Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-12-01T23:34:01Z No. of bitstreams: 1 SergioRobertoDantas_DISSERT.pdf: 1439747 bytes, checksum: d876ed77a5433b952a46ba0482101886 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-12-05T21:54:18Z (GMT) No. of bitstreams: 1 SergioRobertoDantas_DISSERT.pdf: 1439747 bytes, checksum: d876ed77a5433b952a46ba0482101886 (MD5) / Made available in DSpace on 2017-12-05T21:54:18Z (GMT). No. of bitstreams: 1 SergioRobertoDantas_DISSERT.pdf: 1439747 bytes, checksum: d876ed77a5433b952a46ba0482101886 (MD5) Previous issue date: 2017-09-06 / Frequentemente, as superf?cies seletivas em frequ?ncias t?m recebido grande aten??o por parte de pesquisadores em todo o mundo, devido a suas caracter?sticas de filtragem. Essas estruturas evolu?ram em termos de fabrica??o. Assim, as geometrias utilizadas, inicialmente, eram fios em forma de grade e, posteriormente, diversos tipos de novas geometrias tais como: elementos retangulares, quadrados, circulares, an?is, espiras quadradas etc., foram utilizadas. Recentemente, elementos fractais e, mais recentemente, multifractais foram empregados. O emprego dessas geometrias ? feito com o objetivo de se obter uma resposta em frequ?ncia espec?fica. Par?metros importantes, como largura de banda e frequ?ncia de resson?ncia s?o atendidos a partir do emprego de uma determinada geometria. Neste trabalho ? proposta uma geometria multifractal com dupla similaridade, que tem como caracter?stica principal baixa sensibilidade ? varia??o da periodicidade com rela??o ? frequ?ncia de resson?ncia. Essa especificidade trar? ganho no que diz respeito ? elabora??o do projeto, pois o controle da largura de banda ? feito apenas com a altera??o da periodicidade. Diversas simula??es foram implementadas no Ansoft Designer e para efeito de comprova??o, estruturas tradicionais foram simuladas, visando ? demonstra??o do efeito da periodicidade na frequ?ncia de resson?ncia e, em seguida, dois prot?tipos foram constru?dos e feitas medi??es para validar experimentalmente as simula??es. / Often, frequency selective surfaces have received wide attention from researchers around the world because of their filtering characteristics. These structures evolved in terms of manufacturing. Thus, the geometries used, initially, were yarns in the form of a grid and later, several types of new geometries such as: rectangular, square, circular, rings, square, etc., were used. Recently, fractals and, more recently, multifractal elements have been employed. The use of these geometries is done in order to obtain a specific frequency response. Important parameters such as bandwidth and resonant frequency are met from the use of a given geometry. In this work a multifractal geometry with double similarity is proposed, which has as main characteristic low sensitivity to the variation of the periodicity with respect to the resonance frequency. This specificity will bring gain with regard to the elaboration of the project, because the control of the bandwidth is made only with the change of periodicity. Several simulations were implemented in Ansoft Designer and for the purpose of proving, traditional structures were simulated, aiming at demonstrating the effect of periodicity on the resonance frequency, and then two prototypes were constructed and measurements were taken to experimentally validate the simulations.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-03-17T19:30:45Z No. of bitstreams: 1 MacksonMatheusFrancaNepomuceno_TESE.pdf: 12126877 bytes, checksum: 07d5c77235cdfd529f0902323ba9b8e0 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-03-17T23:55:08Z (GMT) No. of bitstreams: 1 MacksonMatheusFrancaNepomuceno_TESE.pdf: 12126877 bytes, checksum: 07d5c77235cdfd529f0902323ba9b8e0 (MD5) / Made available in DSpace on 2017-03-17T23:55:08Z (GMT). No. of bitstreams: 1 MacksonMatheusFrancaNepomuceno_TESE.pdf: 12126877 bytes, checksum: 07d5c77235cdfd529f0902323ba9b8e0 (MD5) Previous issue date: 2016-12-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Usando as recentes observa??es da onda gravitacional GW150914 produzida pelo sistema de buracos negros bin?rios coalescentes, a presente tese investiga a natureza fractal e multifractal da varia??o temporal da deforma??o relativa (strain) medido pelos detectores do Observat?rio de Ondas Gravitacionais por Interferometria Laser (LIGO na sigla em ingl?s). Uma sele??o de m?todos e procedimentos, tais como as an?lises R/S e Wavelet, assim como, o m?todo multifractal denotado por MFDMA, foram usados para estimar par?metros estat?sticos que sintetizam a onda gravitacional como uma s?rie temporal complexa. Seja nos dados de Hanford ou Livingston, a an?lise fractal revelou que a referida s?rie apresenta um comportamento com forte persist?ncia e mem?ria de longa dura??o quantificado pelo expoente de Hurst. Al?m disso, a forte aglomera??o das flutua??es encontrados pela an?lise R/S indica o alto grau de depend?ncia por escala, caracter?stica de um sinal multifractal. Por outro lado, a an?lise multifractal atrav?s do m?todo MFDMA sugere que a s?rie temporal apresenta uma predomin?ncia de fracas singularidades em detrimentos ?s fortes, causando uma assimetria no espectro de singularidade D(h). Neste contexto, foram realizados dois