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Previous issue date: 2017-04-13 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Nos ?ltimos anos os estudos sobre sistemas complexos vem ganhando for?a e ferramentas para poder simul?-lo e verificar seu comportamento estatisticamente. Grande parte disso se deve a muitos sistemas que passaram a se comportar de forma n?o-linear e dissipativo. Para esses casos, as geometrias convencionais como a euclidiana, n?o ? poss?vel para a proeza de explica-lo, com isso a geometria dos fractais surgiu como alternativa importante para o trato deste meio, sendo leis de escalas (pot?ncia) se aplicando muito bem para esse sistema sendo exemplificado em forma de s?ries temporais e superf?cies (geometrias bidimensionais e tridimensionais). Assim, uma variedade de m?todos foi contabilizada para esse tratamento, entre eles est?o a an?lise via expoente de Hurst e an?lise multifractal. Nosso trabalho tem como objetivo propor um novo m?todo para analisar multifractalmente imagens bidimensionais, sendo essas imagens advindas de simula??es de nuvens do meio interestelar. Primeiro passo foi gerar 12 simula??es MHD em que se diferenciavam a partir de valores de press?o e campo magn?tico, depois gerada a imagem em 2D que ? aplicado sobre elas o m?todo de tratamento multifractal MFDMA. Com a aplica??o deste m?todo ? poss?vel avaliar as imagens atrav?s de um quadro contendo os expoentes de an?lise multifractal, sendo poss?vel avaliar o comportamento de escala nas imagens e verificar o grau de complexidade, e ainda descobrir quais as fontes causadoras da multifractalidade, usando dois m?todos de an?lise multifractal que s?o embaralhamento dos dados da imagem original e substitui??o dos dados originas a partir da transformada de Fourier. Os resultados mostraram que para todas as imagens o m?todo de embaralhamento consegue destruir a fonte de multifractalidade da imagem original e ainda se comportar como um monofractal, enquanto o outro m?todo ? ineficaz, concluindo que os fatores n?o -lineares n?o est?o inclu?dos dentre as fontes e indicando como fonte de multifractalidade as correla??es de longo alcance. Outro resultado importante ? a rela??o do grau de multifractalidade ?h com a press?o. / In recent years studies on complex systems have been gaining strength and tools to be able to
simulate and verify their behavior statistically.Much of this is due to many systems that have
come to behave in a nonlinear and dissipative way.For these cases conventional geometries such
as Euclidean is not possible for the prowess of explaining it, with this the geometry of the fractals
emerged as an important alternative for the treatment of this medium,being laws of scales
(power) applying very well for this system being exemplified in the form of time series and
surfaces (two-dimensional and three-dimensional geometries).Thus a variety of methods were
counted for this treatment, among them are the analysis via exponent of Hurst and multifractal
analysis.Our work aims to propose a new method to analyze two-dimensional images multifractally,
being these images coming from clouds simulations of the interstellar medium.First
step was to generate 12 MHD simulations in which they differed from values of pressure and
magnetic field, then generated the 2D image that is applied on them the multifractal MFDMA
treatment method.With the application of this method it is possible to evaluate the images through
a frame containing the exponents of multifractal analysis, being possible to evaluate the
scale behavior in the images and verify the degree of complexity, and to find out which sources
cause multifractality,using two methods of multifractal analysis that are shuffling the original
image data and replacing the original data from the Fourier transform.The results show that for
all images the shuffling method can destroy the multifractal source of the original image and
still behave like a monofractal,While the other method is ineffective, concluding that nonlinear
factors are not included among the sources and indicating as a source of multifractality the
long-range correlations. Other important results are the relation of degree of multifractity ?h
with pressure, sonic number of Mach and number of Alfv?n.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/24734 |
| Date | 13 April 2017 |
| Creators | Moraes J?nior, Pedro Ricardo Vasconcelos de |
| Contributors | 57947139334, Martins, Bruno Leonardo Canto, 96670193491, Correia, Caio F?bio Teixeira, 00811344444, 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/masterThesis |
| 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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