Análise fractal da vasculatura arteriolar e venular da retina em pessoas sem doença ocular

Although it has been suggested that retinal vasculature is a diffusion-limited aggregation (DLA) fractal, no study has been dedicated to standardizing its fractal analysis . The aims of this project was to standardize a method to estimate the fractal dimensions of retinal vasculature and to characterize their normal values; to determine if this estimation is dependent on skeletization and on segmentation and calculation methods; to assess the suitability of the DLA model and to determine the usefulness of log-log graphs in characterizing vasculature fractality . To achieve these aims, the information, mass-radius and box counting dimensions of 20 eyes vasculatures were compared when the vessels were manually or computationally segmented; the fractal dimensions of the vasculatures of 60 eyes of healthy volunteers were compared with those of 40 DLA models and the log-log graphs obtained were compared with those of known fractals and those of non-fractals. The main results were: the fractal dimensions of vascular trees were dependent on segmentation methods and dimension calculation methods, but there was no difference between manual segmentation and scale-space, multithreshold and wavelet computational methods; the means of the information and box dimensions for arteriolar trees were 1.29. against 1.34 and 1.35 for the venular trees; the dimension for the DLA models were higher than that for vessels; the log-log graphs were straight, but with varying local slopes, both for vascular trees and for fractals and non-fractals. This results leads to the following conclusions: the estimation of the fractal dimensions for retinal vasculature is dependent on its skeletization and on the segmentation and calculation methods; log-log graphs are not suitable as a fractality test; the means of the information and box counting dimensions for the normal eyes were 1.47 and 1.43, respectively, and the DLA model with optic disc seeding is not sufficient for retinal vascularization modeling

Fractais e Percolação na Recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points

Fractais e percolação na recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.

Ecologia do fitoplâncton impactado por cultivo de tilápia do Nilo, oreochromis niloticus, em tanques-rede no açude Ministro João Alves, Parelhas, Rio Grande do Norte

The dams are limnic ecosystems of great importance for its multiple uses, among them, water supply for the public and to culture of artisanal fish are most relevant. The aim of the present study is to evaluate the physical-chemical characteristics and the phytoplankton community in two chosen sites (Point 1 littoral zone of point source; Point 2 pelagic zone of non-point source) of the Minister João Alves dam, which is also known as Boqueirão de Parelhas/RN. This represents the spatial distribution of the phytoplankton species in order to understand any possible alterations of the water quality and the phytoplankton composition in relation to the water quality originating from the impact of the tilapia, Oreochromis niloticus, culture. The study period also encompasses temporal variations exhibited in two seasons of an annual cycle, one during the dry season (Oct, Nov and Dec of 2008 and Jan of 2009), and the other rainy season (Mar, Apr, May and June of 2008) to extend the observation. The physicalchemical parameters, such as pH, temperature, electrical conductivity, concentration of dissolved oxygen were measured in situ and the values of the inorganic nutrients (nitrate, ammonium and orto-phosfato) and chlorophyll in the laboratory. The quali-quantitative analyses of the phytoplankton had been carried through sedimentation technique and the enumeration of the random of 400 cells, colonies and filaments counted using Sedgwick-Rafter counting chamber. The results of pH varied widely from the acidic to alkaline range with the minimum of 5.8 (± 0.8) and the maximum of 9.2 (± 0.7-0.8), at point 1 and 2. The dissolved oxygen content was higher in the rainy period than that in the dry period. The maximum electrical conductivity was of 1409 μScm-1 in point 1 and 431 minim of μScm-1, in point 2. There was a considerable alteration in the levels of inorganic nutrients such as nitrate-nitrogen, ammoniacal nitrogen and orthophosphate during the two cycles of study period. Phytoplankton assemblages presented a picture of alternate dominance among species Cyanobacteria, Bacillariophyceae and Chlorophyceae. The trophic state index diagnosed to the category of mesotrophic, which is based on the values of chlorophyll, total phosphorus and Secchi-disc measurements. The wind driven turbulence of the water column and the fresh inflow of water (flushing and dilution) during rainy season acted as constraint and did-not allow an exaggerated growth of the species of cyanobacteria. On the basis of the present we conclude that the culture of tilapias in cage-culture fails to produce pollution load that could compromise the quality of the water of the dam, probably be due to small dimension of the culture in relation to the size, volume of the water and the reservoir capacity support its own environment