφ, em que os setores elétrico e magnético são acoplados pelo parâmetro de quebra (vetor violador k). Usa-se então o método de Green para obter as soluções clássicas desta eletrodinâmica. Observa-se que os coeficientes violadores de Lorentz contribuem em primeira ordem para os setores elétrico e magnético. Propõe-se um experimento de factível realização em laboratório, para estipular um limite superior para a magnitude do ”background”(k < 10−16). Tratamos em seguida a eletrodinâmica advinda do setor de paridade par. As soluções para o setor elétrico e magnético são obtidas similarmente pelo método de Green. Com tais soluções, conseguimos impor um limite superior sobre os parâmetros: (eκe−)ib < 2.9 × 10−20. Por fim, calculamos o propagador desta teoria, tanto para o setor paridade-par quanto para o setor paridade ímpar, e usamo-lo para obter informações sobre a causalidade, estabilidade e unitariedade do modelo.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-07T18:34:00Z No. of bitstreams: 1 FredericoSantos.pdf: 963672 bytes, checksum: 82f7ae1b28b9c136b94c6c04439b8c32 (MD5) / Made available in DSpace on 2017-06-07T18:34:00Z (GMT). No. of bitstreams: 1 FredericoSantos.pdf: 963672 bytes, checksum: 82f7ae1b28b9c136b94c6c04439b8c32 (MD5) Previous issue date: 2010-12-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / The standard model extension is a theoretical framework which includes the possibility of Lorentz symmetry violation in the Standard Model of elementary interactions. In electrodynamics, this possibility is represented by the term, Kμν∝βFμνF∝β , that violates Lorentz symmetry without jeopardizing CPT symmetry, and the term ε∝μβνV∝Aμ∂βAν, which violates Lorentz and CPT symmetries. These additional terms are inserted in the Maxwell Lagrangena and alter the field equations, as well. In this work we study the influence of Lorentz violation in the photonic sector on fermion scattering processes, regarding individually the CPT-odd and CPT-even coefficients. At first, we present a review through some topics of great interest, as the Dirac equation, Dirac propagator, scattering matrix, Feynman rules, Casimir trick, and the evaluation of the differential cross sections. Next, we implemented the developed techniques to carry out the corrections (to the cross sections) induced by the Lorentz-violating terms. Our results reveal as each Lorentz-violating component changes the cross section. In the CPT-even case, we observed that the contribution of the term tr to the process e− + μ− → e− + μ− is of difficult detection once it can be disguised between the radioactive corrections. The contributions coming from the vector i imply an angular dependence in the differential cross section of the process e− + μ− → e− + μ−, and do not contribute for the process e− + e+ → μ− + μ+. The CPT-even coefficients, (Ke−)ij , lead to significant contributions in both cases. We highlight its influence in the pair electron-positron annihilation process, where they act as the only components that imply sensitive contributions. The contribution stemming from the CPT-odd sector, represented by the Carroll-Field-Jackiw term, is of less relevance, since the contribute are second order ones. Although we have initially developed a perturbative procedure for evaluating the cross section correction, it was also possible to evaluate the exact propagators of the CPT-odd and CPT-even sectors in a tensor closed form. Such tensor expressions may be used to rederive the cross section corrections. / O Modelo Padrão Estendido (MPE)é um arcabouço teórico que considera a possibilidade de violação de simetria de Lorentz no Modelo Padrão das interações elementares. Na eletrodinâmica, esta possibilidade é representada pelo termo Kμν∝βFμνF∝β , que viola a simetria de Lorentz sem violar a simetria CPT, e o termo ε∝μβνV∝Aμ∂βAν, que viola a simetria de Lorentz, juntamente com a simetria CPT. Estes termos extras são incluídos na lagrangena de Maxwell e, consequentemente, também alteram a equação de movimento dos campos. Neste trabalho consideramos a influência da violação de Lorentz no setor fotônico em processos de espalhamento de férmions, e− + μ− ! e− + μ− e e− + e+ ! μ− + μ+, considerando individualmente o setor CPT-ímpar e CPT-par em suas componentes não-birrefringentes. No primeiro momento, apresentamos uma revisão de tópicos de interesse, passando pela equação de Dirac, propagador de Dirac, matriz de espalhamento, regras de Feynman, truque de