This thesis deals with nonlinear physics and chaos theory from its begining, through the main people to its application in various fields. This work has also part of fractals and fractal geometry. There are also source codes of various examples.

Submitted by (lucia.rodrigues@ufrpe.br) on 2016-06-01T16:45:23Z No. of bitstreams: 1 Fernanda Katharine de Souza Lins Borba.pdf: 4059966 bytes, checksum: cce20c494a8d5b3926e4508d0ff50750 (MD5) / Made available in DSpace on 2016-06-01T16:45:23Z (GMT). No. of bitstreams: 1 Fernanda Katharine de Souza Lins Borba.pdf: 4059966 bytes, checksum: cce20c494a8d5b3926e4508d0ff50750 (MD5) Previous issue date: 2012-02-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Chondroitin Sulfate (CS) and Glucosamine Sulfate (GS) are functional constituents of vertebrate tissues. GS is an amino sugar and CS is part of the glucosaminoglycans group (GAGs). Studies have suggested CS and GS to have anti-inflammatory properties, however it has also been shown that these compounds promote scarring and proliferation of fibroblasts, which express molecules important for blood vessel growth (angiogenesis). This study was aimed at evaluating the effects of CS and GS on in vitro models regarding cell viability (cytotoxicity - MTT), proliferation (BrdU incorporation) and differentiation (tubulogenesis in Matrigel support) on human umbilical vein endothelial cells (HUVEC line). In vivo angiogenesis was also evaluated in (1) extraembryonic membranes of Gallus domesticus (number of chorioallantoic vessels - CAM assay and vitelinic YSM assay; and fractal geometry analysis); (2) and subcutaneous tissue of adult mice (Mus muscullus) by hemoglobin quantification (Spectroscopy) in Gelfoam implants. In the HUVEC assay, both CS and GS (1-3000 g/mL) displayed partial cytotoxic effect (~50% viability), but only in the highest tested concentrations (3000 and 1000 g/mL). It was observed that CS (3 g/mL), but not GS, promoted proliferation and tubulogenesis of HUVEC in 40% (P < 0.05) and 64% (P < 0.05), respectively, relative to control (RPMI-1640 medium). These effects did not significantly differ from the respective 28% and 53% promoted by the well known angiogenic growth factor FGF-2 (50 ng/mL). In the in vivo vasculoangiogenesis YSM assay on 2 to 4-day old embryos, GS (0.001-0.1mg/disk) and, to a lesser extent, CS (0.030-0.1mg/disk) increased the amount of vessels relative to control (P < 0.05). The effects of administration of CS and GS (0.1mg/disk) did not differ from what was observed in groups treated with 50 ng/mL FGF2. In the CAM angiogenesis assay on 6 to 8-days old embryos, again both CS and GS increased the amount of vessels relative to control, but only in concentrations as high as 2.0 mg/disk. This effect was no different from what was observed in groups treated with 50 ng/mL FGF2. The pro-angiogenic effects of CS (2 mg/disk) in embryonary angiogenesis were confirmed in the advanced angiogenesis of mice: only the group treated with CS (2 mg/implant) displayed a significant increase in the amount of blood vessels, expressed as hemoglobin content (0.52 ± 0.08g/dL), relative to control (vehicle; PBS; 0.20 ± 0.07 g/dL). This pro-angiogenic effect was no different than that of FGF2 (0.53 ± 0.1g/dL). The in vitro and in vivo results indicate the pro-angiogenic properties of CS and GS. However, CS (GAG) was the more effective compound in the tests performed. As a constituent of proteoglycans, it is suggested that CS exerts its effects by interacting with FGF and other angiogenic factors in