Propriedades críticas do processo epidêmico difusivo com interação de Lévy

The diffusive epidemic process (PED) is a nonequilibrium stochastic model which, exhibits a phase trnasition to an absorbing state. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants DA and DB, respectively. According to a Wilson renormalization calculation, the system presents a first-order phase transition, for the case DA > DB. Several researches performed simulation works for test this is conjecture, but it was not possible to observe this first-order phase transition. The explanation given was that we needed to perform simulation to higher dimensions. In this work had the motivation to investigate the critical behavior of a diffusive epidemic propagation with Lévy interaction(PEDL), in one-dimension. The Lévy distribution has the interaction of diffusion of all sizes taking the one-dimensional system for a higher-dimensional. We try to explain this is controversy that remains unresolved, for the case DA > DB. For this work, we use the Monte Carlo Method with resuscitation. This is method is to add a sick individual in the system when the order parameter (sick density) go to zero. We apply a finite size scalling for estimates the critical point and the exponent critical =, e z, for the case DA > DB

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)