Aplicações da teoria da percolação à modelagem e simulação de reservatórios de petróleo

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 ß 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

Estudo de propriedades críticas em sistemas complexos: método de procura automática em sistemas tipo Ising e percolação de longo alcance

The new technique for automatic search of the order parameters and critical properties is applied to several well-know physical systems, testing the efficiency of such a procedure, in order to apply it for complex systems in general. The automatic-search method is combined with Monte Carlo simulations, which makes use of a given dynamical rule for the time evolution of the system. In the problems inves¬tigated, the Metropolis and Glauber dynamics produced essentially equivalent results. We present a brief introduction to critical phenomena and phase transitions. We describe the automatic-search method and discuss some previous works, where the method has been applied successfully. We apply the method for the ferromagnetic fsing model, computing the critical fron¬tiers and the magnetization exponent (3 for several geometric lattices. We also apply the method for the site-diluted ferromagnetic Ising model on a square lattice, computing its critical frontier, as well as the magnetization exponent f3 and the susceptibility exponent 7. We verify that the universality class of the system remains unchanged when the site dilution is introduced. We study the problem of long-range bond percolation in a diluted linear chain and discuss the non-extensivity questions inherent to long-range-interaction systems. Finally we present our conclusions and possible extensions of this work

Não-extensividade em percolação por ligações de longo - alcance

A linear chain do not present phase transition at any finite temperature in a one dimensional system considering only first neighbors interaction. An example is the Ising ferromagnet in which his critical temperature lies at zero degree. Analogously, in percolation like disordered geometrical systems, the critical point is given by the critical probability equals to one. However, this situation can be drastically changed if we consider long-range bonds, replacing the probability distribution by a function like . In this kind of distribution the limit α → ∞ corresponds to the usual first neighbor bond case. In the other hand α = 0 corresponds to the well know "molecular field" situation. In this thesis we studied the behavior of Pc as a function of a to the bond percolation specially in d = 1. Our goal was to check a conjecture proposed by Tsallis in the context of his Generalized Statistics (a generalization to the Boltzmann-Gibbs statistics). By this conjecture, the scaling laws that depend with the size of the system N, vary in fact with the quantitie

The Pair-Bond Formation and Its Role in the Stimulation of Reproductive Function in Female Common Marmosets (Callithrix jacchus)

SILVA, H.P.A.; SOUSA, M.B.C. The pair-bond formation and its role in the stimulation of reproductive function in female common marmosets (collithrix Jacchus). International Journal of Primatology, v, 18, n.3, p.387-400, 1997.

Estudo de sistemas complexos com interações de longo alcance : percolação, redes e tráfego

In this thesis we investigate physical problems which present a high degree of complexity using tools and models of Statistical Mechanics. We give a special attention to systems with long-range interactions, such as one-dimensional long-range bondpercolation, complex networks without metric and vehicular traffic. The flux in linear chain (percolation) with bond between first neighbor only happens if pc = 1, but when we consider long-range interactions , the situation is completely different, i.e., the transitions between the percolating phase and non-percolating phase happens for pc < 1. This kind of transition happens even when the system is diluted ( dilution of sites ). Some of these effects are investigated in this work, for example, the extensivity of the system, the relation between critical properties and the dilution, etc. In particular we show that the dilution does not change the universality of the system. In another work, we analyze the implications of using a power law quality distribution for vertices in the growth dynamics of a network studied by Bianconi and Barabási. It incorporates in the preferential attachment the different ability (fitness) of the nodes to compete for links. Finally, we study the vehicular traffic on road networks when it is submitted to an increasing flux of cars. In this way, we develop two models which enable the analysis of the total flux on each road as well as the flux leaving the system and the behavior of the total number of congested roads

The Pair-Bond Formation and Its Role in the Stimulation of Reproductive Function in Female Common Marmosets (Callithrix jacchus)

SILVA, H.P.A.; SOUSA, M.B.C. The pair-bond formation and its role in the stimulation of reproductive function in female common marmosets (collithrix Jacchus). International Journal of Primatology, v, 18, n.3, p.387-400, 1997.