Resumo em Inglês:

A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the relaxation of the system toward its stationary system. Bases on the first behavior, static phase transitions (discontinuous changes in the stationary profiles of the system) are studied. Based on the second behavior, dynamical phase transitions (discontinuous changes in the relaxation-times of the system) are studied. The investigation is specialized on systems in which the evolution equation of one-point functions are closed (the autonomous systems)

Resumo em Inglês:

Phase transitions of reaction-diffusion systems with a site occupation restriction, particle creation requiring n > 2 parents, and in which explicit diffusion of single particles (A) is possible, are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of nonequilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some recent numerical analyses. Simulation results for one- and two-dimensional binary spreading model, 2A -> 4A, 4A -> 2A, reveal a new type of mean-field criticality characterized by the critical exponents a = 1/3 and b = 1/2, as suggested in a recent preprint [cond-mat/0210615]

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This work presents an analytical investigation for a Self-Organized Criticality abelian model that describes basic properties of rainfall phenomena. The knowledge of the exact solution for the probability that a site topples when mass is added to any other site of the lattice leads to a large number properties of the model, including the exponent of the power law that describes presence of the events as function of their magnitude. It is shown that the model belongs to the same universality class of a first model proposed by Dhar and Ramaswamy (DR). However, for finite size lattices, it is found that its exponent is larger than that one for the DR model.

Resumo em Inglês:

A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit nonequilibrium phase transitions, which can be classified into universality classes. Here we study in detail one such class that can be mapped into a Kardar-Parisi-Zhang (KPZ) interface equation with a positive (negative) non-linearity in the presence of a bounding lower (upper) wall. The wall limits the possible values taken by the height variable, introducing a lower (upper) cut-off, and induces a phase transition between a pinned (active) and a depinned (absorbing) phase. This transition is studied here using mean field and field theoretical arguments, as well as from a numerical point of view. Its main properties and critical features, as well as some challenging theoretical difficulties, are reported. The differences with other multiplicative noise and bounded-KPZ universality classes are stressed, and the effects caused by the introduction of "attractive" walls, relevant in some physical contexts, are also analyzed.

Resumo em Inglês:

We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable partial reflector. These processes serve as simplified models of infection in a medium with a history-dependent susceptibility, and for spreading in systems with an infinite number of absorbing configurations. The memory may take the form of a historydependent step length, or be the result of a partial reflector whose position marks the maximum distance the walker has ventured from the origin. In each case, a process with memory is rendered Markovian by a suitable expansion of the state space. Asymptotic analysis of the probability generating function shows that, for large t, the survival probability decays as S(t) ~ t -d, where d varies with the parameters of the model. We report new results for a hard partial reflector, i.e., one that moves forward only when the walker does. When the walker tries to jump to the site R occupied by the reflector, it is reflected back with probability r, and stays at R with probability 1 - r; only in the latter case does the reflector move (R ® R+1). For this model, d = 1/2(1 - r), and becomes arbitrarily large as r approaches 1. This prediction is confirmed via iteration of the transition matrix, which also reveals slowly-decaying corrections to scaling.

Resumo em Inglês:

We study the damage spreading in the one-dimensional Ising model by means of the stochastic dynamics resulting from coupling the system and its replica by a family of algorithms that interpolate between the heat bath and the Hinrichsen-Domany algorithms. At high temperatures the dynamics is exactly mapped to the Domany-Kinzel probabilistic cellular automaton. Using a mean-field approximation and Monte Carlo simulations we find the critical line that separates the phase where the damage spreads from the one where it does not.

Resumo em Inglês:

We present a pedagogical account of the Lee-Yang theory of equilibrium phase transitions and review recent advances in applying this theory to nonequilibrium systems. Through both general considerations and explicit studies of specific models, we show that the Lee-Yang approach can be used to locate and classify phase transitions in nonequilibrium steady states.

Resumo em Inglês:

In this paper we review and discuss some fundamental aspects of the random version of the Olami-Feder- Christensen model, and its relevance for the understanding of self-organized criticality (SOC). We review the universal character of the exponent <img width=32 height=32 id="_x0000_i1026" src="../../img/revistas/bjp/v33n3/a09img01.gif" align=absmiddle > or = 3/2, related to avalanche size distributions in random SOC models, and its connection to branching processes theory. We also generalize previous results, that had been obtained for the random OFC model with four neighbors, to any coordination number. Finally we present some connections between our generalization and recent discussions involving the branching rate approach to this model.

Resumo em Inglês:

We studied in this work a competitive reaction model between monomers on a catalyst. The catalyst is represented by hypercubic lattices in d = 1, 2 and 3 dimensions. The model is described by the following reactions: A + A -> A2 and A + B -> AB, where A and B are two monomers that arrive at the surface with probabilities yA and yB, respectively. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that, for all d, the model exhibits a continuous phase transition between an active steady state and a B-absorbing state, when the parameter yA is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents b,n^ and the dynamical critical exponents n||, d, h and z. The results found for this competitive reaction model are in accordance with the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class.

