Cellulose powders from various sources were manufactured and characterized to investigate the influence of their crystallinity index, surface area, and pore volume on sorption phenomena and the relevant pharmaceutical functionality. The influence of the cellulose crystallinity index on moisture sorption was important at low and intermediate relative humidities. At high relative humidities, properties such as surface area and pore volume took precedence in governing the moisture sorption process. The theory of physical adsorption of gases onto fractal surfaces was useful for understanding the distribution of water in cellulose and the inner nanoscale structure of cellulose particles. It was found that, as a consequence of swelling, moisture induces a fractal nanopore network in cellulose powders that have a low or intermediate degree of crystallinity. On the other hand, no swelling occurs in highly crystalline cellulose powders and moisture sorption is restricted to the walls of the open pores. No correlation was found between the cellulose crystallinity index and the incorporation and release of nicotine in cellulose mixtures. By loading nicotine in highly porous matrices of the Cladophora sp. algae cellulose, higher stability against oxidative degradation, higher loading capacity, and more steady release into an air-stream was achieved than when commercially available microcrystalline cellulose was loaded. It was also shown that, by manipulating the structure of cellulose, the undesired hydrolysis of acetylsalicylic acid in mixtures with cellulose can be avoided. It was suggested that a broad hysteresis loop between the moisture adsorption and desorption curves of isotherms at low relative humidities could be indicative of an improved compatibility between acetylsalicylic acid and cellulose. In all, this thesis demonstrates how the pharmaceutical functionality of microcrystalline cellulose can be improved via engineering of the structure of native cellulose powders.

Diffusive mass transport within porous SOFC components is explored using two modeling approaches that can better inform the SOFC electrode design process. These approaches include performance metrics for electrode cross-sectional design and a fractal approach for modeling mass transport within the pore structure of the electrode reaction zone. The performance metrics presented are based on existing analytical models for transport within SOFC electrodes. These metrics include a correction factor for button-cell partial pressure predictions and two forms of dimensionless reactant depletion current density. The performance impacts of multi-dimensional transport phenomena are addressed through the development of design maps that capture the trade-offs inherent in the reduction of mass transport losses within SOFC electrode cross-sections. As a complement to these bulk electrode models, a fractal model is presented for modeling diffusion within the electrochemically active region of an SOFC electrode. The porous electrode is separated into bulk and reaction zone regions, with the bulk electrode modeled in one-dimension based on the dusty-gas formalism. The reaction zone is modeled in detail with a two-dimensional finite element model using a regular Koch pore cross-section as a fractal template for the pore structure. Drawing on concepts from the analysis of porous catalysts, this model leads to a straightforward means of assessing the performance impacts of reaction zone microstructure. Together, the modeling approaches presented provide key insights into the impacts of bulk and microstructural geometry on the performance of porous SOFC components.

Darbe pateikiamas naujas lokaliojo koliažo principu grįstas fraktalinių interpoliacinių funkcijų generavimo algoritmas (procedūra) su pilna kompiuterine realizacija. Siūlomas įrankis orientuotas į realaus pasaulio objektų (sistem��), pasižyminčių "atsikartojimu savyje" (fraktališkumu), modeliavimą. Atlikti preliminarūs eksperimentai patvirtina metodo perspektyvumą. / In the paper, a new method (tool) for the generation of fractal interpolation functions is presented. The proposed interpolation tool is oriented to process data arrays having links with real-world objects. The interpolation process itself explores self-similiarities found within data arrays under processing, as well as exciting properties of the local collage theorem. Some preliminary experimental results are presented.

