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.

Pecolação em uma rede multifractal

In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf

Fractal analysis of eroded surfaces by digital image processing

Jet impingement erosion test rig has been used to erode titanium alloy specimens (Ti-4Al-4V). Eroded surface profiles have been obtained by vertical sectioning method for light microscopy observation. Mixed fractals have been measured from profile images by a digital image processing and analysis technique. The use of this technique allows glimpsing a quantitative correlation among material properties, fractal surface topography and erosion phenomena. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Fractal analysis along stretch zone for an aluminum alloy

The topography of fracture surface along stretch zone front for Al7050 is analyzed about its fractal behavior and compared against local distributions of microstructural parameters and stretch zone height, considered here as a toughness parameter. Major influence on microscale was presented by precipitation density. Larger grains should be significant on topographic behavior at macroscale, besides the local toughness measured along stretch zone. The large scattering of fractal measurements along specimen width should limit the validity of models relating fractal values and fracture toughness. It is proposed that models based on mixed fractals must also consider some dispersion parameter instead of mean fractal measurements due to the overall complexity of fracture relief formation. It is suggested that sampling for fractal measurement must be restricted to plane strain region along fracture surface, due to smaller scattering in this region. (C) 2004 Elsevier B.V. All rights reserved.

Universaidade em sistemas da mecâniaestatística de não equilíbrio com estados absorventes e percolação geográfica

Complex systems have stimulated much interest in the scientific community in the last twenty years. Examples this area are the Domany-Kinzel cellular automaton and Contact Process that are studied in the first chapter this tesis. We determine the critical behavior of these systems using the spontaneous-search method and short-time dynamics (STD). Ours results confirm that the DKCA e CP belong to universality class of Directed Percolation. In the second chapter, we study the particle difusion in two models of stochastic sandpiles. We characterize the difusion through diffusion constant D, definite through in the relation h(x)2i = 2Dt. The results of our simulations, using finite size scalling and STD, show that the diffusion constant can be used to study critical properties. Both models belong to universality class of Conserved Directed Percolation. We also study that the mean-square particle displacement in time, and characterize its dependence on the initial configuration and particle density. In the third chapter, we introduce a computacional model, called Geographic Percolation, to study watersheds, fractals with aplications in various areas of science. In this model, sites of a network are assigned values between 0 and 1 following a given probability distribution, we order this values, keeping always its localization, and search pk site that percolate network. Once we find this site, we remove it from the network, and search for the next that has the network to percole newly. We repeat these steps until the complete occupation of the network. We study the model in 2 and 3 dimension, and compare the bidimensional case with networks form at start real data (Alps e Himalayas)

Bioglass Associated With Leukocyte-Poor Platelet-Rich Plasma in the Rabbit Maxillary Sinus: Histomorphometric, Densitometric, and Fractal Analysis

The objective of the present study was to evaluate the outcomes of autogenous bone graft (AB) and bioglass (BG) associated or not with leukocyte-poor platelet-rich plasma (LP-PRP) in the rabbit maxillary sinus (MS) by histomorphometric and radiographic analysis. Twenty rabbits divided into 2 groups (G1, G2) were submitted to sinus lift surgery. In G1, 10 MS were grafted with AB and 10 MS were grafted with BG. In G2, 10 MS were grafted with AB + LP-PRP and 10 MS were grafted with BG + LP-PRP. After 90 days, the animals were killed and specimens were obtained, x-rayed, and submitted to histomorphometric, radiographic bone density (RD) and fractal dimension analysis. Radiographic bone density mean values (SD), expressed as aluminum equivalent in mm, of AB, BG, AB + LP-PRP, and BG + LP-PRP groups were 1.79 (0.31), 2.04 (0.39), 1.61 (0.28), and 1.53 (0.30), respectively. Significant differences (P < 0.05) were observed between BG and AB, and BG + PRP and BG. Fractal dimension mean values were 1.48 (0.04), 1.35 (0.08), 1.44 (0.04), and 1.44 (0.06), respectively. Significant differences were observed between BG and AB, and AB + LP-PRP and BG. Mean values for the percentage of bone inside MS were 63.30 (8.60), 52.65 (10.41), 55.25 (7.01), and 51.07 (10.25), respectively. No differences were found. No correlations were observed among percentage of bone, RD and FD. Histological analysis showed that MS treated with AB presented mature and new bone formation. The other groups showed minor bone formation. Within the limitations of this study, the results indicated that at a 90-day time end point, AB yielded better results than AB + LP-PRP, BG, and BG + LP-PRP and should be considered the primary material for MS augmentation.

On turbulent, erratic and other dynamical properties of Zadeh's extensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Soliton parameters and chaotic sets

In this work we apply a nonperturbative approach to analyze soliton bifurcation ill the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is non-restrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations ill the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena. (C) 2009 Published by Elsevier Ltd.

Low dimensional behavior in three-dimensional coupled map lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multifractal regime transition in a modified minority game model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Basins of attraction changes by amplitude constraining of oscillators with limited power supply

We investigate the dynamics of a Duffing oscillator driven by a limited power supply, such that the source of forcing is considered to be another oscillator, coupled to the first one. The resulting dynamics come from the interaction between both systems. Moreover, the Duffing oscillator is subjected to collisions with a rigid wall (amplitude constraint). Newtonian laws of impact are combined with the equations of motion of the two coupled oscillators. Their solutions in phase space display periodic (and chaotic) attractors, whose amplitudes, especially when they are too large, can be controlled by choosing the wall position in suitable ways. Moreover, their basins of attraction are significantly modified, with effects on the final state system sensitivity. (c) 2005 Elsevier Ltd. All rights reserved.

Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving; the equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure. (C) 2004 Elsevier Ltd. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.