Conselho Nacional de Desenvolvimento Científico e Tecnológico / A relação entre porosidade e permeabilidade desperta o interesse de pesquisadores e engenheiros por causa de suas diversas aplicações. Tais como na utilização de filtros, materiais pouco permeáveis, reservatórios naturais, etc. Ao longo do século XX, diversos trabalhos propondo tal relação foram apresentados na literatura e grande parte desses trabalhos desenvolvem modelos baseados na equação clássica de Kozeny-Carman. Nesta dissertação, propomos um modelo mais robusto que a formulação clássica de Kozeny-Carman, ou seja, que não apresenta as limitações dessa equação clássica. Além disso, um estudo baseado na Teoria dos Meios Fractais indica que o modelo estudado, nesta dissertação, generaliza diversas equações que fornecem a relação entre porosidade e permeabilidade. Por fim, será mostrado que o modelo proposto é capaz de descrever a relação entre porosidade e permeabilidade de diversos materiais porosos de natureza fractal. / The relationship between porosity and permeability attracts the attention of researchers and engineers because of their various applications. Such as in utilization of filters, waterproof materials, natural reservoirs, for example.Throughout the twentieth century, several works proposed in the literature they study the relation porosity-permeability, and much of this works they develop models based on the classical equation of Kozeny-Carman. In this dissertation, we propose a model more robust than the classical formulation of Kozeny-Carman, ie, that does not have the limitations of the equation classical. Furthermore, a study based on the Theory of the Media Fractals indicates that the model studied in this dissertation provide the relationship between porosity and permeability of several models presented in the literature. Finally, it will shown that the model proposed is able to describe the relationship between porosity and permeability of porous materials of various fractal nature.

Este trabalho tem por objetivo avaliar a emissão de metano em dois reservatórios amazônicos, Tucuruí e Samuel. A análise leva em consideração flutuações da área/cota e medidas isotópicas e de fluxos de d13CH4 obtidas em campo, as quais são influenciadas por diversos fatores simultaneamente, como ventos, pressão atmosférica, oxidação na coluna d´água e outros. A composição isotópica do metano em bolhas do sedimento indica que a principal via metanogênica é a redução de CO2. Os resultados também mostram que as emissões em reservatórios rasos são bem mais elevadas que nos mais profundos. Usando conceitos e técnicas da teoria fractal, baseada fundamentalmente em leis de potência, um modelo entre nível de água, área do reservatório e fluxo de metano permitiu estimar a emissão do reservatório de Tucuruí, num horizonte de 100 anos de vida útil, em 2,5 ± 2,7 x 10^6 toneladas de CH4. As emissões locais são amplificadas com a diminuição da cota, porém a emissão total do reservatório diminui, em função da contração da área do reservatório. Num cenário mais otimista, as emissões de Tucuruí em CO2 equivalentes devem ser 0,13 ± 0,14 x 10^6 toneladas de C/ano. / The purpose of this work is evaluating methane emissions from two Amazonian reservoirs, Tucuruí and Samuel. The analysis considers fluctuations of the reservoir area-height and isotopic measurements and fluxes of d13CH4 acquired in the field, which are influenced by many factors simultaneously, such as winds, atmospheric pressure, oxidation in the water column, and others. Isotopic composition of methane in bubbles indicates that CO2 reduction is a major pathway for methane production in the sediments. The results also show that fluxes are higher in shallow reservoirs than in deeper ones. Using concepts and techniques of fractal theory, fundamentally based on power law functions, and considering a time horizon of 100 years, a model between water level, flux and reservoir area of Tucuruí allowed to estimate methane emission from Tucuruí at about 2,5 ± 2,7 x 10^6 tons of CH4. When water levels drop local methane emissions are enhanced, although, total reservoir emission decreases, due to the shrinking of the reservoir area. Over an optimistic scenario, the emissions of Tucuruí reservoir in CO2 equivalents would be around 0,13 ± 0,14 x 10^6 tons C/year.

