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

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

Obtenção e caracterização do sistema compósito alginato de sódio-dióxido de titânio em formas de pó e de membrana

The alginates are copolymers of 1→4-linked β-D-mannuronic acid (M) and α-Lguluronic acid (G) residues that are arranjed in a block structure along a linear chain. Titanium dioxide, TiO2, is a ceramic material and can exist in three distinct crystallography forms: anatase, brookite and rutile. composites of organic and inorganic materials have better properties than the components alone. Thus, this study aims to synthesize, characterize and analyze the composite NaAlg-TiO2 in the form of powder and film. The synthesis of composite powders was performed using the sol-gel process and obtain the composite film was performed using the slow evaporation process, then the composites were analyzed by infrared spectroscopy, fluorescence x ray, thermal analysis, attenuated total reflection (ATR), x ray diffraction and impedance spectroscopy. The X ray diffraction patterns of composite powders show that with increasing calcination temperature, there were no complete transition of rutile-anatase crystalline phase, since at all temperatures studied (300, 500, 700, 900 and 1100ºC) were observed peaks of anatase phase. Thermal analysis shows that at 400°C caused the decomposition of sodium alginate in sodium carbonate and above 600°C, we observe an exothermic peak related to the decomposition of sodium carbonate and in the presence of titanium dioxide becomes sodium titanate. The XRD results confirm the formation of sodium carbonate at 700ºC and the formation sodium titanate in the temperature range 900-1100ºC. The sodium titanate influenced the electrical properties of the material, because with increasing temperature there was a decrease in conductivity, probably due to the creation of Ti vacancies, since the sodium can induce the reduction of surface Ti4+ ions into Ti3+ species. The infrared spectra of the composites in the form of powder and film showed a small shift in the bands compared to the spectrum of pure alginate, indicating that these shifts, even small ones, have evidence of miscibility between the polymer and ceramic material

Análise estrutural e avaliação do efeito condroitim sulfato extraído de tilápia (Oreochromis niloticus) em modelo de peritonite aguda

Chondroitin sulfate (CS) is a naturally glycosaminoglycan found in the extracellular matrix of connective tissues and it may be extracted and purified those tissues. CS is involved in various biological functions, which may be related to the having structural variability, despite the simplicity of the linear chain structure from this molecule. Researches in biotechnology and pharmaceutical field with wastes from aquaculture has been developed in Brazil. In recent decades, tilapia (Oreochromis niloticus), native fish from Africa, has been one of the most cultivated species in various regions of the world, including Brazil. The tilapia farming is a cost-effective activity, however, it generates large amount of wastes that are discarded by producers. It is understood that waste from tilapia can be used in research as a source of molecules with important biotechnological applications, which also helps in reducing environmental impacts and promote the development of an ecofriendly activity. Thus, nile tilapia viscera were subjected to proteolysis, then the glycosaminoglycans were complexed with ion exchange resin (Lewatit), it was fractionated with increasing volumes of acetone and purified by ion exchange chromatography DEAE-Sephacel. Further, the fraction was analyzed by agarose gel electrophoresis and nuclear magnetic resonance (NMR). The electrophoretic profile of the compound together the analysis of 1H NMR spectra and the HSQC correlation allow to affirm that the compound corresponds to a molecule like chondroitin sulfate. MTT assay was used to assess cell viability in the presence of CS tilapia isolated and showed that the compound is not cytotoxic to normal cells such as cells from the mouse embryo fibroblast (3T3). Then, this compound was tested for the ability to reduce the influx of leukocytes in model of acute peritonitis (in vivo) induced by sodium thioglycolate. In this context, it was done total and differential leukocytes counting in the blood and peritoneal fluid collected respectively from vena cava and the peritoneal cavity of the animals subjected to the experiment. The chondroitin sulfate for the first time isolated from tilapia (CST ) was able to reduce the migration of leukocytes to the peritoneal cavity of inflamed mice until 80.4 per cent at a dose 10µg/kg. The results also show that there was a significant reduction (p<0.001) of the population of polymorphonuclear leukocytes from peritoneal cavity in the three tested doses (0.1µg/kg; 1µg/kg and 10µg/kg) when it was compared to the positive control (just thioglycolate). Therefore, since the CST structure and mechanism of action has been completely elucidated, this compound may have potential for therapeutic use in inflammatory diseases