the extracellular matrix, stabilizing the receptor, and thus positively modulating the pro-angiogenic signal in endothelial cells. While the cellular mechanisms underlying CS and GS activity demand more specific research, there is an evident potential therapeutic use for both compounds in clinical situations, such as those related to vascular discrepancy. / Sulfato de glucosamina (SG) e Sulfato de condroitina (SC) são constituintes funcionais dos tecidos de vertebrados. O SG é um aminoaçúcar e o SC integra o grupo das glicosaminoglicanas (GAG). Estudos apontam propriedades antiinflamatórias do SC e SG, e demonstram ainda que essas substâncias promovem a cicatrização e a proliferação de fibroblastos, os quais expressam moléculas que atuam na formação de vasos sanguíneos (angiogênese). Os objetivos deste estudo foram avaliar a ação do SC e SG em modelos in vitro sobre a viabilidade (citotoxicidade pelo MTT), proliferação (incorporação por BrdU) e diferenciação (tubulogênese em suporte matrigel) na linhagem de células endoteliais de veia umbilical humana (HUVEC). Também se investigou a angiogênese in vivo: (1) em membranas anexas de embriões de Gallus domesticus (número de vasos corioalantóides - ensaio da CAM, e vitelínicos – ensaio da YSM; e análise por geometria fractal); (2) e no tecido subcutâneo de camundongos adultos por meio de quantificação da hemoglobina em implantes de Gelfoam. No ensaio com HUVEC, SC e SG (1-3000 g/mL) exerceram efeito citotóxico parcial (~50% de viabilidade), e somente nas respectivas maiores concentrações (3000 e 1000 g/mL). Verificou-se que o SC (3 g/mL), mas não o SG, estimulou a proliferação e a tubulogênese de HUVEC em 40% (p < 0,05) e em 64% (p < 0,05) respectivamente, em relação ao controle (meio RPMI-1640). Estes efeitos não diferiram estatisticamente dos 28% e 53%, respectivamente, promovidos pelo bem conhecido fator de crescimento angiogênico FGF-2 (50 ng/mL). No ensaio de vasculo-angiogênese na YSM de embriões de 2-4 dias de idade o SG (0,001-0,1mg/disco) principalmente, e o SC (0,030-0,1mg/disco) aumentaram o número de vasos em relação ao grupo controle (p < 0,05). Os efeitos da administração de SC e SG (0,1 mg/disco) não diferiram do observado no grupo tratado com 50 ng/mL de FGF-2. No ensaio de angiogênese na CAM de embriões de 6-8 dias de idade, ambos, SC e SG também elevaram o número de vasos em relação ao controle na concentração elevada de 2,0 mg/disco. Este efeito também não diferiu do observado no grupo exposto a 50 ng/mL de FGF- 2. O efeito pró-angiogênico do SC (2 mg/disco) na angiogênese embrionária foi confirmado na angiogênese avançada de camundongos adultos. Apenas o grupo que recebeu SC (2 mg/implante) mostrou um aumento significativo de vasos sanguíneos, expresso como conteúdo de hemoglobina (0,52 ± 0,08g/dL), comparado ao controle (veículo; PBS; 0,20 ± 0,07 g/dL). Este efeito pró-angiogênico não diferiu do obtido com FGF2 (0,53 ± 0.1g/dL). Os resultados in vitro e in vivo demonstram as propriedades pró-angiogênicas do SC e SG, contudo o SC (GAG) foi o mais efetivo nos ensaios. Como um constituinte de proteoglicanas, o SC sugere exercer seus efeitos pela interação com o FGF e outros fatores angiogênicos na matriz extracelular, estabilizando-os nos receptores e modulando assim, positivamente, o sinal pró-angiogênico nas células endoteliais. Embora mecanismos celulares subjacentes à atividade de SC e SG demandem mais estudos, evidencia-se um potencial papel terapêutico das duas substâncias em situações clínicas relacionadas à defasagem vascular.

