Comment on ``Self-organized criticality and absorbing states: Lessons from the Ising model"

According to Pruessner and Peters [Phys. Rev. E {\bf 73}, 025106(R) (2006)], the finite size scaling exponents of the order parameter in sandpile models depend on the tuning of driving and dissipation rates with system size. We point out that the same is not true for {\em avalanches} in the slow driving limit.Comment: 3 pages, 1 figure, to appear in Phys. Rev.

Renormalization group of probabilistic cellular automata with one absorbing state

We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small transition probability one of the cellular automata reduces to the contact process revealing that the cellular automata are in the same universality class as that process, as expected. Better numerical results are obtained as the approximations for the stationary distribution are improved.Comment: Errors in some formulas have been corrected. Additional material available at http://mestre.if.usp.br/~javie

Energy constrained sandpile models

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy $E$ becomes the only parameter governing the dynamical behavior of the system. Both models show scale free behavior at a critical value $E_c$ of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different universality class than self-organized critical sandpiles. Despite this difference, the activity (avalanche) probability distributions appear to coincide with the one of the standard self-organized critical sandpile.Comment: 4 pages including 3 figure

Statistical Agent Based Modelization of the Phenomenon of Drug Abuse

We introduce a statistical agent based model to describe the phenomenon of drug abuse and its dynamical evolution at the individual and global level. The agents are heterogeneous with respect to their intrinsic inclination to drugs, to their budget attitude and social environment. The various levels of drug use were inspired by the professional description of the phenomenon and this permits a direct comparison with all available data. We show that certain elements have a great importance to start the use of drugs, for example the rare events in the personal experiences which permit to overcame the barrier of drug use occasionally. The analysis of how the system reacts to perturbations is very important to understand its key elements and it provides strategies for effective policy making. The present model represents the first step of a realistic description of this phenomenon and can be easily generalized in various directions.Comment: 12 pages, 5 figure

Roughness of Sandpile Surfaces

We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields different asymptotic scaling exponents. Using approximate analytical arguments and extensive numerical studies we conclude that this ambiguity is due to the special scaling properties of the nonlinear steady state surface. We also find that there is no such ambiguity for non-SOC models, although there may be intermediate crossovers to different roughness values. Such crossovers need to be distinguished from the true asymptotic behaviour, as in the case of a noncritical disordered sandpile model studied in [10].Comment: 5 pages, 4 figures. Accepted for publication in Phys. Rev.

Universality in sandpiles

We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered a systematic bias. We identify the correct scaling behavior and conclude that sandpiles with stochastic and deterministic toppling rules belong to the same universality class.Comment: 4 pages, 4 ps figures; submitted to Phys. Rev.

Application of a renormalization group algorithm to nonequilibrium cellular automata with one absorbing state

We improve a recently proposed dynamically driven renormalization group algorithm for cellular automata systems with one absorbing state, introducing spatial correlations in the expression for the transition probabilities. We implement the renormalization group scheme considering three different approximations which take into account correlations in the stationary probability distribution. The improved scheme is applied to a probabilistic cellular automaton already introduced in the literature.Comment: 7 pages, 4 figures, to be published in Phys. Rev.

Critical behavior of a one-dimensional fixed-energy stochastic sandpile

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $\zeta_c$ of the particle density. Critical exponents are obtained from extensive simulations, which treat both stationary and transient properties. In contrast with other one-dimensional sandpiles, the model appears to exhibit finite-size scaling, though anomalies exist in the scaling of relaxation times and in the approach to the stationary state. The latter appear to depend strongly on the nature of the initial configuration. The critical exponents differ from those expected at a linear interface depinning transition in a medium with point disorder, and from those of directed percolation.Comment: 15 pages, 11 figure

Mean-field behavior of the sandpile model below the upper critical dimension

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in $d=4$ significantly differ from mean-field predictions, thus suggesting an upper critical dimension $d_c\geq 5$. Using the relations among the dissipation rate $\epsilon$ and the finite lattice size $L$, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.Comment: 4 RevTex pages, 2 eps figures embedde

Invasion threshold in heterogeneous metapopulation networks

We study the dynamics of epidemic and reaction-diffusion processes in metapopulation models with heterogeneous connectivity pattern. In SIR-like processes, along with the standard local epidemic threshold, the system exhibits a global invasion threshold. We provide an explicit expression of the threshold that sets a critical value of the diffusion/mobility rate below which the epidemic is not able to spread to a macroscopic fraction of subpopulations. The invasion threshold is found to be affected by the topological fluctuations of the metapopulation network. The presented results provide a general framework for the understanding of the effect of travel restrictions in epidemic containment.Comment: 4 pages, 2 figure