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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.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/22338 |
| Date | 12 December 2016 |
| Creators | Nepomuceno, Mackson Matheus Fran?a |
| Contributors | 57947139334, http://lattes.cnpq.br/2709876077692695, Medeiros, Jos? Renan de, 08896135400, http://lattes.cnpq.br/9151590034650501, Mohan, Madras Viswanathan Gandhi, 04295882755, http://lattes.cnpq.br/1995273890709490, Aguiar, Odylio Denys de, 85144703887, http://lattes.cnpq.br/3325984959083987, Holanda, Rodrigo Fernandes Lira de, 00832667471, http://lattes.cnpq.br/2669928747407450, Freitas, Daniel Brito de |
| Publisher | PROGRAMA DE P?S-GRADUA??O EM F?SICA, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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