Estudo das propriedades críticas do processo epidêmico por par com difusão de pares

The pair contact process - PCP is a nonequilibrium stochastic model which, like the basic contact process - CP, exhibits a phase transition to an absorbing state. While the absorbing state CP corresponds to a unique configuration (empty lattice), the PCP process infinitely many. Numerical and theoretical studies, nevertheless, indicate that the PCP belongs to the same universality class as the CP (direct percolation class), but with anomalies in the critical spreading dynamics. An infinite number of absorbing configurations arise in the PCP because all process (creation and annihilation) require a nearest-neighbor pair of particles. The diffusive pair contact process - PCPD) was proposed by Grassberger in 1982. But the interest in the problem follows its rediscovery by the Langevin description. On the basis of numerical results and renormalization group arguments, Carlon, Henkel and Schollwöck (2001), suggested that certain critical exponents in the PCPD had values similar to those of the party-conserving - PC class. On the other hand, Hinrichsen (2001), reported simulation results inconsistent with the PC class, and proposed that the PCPD belongs to a new universality class. The controversy regarding the universality of the PCPD remains unresolved. In the PCPD, a nearest-neighbor pair of particles is necessary for the process of creation and annihilation, but the particles to diffuse individually. In this work we study the PCPD with diffusion of pair, in which isolated particles cannot move; a nearest-neighbor pair diffuses as a unit. Using quasistationary simulation, we determined with good precision the critical point and critical exponents for three values of the diffusive probability: D=0.5 and D=0.1. For D=0.5: PC=0.89007(3), β/v=0.252(9), z=1.573(1), =1.10(2), m=1.1758(24). For D=0.1: PC=0.9172(1), β/v=0.252(9), z=1.579(11), =1.11(4), m=1.173(4)

Dinâmica Estocástica e Cosmologia: alguns resultados analíticos

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Um estudo na teoria do movimento brownianno com viscosidade variável

In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined. The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly. However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1

Estudo das propriedades críticas do processo epidêmico por par com difusão de pares

The pair contact process - PCP is a nonequilibrium stochastic model which, like the basic contact process - CP, exhibits a phase transition to an absorbing state. While the absorbing state CP corresponds to a unique configuration (empty lattice), the PCP process infinitely many. Numerical and theoretical studies, nevertheless, indicate that the PCP belongs to the same universality class as the CP (direct percolation class), but with anomalies in the critical spreading dynamics. An infinite number of absorbing configurations arise in the PCP because all process (creation and annihilation) require a nearest-neighbor pair of particles. The diffusive pair contact process - PCPD) was proposed by Grassberger in 1982. But the interest in the problem follows its rediscovery by the Langevin description. On the basis of numerical results and renormalization group arguments, Carlon, Henkel and Schollwöck (2001), suggested that certain critical exponents in the PCPD had values similar to those of the party-conserving - PC class. On the other hand, Hinrichsen (2001), reported simulation results inconsistent with the PC class, and proposed that the PCPD belongs to a new universality class. The controversy regarding the universality of the PCPD remains unresolved. In the PCPD, a nearest-neighbor pair of particles is necessary for the process of creation and annihilation, but the particles to diffuse individually. In this work we study the PCPD with diffusion of pair, in which isolated particles cannot move; a nearest-neighbor pair diffuses as a unit. Using quasistationary simulation, we determined with good precision the critical point and critical exponents for three values of the diffusive probability: D=0.5 and D=0.1. For D=0.5: PC=0.89007(3), β/v=0.252(9), z=1.573(1), =1.10(2), m=1.1758(24). For D=0.1: PC=0.9172(1), β/v=0.252(9), z=1.579(11), =1.11(4), m=1.173(4)