Casimir, finalizando com o cálculo das seções de choque diferenciais para processos elementares. Em seguida, implementamos as técnicas desenvolvidas para calcular o incremento à seção de choque, oriundo da violação de simetria de Lorentz no setor fotônico. Em nossos resultados, obtivemos como cada componente de violação de Lorentz altera a seção de choque. No caso CPT-par, observamos que a contribuição do termo Kir ao processo e− + e+ → μ− + μ+ é de difícil verificação, pois se confunde com as contribuições radioativas. Já as contribuições advindas do vetor Ki, inserem uma dependência angular na seção de choque diferencial do processo e− + μ− → e− + μ−, mas não contribui no processo e− + e+ → μ− + μ+. Os coeficientes paridade-par, (Ke−)ij , implicam em contribuições relevantes em ambos os processos, e destacamos sua influência no processo de aniquilação elétron-pósitron, onde atuam como únicas componentes que contribuem de forma notável. A contribuição do setor CPT-ímpar (termo de Carroll-Field-Jackiw) é comparativamente de menor relevância, já que as contribuições à seção de choque aparecem apenas em segunda ordem. Embora tenhamos inicialmente desenvolvido um procedimento perturbativo para calcular as contribuições dos parâmetros de quebra de Lorentz à seção de choque, também foi possível obter os propagadores de Feynman exatos tanto para o setor CPT-ímpar quanto para o setor CPT-par. Tais expressões podem ser usadas para recalcular as seções de choque.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-07T18:48:31Z No. of bitstreams: 1 AlexsandroLucenaMota.pdf: 2757687 bytes, checksum: 04b1d52c9ca203ed571f49aacf10eeac (MD5) / Made available in DSpace on 2017-06-07T18:48:31Z (GMT). No. of bitstreams: 1 AlexsandroLucenaMota.pdf: 2757687 bytes, checksum: 04b1d52c9ca203ed571f49aacf10eeac (MD5) Previous issue date: 2014-09-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The first studies on Lorentz-violating BPS vórtices were accomplished within the framework of the Standard Model Extension (SME). Specifically, it was studied the effects of the Lorentz violation in the vortex solutions presented in the Maxwell-Higgs electrodynamics. The formation of vórtices was also analyzed in (1+2)-dimensional models obtained by dimensional reduction of the SME Abelian sector. Among the several effects of the Lorentz violation we can mention: the control of both the amplitude as the width of the vortex, magnetic field reversion, magnetic flux quantization with explicit dependence on the Lorentz-violating coefficients. In this dissertation we study the existence of topological BPS vórtices in a Maxwell-Higgs model in which the covariant derivative is modified by the addition of a CPT-odd term, which breaks the CPT- and Lorentz symmetry due to the presence of a vectorial background. The interaction generating a set of self-dual or first-order equations includes a potential jφj4 and a derivative coupling j@iφj4. Although the self-dual equations are very different of those belonging to the usual MaxwellHiggs model, the new vortex solutions behave just like the Aharonov-Nielsen-Olesen ones, but the mass scale depends explicitly on the Lorentz-violating coefficient. / Os primeiros estudos sobre vórtices BPS no contexto da violação da simetria de Lorentz foram realizadas no marco teórico do modelo padrão estendido (MPE). Especificamente, foram estudados os efeitos da quebra de Lorentz sobre os vórtices existentes na eletrodinâmica de Maxwell-Higgs. Também, foram estudadas a formação de vórtices em modelos (1+2)-dimensionais obtidos via redução dimensional do setor Abeliano do MPE. Entre os diversos efeitos da quebra de Lorentz podemos citar: controle da amplitude e largura do vórtice, inversão do campo magnético, fluxo magnético quantizado com dependência explícita nos coeficientes da quebra de Lorentz, etc. Nesta dissertação estudamos a existência de vórtices topológicos em um modelo de MaxwellHiggs cuja derivada covariante é modificada pela inclusão de um termo CPT-ímpar, o qual quebra a simetria de Lorentz devido a presença de um campo de fundo vetorial. A interação, que gera um sistema de equações auto-duais de primeira ordem, inclui um potencial jφj4 e um acoplamento derivativo j@iφj4. A pesar das equações auto-duais serem bem diferentes daquelas do modelo de Maxwell-Higgs, os vórtices obtidos se comportam como aqueles de Aharonov-Nielsen-Olesen, mas a escala de massa depende explicitamente do coeficiente que controla a quebra de Lorentz.