[pt] A geometria fractal não é um conteúdo abordado usualmente na educação básica. O presente trabalho disserta sobre essa geometria, com o objetivo de divulgar e ampliar o conhecimento sobre ela, principalmente para professores que atuam nesse nível de escolaridade. É iniciado com um breve histórico do surgimento dos fractais, até sua definição formal, exibindo exemplos clássicos e uma pequena biografia de seus criadores. Em seguida, é apresentada uma seleção de conteúdos matemáticos que naturalmente podem ser trabalhados a partir dessa geometria. Algumas propostas de atividades que possuem fractais e podem ser aplicadas em diversos níveis da educação básica também são apresentadas. Por fim, é retratada a experiência da realização de uma das atividades propostas em uma turma de nono ano de uma escola pública do município do Rio de Janeiro. Acreditamos que a beleza e o apelo visual dos fractais atuem como elementos motivadores e inovadores para que temas importantes do currículo da educação básica sejam abordados de forma mais significativa. / [en] Fractal geometry is not a content usually addressed in basic education. This paper discusses this geometry with the purpose of disseminating and expanding knowledge about it, especially for teachers who work at this level of education. It begins with a brief history of the emergence of the fractals until its formal definition, exhibiting classic examples and a small biography of its creators. Then, we present a selection of mathematical contents of basic education that can, of course, be worked from this geometry. Some proposed activities that involve fractals and are suitable for applications at various levels of this school segment are also presented. Finally, the experience of one of the proposed activities in a 9th grade class of a public school in the city of Rio de Janeiro is portrayed. We believe that the beauty and visual appeal of fractals act as motivating and innovative elements for important themes in the basic education curriculum to be addressed in a more meaningful way.

Submitted by Lara Oliveira (lara@ufersa.edu.br) on 2017-07-18T21:43:56Z No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-25T14:46:31Z (GMT) No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-25T14:46:56Z (GMT) No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Made available in DSpace on 2017-07-25T14:47:21Z (GMT). No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) Previous issue date: 2013-11-22 / The microstrip antennas are in constant evidence in current research due to its numerous advantages. Fractal geometry proposed by Mandelbrot(1975 ) combined with the performance and convenience of planar structures are an excellent combination used in the design of antennas in order to reduce the dimensions and enhance its bandwidth, and allows the emergence of best bands frequency by virtue of ownership of high -similarity. Compared with the conventional microstrip antennas, patch antennas with fractal type substrates have lower resonance frequency, enabling the manufacture of even more compact antennas. The aim of this work consists of the design of patch antennas with dielectric substrates organized almost periodic basis through the use of fractal geometry sequence Cantor applied to a circular patch antenna fed by microstrip line, designed for a resonant frequency of 10 GHz. Analysis of this microstrip antenna is made in various types of dielectric substrates by simulation through software commercial Ansoft HFSS - Designer, used for accurate analysis of the electromagnetic behavior of the antennas by the finite element method by presenting results from resonant frequency and radiation pattern, making comparisons with other results in the literature. This dissertation also presents a bibliographic study on theories of antennas while also addressing about fractal geometry, emphasizing its characteristics and properties as well as its applicability. This paper also presents a study of almost periodic structures and their mathematical formalism considered throughout this work / As antenas de microfita estão em constante evidência nas pesquisas atuais, devido às suas inúmeras vantagens. A geometria fractal proposta por Mandelbrot (1975) aliada ao bom desempenho e comodidade das estruturas planares são uma excelente combinação utilizada no projeto de antenas com o intuito de reduzir suas dimensões e realçar sua largura de banda, além de permitir o surgimento de melhores bandas de frequência em consequência da propriedade da alto-similaridade. Em comparação com as antenas em microfita convencionais, as antenas tipo patch com substratos fractais apresentam frequência de ressonância inferiores, possibilitando a fabricação de antenas ainda mais compactas. O objetivo desse trabalho consiste no projeto de antenas patch com substrato dielétrico organizado de forma quase periódica por meio da utilização da geometria fractal da sequência de Cantor aplicada a uma antena de patch circular alimentada por linha de microfita, projetada para uma frequência ressonância de 10 GHz. É feita análise dessa antena de microfita em vários tipos de substratos dielétricos por simulação através do software comercial Ansoft Designer-HFSS, usado para análise precisa do comportamento eletromagnético das antenas através do método dos elementos finitos apresentando resultados de frequência de ressonância, diagrama de radiação, carta de Smith e de campos elétricos e magnéticos fazendo-se comparações com outros resultados obtidos na literatura. Esta dissertação ainda apresenta um estudo bibliográfico em teorias de antenas, abordando também a respeito da geometria fractal, dando ênfase a suas características e propriedades como também a sua aplicabilidade. Este trabalho ainda apresenta um estudo sobre as estruturas quase periódicas e seu formalismo matemático / 2017-07-18

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.

