Os Polímeros como Sistemas Complexos

Neste trabalho, através de simulações computacionais, identificamos os fenômenos físicos associados ao crescimento e a dinâmica de polímeros como sistemas complexos exibindo comportamentos não linearidades, caos, criticalidade auto-organizada, entre outros. No primeiro capítulo, iniciamos com uma breve introdução onde descrevemos alguns conceitos básicos importantes ao entendimento do nosso trabalho. O capítulo 2 consiste na descrição do nosso estudo da distribuição de segmentos num polímero ramificado. Baseado em cálculos semelhantes aos usados em cadeias poliméricas lineares, utilizamos o modelo de crescimento para polímeros ramificados (Branched Polymer Growth Model - BPGM) proposto por Lucena et al., e analisamos a distribuição de probabilidade dos monômeros num polímero ramificado em 2 dimensões, até então desconhecida. No capítulo seguinte estudamos a classe de universalidade dos polímeros ramificados gerados pelo BPGM. Utilizando simulações computacionais em 3 dimensões do modelo proposto por Lucena et al., calculamos algumas dimensões críticas (dimensões fractal, mínima e química) para tentar elucidar a questão da classe de universalidade. Ainda neste Capítulo, descrevemos um novo modelo para a simulação de polímeros ramificados que foi por nós desenvolvido de modo a poupar esforço computacional. Em seguida, no capítulo 4 estudamos o comportamento caótico do crescimento de polímeros gerados pelo BPGM. Partimos de polímeros criticamente organizados e utilizamos uma técnica muito semelhante aquela usada em transições de fase em Modelos de Ising para estudar propagação de danos chamada de Distância de Hamming. Vimos que a distância de Hamming para o caso dos polímeros ramificados se comporta como uma lei de potência, indicando um caráter não-extensivo na dinâmica de crescimento. No Capítulo 5 analisamos o movimento molecular de cadeias poliméricas na presença de obstáculos e de gradientes de potenciais. Usamos um modelo generalizado de reptação para estudar a difusão de polímeros lineares em meios desordenados. Investigamos a evolução temporal destas cadeias em redes quadradas e medimos os tempos característicos de transporte t. Finalizamos esta dissertação com um capítulo contendo a conclusão geral denoss o trabalho (Capítulo 6), mais dois apêndices (Apêndices A e B) contendo a fenomenologia básica para alguns conceitos que utilizaremos ao longo desta tese (Fractais e Percolação respectivamente) e um terceiro e ´ultimo apêndice (Apêndice C) contendo uma descrição de um programa de computador para simular o crescimentos de polímeros ramificados em uma rede quadrada

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

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

Representações espectrais de sistemas complexos: aplicações à síntese de superfícies brownianas fracionárias anisotrópicas, filtragem de sinais e identificação de correlações

In this thesis, we study the application of spectral representations to the solution of problems in seismic exploration, the synthesis of fractal surfaces and the identification of correlations between one-dimensional signals. We apply a new approach, called Wavelet Coherency, to the study of stratigraphic correlation in well log signals, as an attempt to identify layers from the same geological formation, showing that the representation in wavelet space, with introduction of scale domain, can facilitate the process of comparing patterns in geophysical signals. We have introduced a new model for the generation of anisotropic fractional brownian surfaces based on curvelet transform, a new multiscale tool which can be seen as a generalization of the wavelet transform to include the direction component in multidimensional spaces. We have tested our model with a modified version of the Directional Average Method (DAM) to evaluate the anisotropy of fractional brownian surfaces. We also used the directional behavior of the curvelets to attack an important problem in seismic exploration: the atenuation of the ground roll, present in seismograms as a result of surface Rayleigh waves. The techniques employed are effective, leading to sparse representation of the signals, and, consequently, to good resolutions