Made available in DSpace on 2016-03-15T19:37:49Z (GMT). No. of bitstreams: 1 Paulo Cesar da Costa.pdf: 4253113 bytes, checksum: 8fe9dda35243a879336e5fa6037d55cb (MD5) Previous issue date: 2014-02-18 / The concepts of fractal geometry, which were developed in 1975 by Mandelbrot, complement Euclidean geometry as they provide theoretical dimensional fundamentals for shapes whose irregularities cannot be properly interpreted by classical topological definitions. The standards of this irregular morphology, found in abundance in nature, can be recognized in the construction processes of various fractals anthropic figures, mainly when combined with computational technology. Professionals and researchers from several knowledge fields are exploring these concepts to simulate or create models of irregular shapes, with detail levels hitherto inconceivable. Earth sciences supported by geotechnologies have great potential for applying Mandelbrot s theories as a conceptual reference for analyzing phenomena presenting fractal behaviors, belonging to different application areas as geomorphology, climatology and urban and landscapes studies. In this approach, the fractal dimension of the territorial space occupied by cities is considered an indicator for understanding occupation patterns as one of the factors to be considered in urban planning policies, e.g., to propose projects for more appropriate investments distribution and development of infrastructure. In this work, these concepts were applied by using the box-counting method to calculate the fractal dimension of urban forms from eight Brazilian state capitals by using the Municipal Human Development Index (MHDI) as the selection criteria: four cities ranked among the top of the list and four cities classified among the last positions of the state capitals. The results were analyzed in order to identify possible relationships or trends among these indicators, namely, fractal dimension and MHDI, that may support future studies and urban planning. These relationships were not confirmed: the eight studied cities presented heterogeneous fractal dimension values and no trends were verified. However, it was concluded that the fractal dimension of urban form is related to its scattering pattern and occupation over the geographical territorial space and may be an indicator of the occupation density from the urban area. / Os conceitos da geometria fractal, desenvolvida em 1975 por Mandelbrot, complementam os da geometria euclidiana à medida que fornecem um arcabouço teórico de cálculo dimensional para diversas formas cujas irregularidades apresentam características que não podem ser interpretadas adequadamente pelas definições topológicas clássicas. Os padrões dessa morfologia irregular, encontrada em abundância na natureza, podem ser reproduzidos em processos de construção de figuras fractais desenvolvidas pelo homem, especialmente quando combinadas com a tecnologia computacional. Profissionais e pesquisadores de diversas áreas de conhecimento passaram a explorar esses conceitos a fim de simular ou criar modelos de formas irregulares, com níveis de detalhe até então inconcebíveis. As ciências da Terra, com o apoio de ferramentas de geotecnologia, apresentam grande potencial de se apropriar das teorias da geometria de Mandelbrot, como referência conceitual aos estudos de fenômenos que apresentam comportamento fractal, pertencentes a várias áreas de aplicação como a geomorfologia, climatologia e os estudos urbanos e de paisagens. Nessa abordagem, a dimensão fractal do espaço territorial ocupado pelas cidades vem sendo considerada indicador importante para entendimento desse padrão de ocupação, contribuindo como um dos fatores a ser considerados nas políticas de planejamento urbano e, por exemplo, propor projetos de distribuição de investimentos e desenvolvimento de infraestrutura mais adequados. Neste trabalho, esses conceitos foram aplicados por meio da utilização do método da contagem de quadrados para calcular a dimensão fractal das formas urbanas de oito capitais brasileiras, utilizando o Índice de Desenvolvimento Humano Municipal (IDHM) de 2010, publicado em julho de 2013, como critério de seleção. Foram escolhidas quatro cidades classificadas entre as primeiras da lista e outras quatro que ocupam as últimas posições entre as capitais estaduais, com o objetivo de encontrar possíveis relações ou tendências entre esses indicadores dimensão fractal e IDHM que pudessem subsidiar futuros estudos e planejamentos urbanos. Os resultados obtidos não revelaram a existência de tais relações: as oito cidades estudadas apresentaram valores dimensionais heterogêneos, sem registro de tendências. No entanto, foi possível concluir que a dimensão fractal de uma forma urbana está relacionada ao seu padrão de espalhamento e ocupação do espaço territorial geográfico e pode ser considerada um indicador da densidade de ocupação da área urbana.