Fluxos de dados são usualmente caracterizados por grandes quantidades de dados gerados continuamente em processos síncronos ou assíncronos potencialmente infinitos, em aplicações como: sistemas meteorológicos, processos industriais, tráfego de veículos, transações financeiras, redes de sensores, entre outras. Além disso, o comportamento dos dados tende a sofrer alterações significativas ao longo do tempo, definindo data streams evolutivos. Estas alterações podem significar eventos temporários (como anomalias ou eventos extremos) ou mudanças relevantes no processo de geração da stream (que resultam em alterações na distribuição dos dados). Além disso, esses conjuntos de dados podem possuir características espaciais, como a localização geográfica de sensores, que podem ser úteis no processo de análise. A detecção dessas variações de comportamento que considere os aspectos da evolução temporal, assim como as características espaciais dos dados, é relevante em alguns tipos de aplicação, como o monitoramento de eventos climáticos extremos em pesquisas na área de Agrometeorologia. Nesse contexto, esse projeto de mestrado propõe uma técnica para auxiliar a análise espaço-temporal em data streams multidimensionais que contenham informações espaciais e não espaciais. A abordagem adotada é baseada em conceitos da Teoria de Fractais, utilizados para análise de comportamento temporal, assim como técnicas para manipulação de data streams e estruturas de dados hierárquicas, visando permitir uma análise que leve em consideração os aspectos espaciais e não espaciais simultaneamente. A técnica desenvolvida foi aplicada a dados agrometeorológicos, visando identificar comportamentos distintos considerando diferentes sub-regiões definidas pelas características espaciais dos dados. Portanto, os resultados deste trabalho incluem contribuições para a área de mineração de dados e de apoio a pesquisas em Agrometeorologia. / Data streams are usually characterized by large amounts of data generated continuously in synchronous or asynchronous potentially infinite processes, in applications such as: meteorological systems, industrial processes, vehicle traffic, financial transactions, sensor networks, among others. In addition, the behavior of the data tends to change significantly over time, defining evolutionary data streams. These changes may mean temporary events (such as anomalies or extreme events) or relevant changes in the process of generating the stream (that result in changes in the distribution of the data). Furthermore, these data sets can have spatial characteristics such as geographic location of sensors, which can be useful in the analysis process. The detection of these behavioral changes considering aspects of evolution, as well as the spatial characteristics of the data, is relevant for some types of applications, such as monitoring of extreme weather events in Agrometeorology researches. In this context, this project proposes a technique to help spatio-temporal analysis in multidimensional data streams containing spatial and non-spatial information. The adopted approach is based on concepts of the Fractal Theory, used for temporal behavior analysis, as well as techniques for data streams handling also hierarchical data structures, allowing analysis tasks that take into account the spatial and non-spatial aspects simultaneously. The developed technique has been applied to agro-meteorological data to identify different behaviors considering different sub-regions defined by the spatial characteristics of the data. Therefore, results from this work include contribution to data mining area and support research in Agrometeorology.