tipos de procedimentos que analisam as poss?veis fontes de multifractalidade presentes na s?rie temporal. Os resultados mostram que procedimentos apontam para a exist?ncia de dois regimes de multifractalidade na s?rie temporal separados pela regi?o onde ocorre a colis?o dos buracos negros, referentes aos dados de Hanford, e, para os dados de Livingston, pr?ximo ao final da fase de inspiraliza??o. Em seguinte, foi verificado a evolu??o temporal dos par?metros multifractais, um processo similar ao adotado quando aplica-se a an?lise R/S. Como um resultado, constatou-se que, durante a evolu??o da diversidade lateral esquerda do espectro D(h), esse par?metro sofre um pequeno impulso. A origem f?sica desse impulso pode estar associada ? amplitude da mem?ria derivada do n?vel de polariza??o em rela??o a linha de visada do observador. Essa caracter?stica pode abrir caminho para uma gama de especula??es, dentre elas, que a elasticidade do tecido espa?o-tempo por ser inferida pelo comportamento multifractal da onda gravitacional. / Using the recent observations of the gravitational wave GW150914 produced by the binary black holes coalescing system, the present thesis investigates the fractal and multifractal nature of the temporal variation of the strain measured by the detectors of the Observatory of Gravitational Wave by Laser Interferometry-LIGO. A selection of methods and procedures, such as the R/S andWavelet analysis, as well as the multifractal method denoted by MFDMA, were used to estimate statistical parameters that synthesize the gravitational wave as a complex time series. Whether in the Hanford or Livingston data, the fractal analysis revealed that the series presents a behavior with strong persistence and long-term memory quantified by the Hurst exponent. In addition, the strong agglomeration of the fluctuations found by the R/S analysis indicates the high degree of scale dependence characteristic of a multifractal signal. On the other hand, multifractal analysis using the MFDMA method suggests that the time-series presents a predominance of weak singularities in detriments to the strong, causing an asymmetry in the singularity spectrum D(h). In this context, two types of procedures were performed that analyze the possible sources of multifractality present in the time-series. The results show that procedures point to the existence of two multifractality regimes in the time series separated by the region where the black holes collide, referring to the Hanford data, and, for the Livingston data, near the end of the inspiral phase. Then, the temporal evolution of the multifractal parameters was verified, a process similar to that adopted when applying the R/S analysis. As a result, it was found that, during the evolution of the left lateral diversity of the spectrum D(h), this parameter undergoes a small impulse. The physical origin of this pulse may be associated with the amplitude of the memory derived from the polarization level in relation to the observer?s line of sight. This feature may open the way for a range of speculations, among them, the elasticity of the space-time fabric to be inferred by the multifractal behavior of the gravitational wave.

In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained. Firstly, starting with Connes' spectral triple for a non-empty compact totally disconnected subset E of {R} with no isolated points, we develop a noncommutative coarse multifractal formalism. Specifically, we show how multifractal properties of a measure supported on E can be expressed in terms of a spectral triple and the Dixmier trace of certain operators. If E satisfies a given porosity condition, then we prove that the coarse multifractal box-counting dimension can be recovered. We show that for a self-similar measure μ, given by an iterated function system S defined on a compact subset of {R} satisfying the strong separation condition, our noncommutative coarse multifractal formalism gives rise to a noncommutative integral which recovers the self-similar multifractal measure ν associated to μ, and we establish a relationship between the noncommutative volume of such a noncommutative integral and the measure theoretical entropy of ν with respect to S. Secondly, motivated by the results of Antonescu-Ivan and Christensen, we construct a family of (1, +)-summable spectral triples for a one-sided topologically exact subshift of finite type (∑{{A}} {{N}}, σ). These spectral triples are constructed using equilibrium measures obtained from the Perron-Frobenius-Ruelle operator, whose potential function is non-arithemetic and Hölder continuous. We show that the Connes' pseudo-metric, given by any one of these spectral triples, is a metric and that the metric topology agrees with the weak*-topology on the state space {S}(C(∑{{A}} {{N}}); {C}). For each equilibrium measure ν[subscript(φ)] we show that the noncommuative volume of the associated spectral triple is equal to the reciprocal of the measure theoretical entropy of ν[subscript(φ)] with respect to the left shift σ (where it is assumed, without loss of generality, that the pressure of the potential function is equal to zero). We also show that the measure ν[subscript(φ)] can be fully recovered from the noncommutative integration theory.