La méthode de minimisation de l'intégrale d'action (principe variationnel) permet d’obtenir les équations de propagation des ondes. Cette méthode a été généralisée aux milieux poreux de dimensions fractales, pour étudier la propagation acoustique dans le domaine temporel, en se basant sur le modèle du fluide équivalent. L'équation obtenue réécrite dans le domaine fréquentiel représente une généralisation de l'équation d'Helmholtz. Dans le cadre du modèle d'Allard-Johnson, l'équation de propagation a été résolue de manière analytique dans le domaine temporel, dans les régimes des hautes et des basses fréquences. La résolution a été faite par la méthode de la transformée de Laplace, et a porté sur un milieu poreux semi-infini. Il a été trouvé que la vitesse de propagation dépend de la dimension fractale. Pour un matériau poreux fractal d'épaisseur finie qui reçoit une onde acoustique en incidence normale, les conditions d’Euler ont été utilisées pour déterminer les champs réfléchi et transmis. La résolution du problème direct a été faite dans le domaine temporel, par la méthode de la transformée de Laplace, et par l’usage des fonctions de Mittag-Leffler. Le problème inverse a été résolu par la méthode de minimisation aux sens des moindres carrés. Des tests ont été effectués avec succès sur des données expérimentales, en utilisant des programmes numériques développés à partir du formalisme établi dans cette thèse. La résolution du problème inverse a permis de retrouver les paramètres acoustiques de mousses poreuses, dans les régimes des hautes et des basses fréquences. / The action integral minimization method (variational principle) provides the wave propagation equations. This method has been generalized to fractal dimensional porous media to study the acoustic propagation in the time domain, based on the equivalent fluid model. The resulting equation rewritten in the frequency domain represents a generalization for the Helmholtz equation. As part of the Allard-Johnson model, the propagation equation was solved analytically in the time domain, for both high and low frequencies fields. The resolution was made by the method of the Laplace transform, and focused on a semi-infinite porous medium. It was found that the wave velocity depends on the fractal dimension.For a fractal porous material of finite thickness which receives an acoustic wave at normal incidence, the Euler conditions were used to determine the reflected and transmitted fields. The resolution of the direct problem was made in the time domain by the method of the Laplace transform, and through the use of the Mittag-Leffler functions. The inverse problem was solved by the method of minimizing the least squares sense. Tests have been performed successfully on experimental data; programs written from the formalism developed in this work have allowed finding the acoustic parameters of porous foams, in the fields of high and low frequencies.

Un modèle complet permettant de simuler la dynamique d'un nano-aérosol est présenté et discuté. On considère une équation Eulérienne de type « Diffusion-Inertia » réécrite en moments en incluant un terme source de coagulation. Le phénomène de dépôt est pris en compte par l'intermédiaire d'une condition aux limites sur le flux de moments à la paroi. L'expression de la granulométrie en moments permet d'obtenir une très bonne efficacité de calcul et rend ainsi le modèle utilisable pour des applications industrielles ou en santé au travail. L'implémentation de cette approche dans un code de CFD est validée sur des cas simples par comparaison avec une méthode des classes ainsi que des données expérimentales. La méthode des moments n'introduit pas de biais particulier et les résultats numériques sont en accord avec les résultats expérimentaux. Un nouveau dispositif expérimental, qui consiste en une enceinte ventilée, est également proposé afin de maîtriser au mieux l'écoulement et de caractériser la morphologie des agrégats générés. La confrontation entre les résultats numériques et expérimentaux met en évidence le fait que la détermination des paramètres fractals est un élément clé de la modélisation / A complete CFD model for nano-aerosol dynamics is presented and discussed. It consists in an Eulerian "Diffusion-Inertia" equation including a coagulation source term which is rewritten in terms of moments. Deposition phenomenon is taken into account by means of a boundary condition on the flux of moments at walls. The moment transformation allows good computational performances and makes thus the model tractable for industrial and occupational health applications. The implementation of this approach into a CFD code is assessed for simple cases by comparison with sectional approach results and experimental data. These comparisons show that the method of moments does not induce particular bias and that numerical results are in good agreement with available experimental data. An experimental set-up, which consists in a ventilated chamber, is also proposed for allowing a good control of the flow and for allowing the investigation of aggregates morphology. The confrontation between numerical and experimental results highlights that the determination of the fractal parameters is a modelling key point