Resumo em Inglês:

Pinning-depinning transitions are roughening transitions separating a growing phase and pinned (or blocked) one, and are frequently connected to transitions into absorbing states. In this review, we discuss lattice growth models exhibiting this type of dynamic transition. Driven growth in media with impurities, the competition between deposition and desorption and deposition of poisoning species are some of the physical mechanisms responsible for the transitions, leading to different types of stochastic growth rules. The growth models are classified according to the those mechanisms and possible applications are shown, which include suggestions of experimental realizations of directed percolation transitions.

Resumo em Inglês:

Spatially distributed genetic populations that compete locally for resources and mate only with sufficiently close neighbors, may give rise to spontaneous pattern formation. Depending on the population parameters, like death rate per generation and size of the competition and mating neighborhoods, isolated groups of individuals, or demes, may appear. The existence of such groups in a population has consequences for genetic diversity and for speciation. In this paper we discuss the robustness of demes formation with respect to two important characteristics of the population: the way individuals recognize the demarcation of the local neighborhoods and the way competition for resources affects the birth rate in an overcrowed situation. Our results indicate that demes are expected to form only for sufficiently sharp demarcations and for sufficiently intense competition.

Resumo em Inglês:

This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are not subject to constrained evolution rules. After a short review of some of these models, the paper discusses how two particularly simple kinds of models, the Potts model and the exclusion models, evolve after a quench at low temperature to glassy states rather than to crystalline states.

Resumo em Inglês:

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe some of the results obtained in the context of synchronization of chaotic dynamical systems. Moreover, we discuss the relation of the synchronization transition with some interfacial models.

Resumo em Inglês:

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product ansatz. Due to the similarity of the master equation and the Schrodinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. Initially, we present the solution of the problem when an arbitrary mixture of molecules, each of then having an arbitrary size (s = 0; 1; 2; ...) in units of lattice spacing, diffuses asymmetrically on the lattice. The solution of the more general problem where we have the diffusion of particles belonging to N distinct classes of particles (c = 1; ... ; N), with hierarchical order and arbitrary sizes, is also presented. Our matrix product ansatz asserts that the amplitudes of an arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed by a product of matrices. The algebraic properties of the matrices defining the ansatz depend on the particular associated Hamiltonian. The absence of contradictions in the algebraic relations defining the algebra ensures the exact integrability of the model. In the case of particles distributed in N > 2 classes, the associativity of this algebra implies the Yang-Baxter relations of the exact integrable model.

Resumo em Inglês:

We present a general field-theoretic strategy to analyze three connected families of continuous phase transitions which occur in nonequilibrium steady-states. We focus on transitions taking place between an active state and one absorbing state, when there exist an infinite number of such absorbing states. In such transitions the order parameter is coupled to an auxiliary field. Three situations arise according to whether the auxiliary field is diffusive and conserved, static and conserved, or finally static and not conserved.

Resumo em Inglês:

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.

Resumo em Inglês:

We review some results concerning the energetic and dynamical consequences of taking a generic hydrophobic model of a random polypeptide chain, where the effective hydrophobic interactions are represented by Hookean springs. Then we present a set of calculations on a microscopic model of hydrophobic interactions, investigating the behaviour of a hydrophobic chain in the vicinity of a hydrophobic boundary. We conclude with some speculations as to the thermodynamics of pre-biotic functions proteins may have discharged very early on in the evolutionary past.

Resumo em Inglês:

The manufacture of high resistance concrete or hard ceramics needs extremely dense granular packings. They can only be realised when the size distribution of grains is strongly polydisperse. Typically powerlaw distributions give the best results. We present a simple packing model for polydisperse distributions, namely a generalized reversible parking lot model. We also discuss the perfectly dense limit, namely Apollonian packings in three dimensions and show in particular the existence of space filling bearings rotating without slip and without torsion.

Resumo em Inglês:

We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical mechanics model. The model is based on percolation and bond-fluctuation dynamics. By opportunely varying some model parameter we are able to describe a crossover from the chemical gelation behaviour to dynamics more typical of colloidal systems. The results suggest a novel connection linking classical gelation, as originally described by Flory, to more recent results on colloidal systems.

Resumo em Inglês:

Studying simple artificial peptides, we show that recently developed simulation techniques enable efficient investigations of secondary structure formation and folding in small peptides.

Resumo em Inglês:

This paper describes an innovative technique, the gradient pattern analysis (GPA), for analysing spatially extended dynamics. The measures obtained from GPA are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. By means of four gradient moments it is possible to quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. The GPA technique is applied for the first time in 3D-simulated molecular chains with the objective of characterizing small symmetry breaking, amplitude and phase disorder due to spatio-temporal fluctuations driven by the spatially extended dynamics of a relaxation regime.