Made available in DSpace on 2016-06-02T20:29:20Z (GMT). No. of bitstreams: 1 5024.pdf: 3530298 bytes, checksum: 5955696c4eaa8dc8b6c5b53a0054a448 (MD5) Previous issue date: 2013-04-11 / The intention of this dissertation is to describe a didactic sequence which aims at giving conditions to students so they are able to construct notions about the applications of fractal geometry and dynamical systems, aiding them in realizing the importance of mathematics to the development of the most diverse fields of human knowledge. Mathematics, so often emphasized in classrooms, privileges its procedural aspect, forcing the student not to perceive it as a dynamic science, linked to the comprehension of phenomena in the several fields of knowledge. Euclidean Geometry, thoroughly advertised, is, in general, more appropriate to the study of shapes found in houses, bridges and machine constructions among others, and the student might be taken to assume that mathematics is distant from the shapes observed beyond the windows of the classroom, such as in clouds, trees, rays that cut the skies and so on. / Este trabalho pretende descrever uma sequência didática que visa dar condições para que os alunos construam noções sobre as aplicações da geometria fractal e dos sistemas dinâmicos, ajudando-os a perceber a importância da matemática para o desenvolvimento dos mais diversificados campos do conhecimento humano. A matemática, muitas vezes enfatizada nas salas de aula, privilegia seu aspecto procedimental, ceifando o aluno de percebê-la como uma ciência dinâmica e ligada à compreensão de fenômenos nas mais diversas áreas do conhecimento. A Geometria Euclidiana, amplamente divulgada é, em geral, mais apropriada para o estudo das formas verificadas nas construções de casas, pontes, máquinas e etc., e o aluno pode ser levado a imaginar que a matemática é distante das formas observadas além das janelas da sala de aula, como nas nuvens, flores, árvores, nos raios que cortam o céu, etc.

Made available in DSpace on 2015-03-26T13:35:25Z (GMT). No. of bitstreams: 1 texto completo.pdf: 4745443 bytes, checksum: e9df978dd48087897127e59c83f364af (MD5) Previous issue date: 2006-03-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we study the pattern formation in the interface between two types of granular materials in a Hele-Shaw cell. Different types of patterns, ranging from almost circular to fingered ones were observed, varying the ratio between the size of the grains and the cell spacing. The transition from patterns with fingers to rounded patterns seems to be continuous. The Fourier transform was obtained for the patterns with and without fingers. Patterns that present fingers showed mode selection, contrary to what happens for the rounded patterns. The dependence of the gyration radius and the number of particles at the border of the pattern was studied as a function of the number of particles inside the pattern. We observed that the gyration radius as well as the number of particles at the border of the pattern follow power laws. Analyses of the pattern border roughness showed that the Hurst exponent decreases as the patterns become more rounded. The roughness does not obey a power law with time. For the patterns with fingers the roughness increases with time and as the patterns become more regular it seem to tend to a saturation value. Finger formation is explained in terms of force transmission through the grains. / Em nosso trabalho, estudamos a formação de padrões na interface entre dois tipos de materiais granulares em uma célula de Hele-Shaw. Diferentes tipos de padrões, variando de desde quase-circulares a até padrões com dedos, formaram- se variando a razão entre o tamanho dos grãos e o espaçamento da célula. A transição de padrões com dedos para padrões arredondados parece ser contínua. Foi obtida a transformada de Fourier para os padrões com e sem dedos, sendo que padrões com dedos apresentam seleção de modos, ao contrário do que ocorre para os padrões sem dedos. A dependência do raio de giração e do número de partículas na borda do padrão foi estudada em função do número de partículas dentro do padrão. Observamos que tanto o raio de giração quanto o número de partículas na borda do padrão obedecem a leis de potência. A análise da rugosidade da borda dos padrões mostrou que o expoente de Hurst decresce à medida que os padrões se tornam mais arredondados. A rugosidade não obedece a uma lei de potência com o tempo. Para padrões com dedos a rugosidade aumenta com o tempo e à medida que os padrões se tornam mais regulares ela parece tender a um valor de saturação. A formação dos dedos é explicada em termos da transmissão de forças através dos grãos.