Visible and near-infrared diffuse reflectance spectroscopy has been demonstrated to be a fast and cheap tool for estimating a large number of chemical and physical soil properties, and effective features extracted from spectra are crucial to correlating with these properties. We adopt a novel methodology for feature extraction of soil spectroscopy based on fractal geometry. The spectrum can be divided into multiple segments with different step–window pairs. For each segmented spectral curve, the fractal dimension value was calculated using variation estimators with power indices 0.5, 1.0 and 2.0. Thus, the fractal feature can be generated by multiplying the fractal dimension value with spectral energy. To assess and compare the performance of new generated features, we took advantage of organic soil samples from the large-scale European Land Use/Land Cover Area Frame Survey (LUCAS). Gradient-boosting regression models built using XGBoost library with soil spectral library were developed to estimate N, pH and soil organic carbon (SOC) contents. Features generated by a variogram estimator performed better than two other estimators and the principal component analysis (PCA). The estimation results for SOC were coefficient of determination (R2) = 0.85, root mean square error (RMSE) = 56.7 g/kg, the ratio of percent deviation (RPD) = 2.59; for pH: R2 = 0.82, RMSE = 0.49 g/kg, RPD = 2.31; and for N: R2 = 0.77, RMSE = 3.01 g/kg, RPD = 2.09. Even better results could be achieved when fractal features were combined with PCA components. Fractal features generated by the proposed method can improve estimation accuracies of soil properties and simultaneously maintain the original spectral curve shape.

Cílem této práce je se seznámení s možnostmi programu Matlab z hlediska detailní analýzy deterministických dynamických systémů. Jedná se především o analýzu časové posloupnosti a o nalezení Lyapunových exponentů. Dalším cílem je navrhnout algoritmus umožňující specifikovat chování systému na základě znalosti příslušných diferenciálních rovnic. To znamená, nalezení chaotických systémů.

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The invention of the Glancing Angle Deposition (GLAD) technique a decade ago enabled the fabrication of nanostructured thin films with highly tailorable structural, electrical, optical, and magnetic properties. Here a three-dimensional atomic-scale growth simulator has been developed to model the growth of thin film materials fabricated with the GLAD technique, utilizing the Monte Carlo (MC) and Kinetic Monte Carlo (KMC) methods; the simulator is capable of predicting film structure under a wide range of deposition conditions with a high degree of accuracy as compared to experiment. The stochastic evaporation and transport of atoms from the vapor source to the substrate is modeled as random ballistic deposition, incorporating the dynamic variation in substrate orientation that is central to the GLAD technique, and surface adatom diffusion is modeled as either an activated random walk (MC), or as energy dependent complete system transitions with rates calculated based on site-specific bond counting (KMC). The Sculptured Nanostructured Film Simulator (SNS) provides a three-dimensional physical prediction of film structure given a set of deposition conditions, enabling the calculation of film properties including porosity, roughness, and fractal dimension. Simulations were performed under various growth conditions in order to gain an understanding of the effects of incident angle, substrate rotation, tilt angle, and temperature on the resulting morphology of the thin film. Analysis of the evolution of film porosity during growth suggests a complex growth dynamic with significant variations with changes in tilt or substrate motion, in good agreement with x-ray reflectivity measurements. Future development will merge the physical structure growth simulator, SNS, with Finite-Difference Time-Domain (FDTD) electromagnetics simulation to allow predictive design of nanostructured optical materials. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-03-31 13:22:11.843