Resumo em Inglês:

We review mean-field and fluctuation-dominated behaviors exhibited by the Seceder Model, which moves an evolving population to various critical states of self-organized segregation, delicately balancing opposed sociological pressures of conformity & dissent, and giving rise to rich ideological condensation phenomena. The secession exponent and finite societal Seceder limits are examined.

Resumo em Inglês:

A 1 = L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18; 22;... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at p c for an annulus with aspect ratio r = 1=2 is estimated as C = 0.876657(45).

Resumo em Inglês:

We study the plausibility of the handicap principle, using a bit-string model to represent both the genoma and the phenotype of the individuals of a population. We find that the distribution of genoma of population selforganizes due to the natural selection. The phenotype represents some trait of the interaction of individuals with others and with the environment so, it also suffers the pressure of natural selection. The handicap is introduced in sexual selection. At time of reproduction, females compare males according to the phenotype, choosing the one who has a phenotype representing the greatest handicap. Our results show that in this way females are able to see the quality of their possible mates and males have no possibility to cheat due to pressure of natural selection.

Resumo em Inglês:

One species is simulated to split into two separate species via random mutations, even if both populations live together in the same environment. This speciation is achieved in the Penna bitstring model of biological ageing, with modified Verhulst factors, and in part by additional bitstrings regulating phenotype and mate selection.

Resumo em Inglês:

In this paper we review the trajectory of a model proposed by Stauffer and Weisbuch in 1992 to describe the evolution of the immune repertoire and present new results about its dynamical behavior. Ten years later this model, which is based on the ideas of the immune network as proposed by Jerne, has been able to describe a multi-connected network and could be used to reproduce immunization and aging experiments performed with mice. The immunization protocol is simulated by introducing small and large perturbations (damages), and in this work we discuss the role of both. Besides its biological implications, the physical aspects of the complex dynamics of this network is very interesting per se. In a very recent paper we studied the aging effects by using auto-correlation functions, and the results obtained apparently indicated that the small perturbations would be more important than the large ones, since their cumulative effects may change the attractor of the dynamics. However our new results indicate that both types of perturbations are important. It is the cooperative effects between both that lead to the complex behavior which allows to reproduce experimental results.

Resumo em Inglês:

The combined influence of linear damping and noise on a dynamical finite-time-singularity model is considered for a single degree of freedom. The noise resolves the finite-time-singularity and replaces it by a first-passagetime distribution with a peak at the singularity and a long time tail. The damping introduces a characteristic cross-over time. In the early time regime the first-passage-time distribution shows a power law behavior with scaling exponent depending on the ratio of the non linear coupling strength to the noise strength. In the late time regime the damping prevails. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.

Resumo em Inglês:

Recently a multifractal object, Qmf, was proposed to allow the study of percolation properties in a multifractal support. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, p c, is a function of r, a parameter of Qmf which is related to its anisotropy. We investigate the relation between p c and the average number of neighbors of the blocks as well as the anisotropy of Qmf.

Resumo em Inglês:

Bootstrap percolation models describe systems as diverse as magnetic materials, fluid flow in rocks and computer storage systems. The models have a common feature of requiring not just a simple connectivity of neighbouring sites, but rather an environment of other suitably occupied sites. Different applications as well as the connection with the mathematical literature on these models is presented. Visualizations that show the compact nature of the clusters are provided.

Resumo em Inglês:

The long-range bond-percolation problem, on a linear chain (d = 1), in the presence of diluted sites (with an occupancy probability p s for an active site) is studied by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance r ij is given by p ij = <img width=32 height=32 id="_x0000_i1026" src="../../img/revistas/bjp/v33n3/a32img01.gif" align=absbottom>, where p represents the usual occupancy probability between nearest-neighbor sites. This model allows one to analyse the competition between long-range bonds (which enhance percolation) and diluted sites (which weaken percolation). By varying the parameter a (a > 0), one may find a crossover between a nonextensive regime and an extensive regime; in particular, the cases a = 0 and a ® ¥ represent, respectively, two well-known limits, namely, the mean-field (infinite-range bonds) and first-neighbor-bond limits. The percolation order parameter, P¥, was investigated numerically for different values of a and p s. Two characteristic values of a were found, which depend on the site-occupancy probability p s, namely, a1(p s) and a2(p s) (a2(p s) > a1(p s) > 0). The parameter P¥ equals unit, "p > 0, for 0 < a < a1(p s) and vanishes, "p < 1, for a > a2(p s). In the interval a1(p s) < a < a2(p s), the parameter P¥ displays a familiar behavior, i.e., 0 for p < p c(a) and finite otherwise. It is shown that both a1(p s) and a2(p s) decrease with the inclusion of diluted sites. For a fixed p s, it is shown that a convenient variable, p* º p*(p, a, N), may be defined in such a way that plots of P¥ versus p* collapse for different sizes and values of a in the nonextensive regime.