Submitted by Mario BC (mario@bc.ufrpe.br) on 2016-08-17T12:00:44Z No. of bitstreams: 1 Edmilson Alves de Andrade Junior.pdf: 1472865 bytes, checksum: c258f03f7b3413a264dd0531684e705d (MD5) / Made available in DSpace on 2016-08-17T12:00:44Z (GMT). No. of bitstreams: 1 Edmilson Alves de Andrade Junior.pdf: 1472865 bytes, checksum: c258f03f7b3413a264dd0531684e705d (MD5) Previous issue date: 2015-02-27 / The objective of this study was to investigate, in a class of future teachers of UFRPE, studying the discipline: "Fundamentos e Vivências em Práticas Interdisciplinares", which the conditions, obstacles and possibilities, so that the contemporary science contributes by through the training of teachers for the necessary renewal of science education. For that, we turn to the case of fractals, taking as a basis the Theory of Personal Constructs of George Kelly (1963), more specifically, the Cycle of Experience. The interlocution was structured in five stages through which students had the opportunity to anticipate and invest in building an interdisciplinary and complex thinking and later confront the new information gained from their preconceptions about the relationship between concept of fractals, the emerging paradigm and the traditional paradigm, with the possibility to modify the preconceptions. Data analysis allowed the following conclusion: the traditional and modern approach, the mathematical rigor of students and predominantly classic relations between the concept and adaptation to the current world have been enriched by a posture in which the dialogue with the uncertainty favors the development of knowledge and thinking. And besides, that is from more complex relationships that stands the perception of interdependence as well as the ideas of contemporary science. / O objetivo deste trabalho foi investigar, numa turma de licenciandos da UFRPE cursando a disciplina: Fundamentos e Vivências em Práticas Interdisciplinares, quais as condições, obstáculos e possibilidades, para que a ciência contemporânea contribua, através da formação de professores, para a necessária renovação do ensino de ciências. Para tanto se recorreu ao caso dos Fractais tendo como base a Teoria dos Construtos Pessoais de George Kelly (1963), mais especificamente o Ciclo da Experiência. A intervenção foi estruturada em cinco etapas, através das quais os alunos tiveram oportunidade de antecipar e investir na construção do pensamento interdisciplinar e complexo e, posteriormente, confrontar as novas informações adquiridas com suas concepções prévias sobre as relações entre o conceito de fractais, o paradigma tradicional e o paradigma emergente vindo a modificá-las. A análise dos dados permitiu a seguinte conclusão: a postura moderna tradicional, o rigor matemático dos alunos e as relações predominantemente clássicas estabelecidas entre o conceito e adequação ao mundo atual foram enriquecidas por uma postura onde o diálogo com a incerteza favorece o conhecer e o pensar e que é a partir das relações mais complexas que a percepção de interdependência se sobressai, bem como as ideias da ciência contemporânea.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work deals with the study of fractal geometry, emphasizing its main features included on natural systems that motivate them. Here some names that contributed to the emergence and development of mathematical fractals, emphasizing examples of natural fractals and the pioneer of Benoit B. Mandelbrot contribution . / Este trabalho trata do estudo da geometria fractal, enfatizando suas principais caracter sticas compreendidas com base nos sistemas naturais que as motivam. Apresentamos alguns nomes que contribuiram para o surgimento e desenvolvimento dos fractais matem aticos, enfatizando os exemplos de fractais naturais e a contribui c~ao do pioneiro Benoit B. Mandelbrot.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-08-17T20:58:41Z No. of bitstreams: 2 Dissertação - Henrique Carvalho Rodrigues - 2016.pdf: 19198998 bytes, checksum: 122b70383157c4896738fffa9aacf681 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-08-17T21:00:26Z (GMT) No. of bitstreams: 2 Dissertação - Henrique Carvalho Rodrigues - 2016.pdf: 19198998 bytes, checksum: 122b70383157c4896738fffa9aacf681 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-17T21:00:26Z (GMT). No. of bitstreams: 2 Dissertação - Henrique Carvalho Rodrigues - 2016.pdf: 19198998 bytes, checksum: 122b70383157c4896738fffa9aacf681 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-05-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work has as main objective the study of non-differentiable functions at all points of your domain and its relation to the construction of fractals. We have introduced important definitions and theorems of analysis for the study of non-differentiable func-tions. The subjects studied include sequences, convergence, balls, continuity and series of functions. We built examples of continuous functions without derivatives and the relationship of this process with the construction of some fractals. / O presente trabalho tem como objetivo principal, o estudo das funções não-diferenciáveis em todos os pontos do seu domínio e sua relação com a construção de fractais. Introduzimos definições e teoremas importantes da análise para o estudo das funções não-diferenciáveis. Os temas estudados incluem: sequências, convergência, bolas, continuidade e séries de funções. Construímos exemplos de funções contínuas sem derivadas e a relação desse processo com a construção de alguns Fractais.