Estudo de Fractalidade e Evolução Dinâmica de Sistemas Complexos

In this work, the study of some complex systems is done with use of two distinct procedures. In the first part, we have studied the usage of Wavelet transform on analysis and characterization of (multi)fractal time series. We have test the reliability of Wavelet Transform Modulus Maxima method (WTMM) in respect to the multifractal formalism, trough the calculation of the singularity spectrum of time series whose fractality is well known a priori. Next, we have use the Wavelet Transform Modulus Maxima method to study the fractality of lungs crackles sounds, a biological time series. Since the crackles sounds are due to the opening of a pulmonary airway bronchi, bronchioles and alveoli which was initially closed, we can get information on the phenomenon of the airway opening cascade of the whole lung. Once this phenomenon is associated with the pulmonar tree architecture, which displays fractal geometry, the analysis and fractal characterization of this noise may provide us with important parameters for comparison between healthy lungs and those affected by disorders that affect the geometry of the tree lung, such as the obstructive and parenchymal degenerative diseases, which occurs, for example, in pulmonary emphysema. In the second part, we study a site percolation model for square lattices, where the percolating cluster grows governed by a control rule, corresponding to a method of automatic search. In this model of percolation, which have characteristics of self-organized criticality, the method does not use the automated search on Leaths algorithm. It uses the following control rule: pt+1 = pt + k(Rc − Rt), where p is the probability of percolation, k is a kinetic parameter where 0 < k < 1 and R is the fraction of percolating finite square lattices with side L, LxL. This rule provides a time series corresponding to the dynamical evolution of the system, in particular the likelihood of percolation p. We proceed an analysis of scaling of the signal obtained in this way. The model used here enables the study of the automatic search method used for site percolation in square lattices, evaluating the dynamics of their parameters when the system goes to the critical point. It shows that the scaling of , the time elapsed until the system reaches the critical point, and tcor, the time required for the system loses its correlations, are both inversely proportional to k, the kinetic parameter of the control rule. We verify yet that the system has two different time scales after: one in which the system shows noise of type 1 f , indicating to be strongly correlated. Another in which it shows white noise, indicating that the correlation is lost. For large intervals of time the dynamics of the system shows ergodicity

A Influência da observabilidade e da visualização radial no projeto de sistemas de monitoramento de redes de computadores

Este trabalho apresenta um levantamento dos problemas associados à influência da observabilidade e da visualização radial no projeto de sistemas de monitoramento para redes de grande magnitude e complexidade. Além disso, se propõe a apresentar soluções para parte desses problemas. Através da utilização da Teoria de Redes Complexas, são abordadas duas questões: (i) a localização e a quantidade de nós necessários para garantir uma aquisição de dados capaz de representar o estado da rede de forma efetiva e (ii) a elaboração de um modelo de visualização das informações da rede capaz de ampliar a capacidade de inferência e de entendimento de suas propriedades. A tese estabelece limites teóricos a estas questões e apresenta um estudo sobre a complexidade do monitoramento eficaz, eficiente e escalável de redes

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)

Comparação da análise de diferentes perfis de poços pelo método DFA

The study of complex systems has become a prestigious area of science, although relatively young . Its importance was demonstrated by the diversity of applications that several studies have already provided to various fields such as biology , economics and Climatology . In physics , the approach of complex systems is creating paradigms that influence markedly the new methods , bringing to Statistical Physics problems macroscopic level no longer restricted to classical studies such as those of thermodynamics . The present work aims to make a comparison and verification of statistical data on clusters of profiles Sonic ( DT ) , Gamma Ray ( GR ) , induction ( ILD ) , neutron ( NPHI ) and density ( RHOB ) to be physical measured quantities during exploratory drilling of fundamental importance to locate , identify and characterize oil reservoirs . Software were used : Statistica , Matlab R2006a , Origin 6.1 and Fortran for comparison and verification of the data profiles of oil wells ceded the field Namorado School by ANP ( National Petroleum Agency ) . It was possible to demonstrate the importance of the DFA method and that it proved quite satisfactory in that work, coming to the conclusion that the data H ( Hurst exponent ) produce spatial data with greater congestion . Therefore , we find that it is possible to find spatial pattern using the Hurst coefficient . The profiles of 56 wells have confirmed the existence of spatial patterns of Hurst exponents , ie parameter B. The profile does not directly assessed catalogs verification of geological lithology , but reveals a non-random spatial distribution

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Um método para localização facial Invariante a rotação

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Estudo da topologia de redes de conexão funcional no córtex sensorial primário e hipocampo durante o sono de ondas lentas