Les émulsions eau/eau (W/W) ont suscité un grand intérêt en raison de leur potentiel d'application dans différentes industries telles que l'agroalimentaire, les produits pharmaceutiques, les cosmétiques et les soins personnels. Le caractère particulier des émulsions W/W est leur stabilisation par ajout de particules. L’objectif de ce travail de thèse est de comprendre cet aspect en étudiant une émulsion modèle W/W à base de dextran et du poly(oxyde d'éthylène) stabilisée par des particules à base de protéines du lactosérum. Dans un premier temps, nous avons étudié l'effet de la morphologie des particules protéiques et leur partitionnement sur la stabilité des émulsions W/W. En particulier, la stabilité s’est révélée dépendre de la structure des particules quand ses derniers étaient sous forme de microgels, d’agrégats fractals ou de fibrilles. Il a été montré que la stabilité s'améliorait lorsque les particules se localiser préférentiellement dans la phase continue. Deuxièmement, nous avons étudié la gélification, des microgels et des agrégats fractals, induite en réduisant le pH entre 6,5 et 3,5 ou en ajoutant 0,3 M NaCl à pH 7,0 aussi bien quand l’excès des particules se situe dans la phase continue ou dispersée. Dans le premier cas, un réseau se formé dans la phase continue de dextran, permettant d’inhiber le crémage des gouttelettes de PEO, les agrégats fractals étant plus efficaces que les microgels. Dans le second cas, des particules protéiques denses pourraient être formées par gélification des gouttelettes de dextran dispersées. Finalement, nous avons exploré l'adsorption des protéines natives sur les particules de latex et leur capacité à stabiliser les émulsions. / Water/water (W/W) emulsions have attracted great interest recently due to their high potential for applications in different industries such as food and beverages, pharmaceutical, cosmetics and personal care. An important issue is the stabilization of W/W emulsions by adding particles. The aim of the research for this thesis was to shed light on this issue by studying a model W/W emulsion formed by mixing dextran and poly(ethylene oxide) with particles based on whey proteins. Firstly, we studied the effect of the morphology of protein particles and their partitioning on the stability of W/W emulsions. The stability was different when microgels, fractal aggregates or fibrils were added. We showed that stability improved when the particles partitioned to the continuous phase. Secondly, we investigated gelation of the fractal aggregates and microgels induced by reducing the pH between 6.5 and 3.5 or by adding 0.3M NaCl at pH 7.0 with excess particles either in the continuous or he dispersed phase. In the first case, a network was formed in the continuous dextran phase, making it possible to arrest creaming of PEO droplets, fractal aggregates being more effective than microgels. In the second case, dense protein particles could be formed by gelation of the dispersed dextran droplets. Thirdly, we explored the effect of adsorbing native proteins unto latex particles on their capacity to stabilize W/W emulsions.

Made available in DSpace on 2014-12-17T15:14:45Z (GMT). No. of bitstreams: 1 MarceloGP.pdf: 817916 bytes, checksum: e6c2bd456547cdc5605c7372ebd841db (MD5) Previous issue date: 2006-09-06 / In this thesis we study some problems related to petroleum reservoirs using methods and concepts of Statistical Physics. The thesis could be divided percolation problem in random multifractal support motivated by its potential application in modelling oil reservoirs. We develped an heterogeneous and anisotropic grid that followin two parts. The first one introduce a study of the percolations a random multifractal distribution of its sites. After, we determine the percolation threshold for this grid, the fractal dimension of the percolating cluster and the critical exponents ? and v. In the second part, we propose an alternative systematic of modelling and simulating oil reservoirs. We introduce a statistical model based in a stochastic formulation do Darcy Law. In this model, the distribution of permeabilities is localy equivalent to the basic model of bond percolation / Nesta tese estudamos alguns problemas relacionados a reservat?rios de petr?leo usando m?todos e conceitos da F?sica Estat?stica. A tese pode ser dividida em duas partes. A primeira apresenta um estudo do problema de percola??o em um suporte multifractal aleat?rio motivado por sua potencial aplica??o na modelagem de reservat?rios de petr?leo. Desenvolvemos uma rede heterog?nea e anisotr?pica que segue uma distribui??o multifractal aleat?ria das ?reas de seus s?tios. Em seguida, determinamos o limiar de percola??o nessa rede, a dimens?o fractal do aglomerado percolante e os expoentes cr?ticos ? e v. Na segunda parte, propomos uma sistem?tica alternativa de modelagem e simula??o de reservat?rios de petr?leo. Introduzimos um modelamento estat?stico baseado em uma formula??o estoc?stica da Lei de Darcy. Nele a distribui??o de permeabilidades no reservat?rio equivale localmente ao modelo b?sico de percola??o por liga??es