Earthquakes are amongst the most destructive of natural phenomena and have been the subject of significant research effort over many decades, to predict the onset of seismic events. Electromagnetic emissions detected prior to earthquakes provide a potential data source for seismic predictions and research suggests that specific pre-seismic electromagnetic activity can be directly related to specific earthquakes although it is still an open issue as to the precise links between these electromagnetic emissions and subsequent earthquakes. In this research, findings of the long memory or the self-organization of several pre-earthquake MHz electromagnetic time-series provide significant outcomes regarding the earthquake prediction. It is also recognised that enhanced radon gas emission has an equally long history as being associated with seismic activity. In general, several anomalous soil radon emissions have been observed prior to earthquakes and this has been recorded all over the world. The abnormal soil radon exhalation from the interior of the earth has been associated with earthquakes and is considered as an important field of research. The research reported in this thesis compared and contrasted the merits of combining electromagnetic emission data and radon exhalation data as precursors of earthquakes with the aim of enhancing earthquake prediction methodology. The findings from the long-memory analysis of radon disturbances in the soil indicated a very significant issue: the radon disturbances in the soil prior to earthquakes exhibit similar behaviour as the MHz RF disturbances of general failure. So, the radon precursors and the MHz electromagnetic correspond to the same pre-earthquake phase. Geological explanations were proposed in view of the asperity model. Persistent and anti-persistent MHz anomalies were due to the micro-cracking of the heterogeneous medium of the earth's crust which may have led the system's evolution towards the global failure. Fractal methods have been used on historical data, to investigate MHz electromagnetic time-series spectra on emissions preceding major earthquakes over the period 2007 to 2014 and the characteristics of enhanced radon emissions have been studied over the period 2008 to 2015 for seismic events occurring in the Aegean Region. It has been found that both the electromagnetic emissions and the radon exhalation data exhibit similar fractal behaviour and are associated with impending seismic activity. Hence both phenomena are relevant to earthquake predictions and should both be employed in any systematic approach to this problem as the varying geological and geographic conditions under which earthquakes can occur, might preclude one or other data from being measurable. According to the several techniques applied in this thesis, all should be employed in sequential steps, albeit the power-law spectral fractal analysis is the most significant to trace long-memory patterns of 1/f processes as those of the processes of earthquakes.

3D fractals can be visualized as 3D objects with complex structure and has unlimited details. This thesis will be about methods to render 3D fractals effectively and efficiently, both to explore it in real-time and to create beautiful high resolution images with high details. The methods discussed is direct volume rendering with ray-casting and cut plane rendering to explore the fractal and an approach that uses super sampling to create high resolution images. Stereoscopic rendering is discussed and how it enhance the visual perception of the fractal

L'invariance d'échelle repose sur l'intuition que les dynamiques temporelles ne sont pas gouvernées par une (ou quelques) échelle(s) caratéristique(s). Cette propriété est massivement utilisée dans la modélisation et l'analyse de données univariées issues d'applications réelles. Son utilisation pratique se heurte pourtant à deux difficultés dans les applications modernes : les propriétés d'invariance d'échelle ne sont plus nécessairement homogènes en temps ou espace ; le caractère multivarié des données rend fortement non linéaires et non convexes les fonctionnelles à minimiser pour l'estimation des paramètres d'invariance d'échelle. La première originalité de ce travail est d'envisager l'étude de l'invariance d'échelle inhomogène comme un problème conjoint de détection/segmentation et estimation et d'en proposer une formulation par minimisation de fonctionnelles vectorielles, construites autour de pénalisation par variation totale, afin d'estimer à la fois les frontières délimitant les changements et les propriétés d'invariance d'échelle de chaque région. La construction d'un algorithme de débruitage par variation totale vectorielle à la volée est proposée. La seconde originalité réside dans la conception d'une procédure de minimisation de fonctionnelle non convexe type « branch and bound » pour l'identification complète de l'extension bivariée, du mouvement brownien fractionnaire, considéré comme référence pour la