Complex network analysis is a powerful tool into research of complex systems like brain networks. This work aims to describe the topological changes in neural functional connectivity networks of neocortex and hippocampus during slow-wave sleep (SWS) in animals submited to a novel experience exposure. Slow-wave sleep is an important sleep stage where occurs reverberations of electrical activities patterns of wakeness, playing a fundamental role in memory consolidation. Although its importance there s a lack of studies that characterize the topological dynamical of functional connectivity networks during that sleep stage. There s no studies that describe the topological modifications that novel exposure leads to this networks. We have observed that several topological properties have been modified after novel exposure and this modification remains for a long time. Major part of this changes in topological properties by novel exposure are related to fault tolerance

Estudo dos óxidos A2B2O7 e ABO3 a base de terras raras, para aplicações térmicas e catalíticas a altas temperaturas

Rare earth elements have recently been involved in a range of advanced technologies like microelectronics, membranes for catalytic conversion and applications in gas sensors. In the family of rare earth elements like cerium can play a key role in such industrial applications. However, the high cost of these materials and the control and efficiencies associated processes required for its use in advanced technologies, are a permanent obstacle to its industrial development. In present study was proposed the creation of phases based on rare earth elements that can be used because of its thermal behavior, ionic conduction and catalytic properties. This way were studied two types of structure (ABO3 and A2B2O7), the basis of rare earths, observing their transport properties of ionic and electronic, as well as their catalytic applications in the treatment of methane. For the process of obtaining the first structure, a new synthesis method based on the use of EDTA citrate mixture was used to develop a precursor, which undergone heat treatment at 950 ° C resulted in the development of submicron phase BaCeO3 powders. The catalytic activity of perovskite begins at 450 ° C to achieve complete conversion at 675 ° C, where at this temperature, the catalytic efficiency of the phase is maximum. The evolution of conductivity with temperature for the perovskite phase revealed a series of electrical changes strongly correlated with structural transitions known in the literature. Finally, we can establish a real correlation between the high catalytic activity observed around the temperature of 650 ° C and increasing the oxygen ionic conductivity. For the second structure, showed clearly that it is possible, through chemical processes optimized to separate the rare earth elements and synthesize a pyrochlore phase TR2Ce2O7 particular formula. This "extracted phase" can be obtained directly at low cost, based on complex systems made of natural minerals and tailings, such as monazite. Moreover, this method is applied to matters of "no cost", which is the case of waste, making a preparation method of phases useful for high technology applications

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

Processo de difusão com agregação e reorganização espontânea em uma rede 2D

Difusive processes are extremely common in Nature. Many complex systems, such as microbial colonies, colloidal aggregates, difusion of fluids, and migration of populations, involve a large number of similar units that form fractal structures. A new model of difusive agregation was proposed recently by Filoche and Sapoval [68]. Based on their work, we develop a model called Difusion with Aggregation and Spontaneous Reorganization . This model consists of a set of particles with excluded volume interactions, which perform random walks on a square lattice. Initially, the lattice is occupied with a density p = N/L2 of particles occupying distinct, randomly chosen positions. One of the particles is selected at random as the active particle. This particle executes a random walk until it visits a site occupied by another particle, j. When this happens, the active particle is rejected back to its previous position (neighboring particle j), and a new active particle is selected at random from the set of N particles. Following an initial transient, the system attains a stationary regime. In this work we study the stationary regime, focusing on scaling properties of the particle distribution, as characterized by the pair correlation function ø(r). The latter is calculated by averaging over a long sequence of configurations generated in the stationary regime, using systems of size 50, 75, 100, 150, . . . , 700. The pair correlation function exhibits distinct behaviors in three diferent density ranges, which we term subcritical, critical, and supercritical. We show that in the subcritical regime, the particle distribution is characterized by a fractal dimension. We also analyze the decay of temporal correlations

Fluxo de fluído através de um meio poroso fractal desordenado. Análise das tensões de cisalhamento e efeito de escala na estimativa das forças viscosas

In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian fluid through a disordered porous medium modeled by a random fractal system similar to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution function follows a power law. They are randomly disposed in a rectangular channel. The velocity field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes and continuity equations at the pore level, where occurs actually the flow of fluids in porous media. The results of numerical simulations allowed us to analyze the distribution of shear stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous forces or of friction with the geometric parameters of the model, including its fractal dimension. Based on the numerical results, we proposed scaling relations involving the relevant parameters of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of the distribution of viscous stresses developed on the surface of obstacles.