modélisation de l'invariance d'échelle univariée. Cette procédure est mise en œuvre en pratique sur des données de trafic Internet dans le contexte de la détection d'anomalies. Dans un troisième temps, nous proposons des contributions spécifiques au débruitage par variation totale : modèle poissonnien d'attache aux données en relation avec un problème de détection d'états pour la fluorescence intermittente ; sélection automatique du paramètre de régularisation. / Scale invariance relies on the intuition that temporal dynamics are not driven by one (or a few) characteristic scale(s). This property is massively used in the modeling and analysis of univariate data stemming from real-world applications. However, its use in practice encounters two difficulties when dealing with modern applications: scaling properties are not necessarily homogenous in time or space ; the multivariate nature of data leads to the minimization of highly non-linear and non-convex functionals in order to estimate the scaling parameters.The first originality of this work is to investigate the study of non-homogenous scale invariance as a joint problem of detection/segmentation and estimation, and to propose its formulation by the minimization of vectorial functionals constructed around a total variation penalization, in order to estimate both the boundaries delimiting the changes and the scaling properties within each region.The second originality lies in the design of a branch and bound minimization procedure of non-convex functional for the full identification of the bivariate extension of fractional Brownian motion, considered as the reference for modeling univariate scale invariance. Such procedure is applied in practice on Internet traffic data in the context of anomaly detection.Thirdly, we propose some contributions specific to total variation denoising: Poisson data-fidelity model related to a state detection problem in intermittent fluorescence ; automatic selection of the regularization parameter.

La compréhension des écoulements multiphasiques en milieu poreux revêt une importance capitale dans de nombreuses applications industrielles et environnementales, à des échelles spatiales et temporelles variées. Par conséquent, la présente étude propose une modélisation des écoulements multiphasiques en milieu poreux par le biais de la méthode Volume de Fluide, et présente des simulations de digitations de Saffman-Taylor, motivées par l'analyse d'expériences de balayage dans des blocs de grès de Bentheimer quasi bidimensionnels initialement saturés en huile extra-lourde par de l'eau. Le code Gerris, permettant des calculs parallèles efficaces à l'aide d'un maillage de type octree, est utilisé. Des tests de précision et de rapidité de calcul sont réalisés à l'aide de divers niveaux de raffinement, ainsi qu'une comparaison avec des simulations de référence dans la littérature. Des simulations 3D dans des milieux réels numérisés sont réalisés avec des résultats encourageants. Même s'il n'est pas encore possible d'atteindre des nombres capillaires réalistes, des écoulements dans des domaines cubiques de 1 mm de côté sont simulés, avec un temps de calcul raisonnable. Des simulations 2D de digitations visqueuses avec injection centrale ou latérale sont également présentées, basées sur la loi de Darcy. L'aspect fractal des digitations est étudié aussi bien à l'aide de la dimension fractale que de la variation de l'aire des motifs obtenus par rapport à leur périmètre. Enfin, des balayages à l'aide de polymères suivant des balayages à l'eau dans un processus en deux temps sont simulés à partir d'une modélisation darcéenne. / Understanding multiphase flow in porous media is of tremendous importance for many industrial and environmental applications at various spatial and temporal scales. The present study consequently focuses on modelling multiphase flows by the Volume-of-Fluid method in porous media and shows simulations of Saffman-Taylor fingering motivated by the analysis of waterflooding experiments of extra-heavy oils in quasi-2D square slab geometries of Bentheimer sandstone. The Gerris code which allows efficient parallel computations with octree mesh refinement is used. It is tested for accuracy and computational speed using several levels of refinement and comparing to reference simulations in the literature. Simulations of real rocks are realised in three dimensions with very promising results. Though it is not yet possible to attain realistic capillary numbers, it is possible to simulate flows in domains of physical size up to 1 mm3 in reasonable CPU time. 2D simulations of viscous fingering with both central and lateral injection are also presented in this study, based on Darcy's law. The fractal aspect of this fingering is studied by considering both its fractal dimension and the variation of the area of the resulting pattern with respect to its arclength. Finally, polymer flooding following waterflooding in a two-step process is simulated with Darcy modelling.