1,568 research outputs found
Anomalous scaling in the Zhang model
We apply the moment analysis technique to analyze large scale simulations of
the Zhang sandpile model. We find that this model shows different scaling
behavior depending on the update mechanism used. With the standard parallel
updating, the Zhang model violates the finite-size scaling hypothesis, and it
also appears to be incompatible with the more general multifractal scaling
form. This makes impossible its affiliation to any one of the known
universality classes of sandpile models. With sequential updating, it shows
scaling for the size and area distribution. The introduction of stochasticity
into the toppling rules of the parallel Zhang model leads to a scaling behavior
compatible with the Manna universality class.Comment: 4 pages. EPJ B (in press
Immunization of complex networks
Complex networks such as the sexual partnership web or the Internet often
show a high degree of redundancy and heterogeneity in their connectivity
properties. This peculiar connectivity provides an ideal environment for the
spreading of infective agents. Here we show that the random uniform
immunization of individuals does not lead to the eradication of infections in
all complex networks. Namely, networks with scale-free properties do not
acquire global immunity from major epidemic outbreaks even in the presence of
unrealistically high densities of randomly immunized individuals. The absence
of any critical immunization threshold is due to the unbounded connectivity
fluctuations of scale-free networks. Successful immunization strategies can be
developed only by taking into account the inhomogeneous connectivity properties
of scale-free networks. In particular, targeted immunization schemes, based on
the nodes' connectivity hierarchy, sharply lower the network's vulnerability to
epidemic attacks
Dynamically Driven Renormalization Group
We present a detailed discussion of a novel dynamical renormalization group
scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general
renormalization method developed for dynamical systems with non-equilibrium
critical steady-state. The method is based on a real space renormalization
scheme driven by a dynamical steady-state condition which acts as a feedback on
the transformation equations. This approach has been applied to open non-linear
systems such as self-organized critical phenomena, and it allows the analytical
evaluation of scaling dimensions and critical exponents. Equilibrium models at
the critical point can also be considered. The explicit application to some
models and the corresponding results are discussed.Comment: Revised version, 50 LaTex pages, 6 postscript figure
Ordering phase transition in the one-dimensional Axelrod model
We study the one-dimensional behavior of a cellular automaton aimed at the
description of the formation and evolution of cultural domains. The model
exhibits a non-equilibrium transition between a phase with all the system
sharing the same culture and a disordered phase of coexisting regions with
different cultural features. Depending on the initial distribution of the
disorder the transition occurs at different values of the model parameters.
This phenomenology is qualitatively captured by a mean-field approach, which
maps the dynamics into a multi-species reaction-diffusion problem.Comment: 11 pages, 10 figures, accepted for publication in EPJ
Self-organized criticality as an absorbing-state phase transition
We explore the connection between self-organized criticality and phase
transitions in models with absorbing states. Sandpile models are found to
exhibit criticality only when a pair of relevant parameters - dissipation
epsilon and driving field h - are set to their critical values. The critical
values of epsilon and h are both equal to zero. The first is due to the absence
of saturation (no bound on energy) in the sandpile model, while the second
result is common to other absorbing-state transitions. The original definition
of the sandpile model places it at the point (epsilon=0, h=0+): it is critical
by definition. We argue power-law avalanche distributions are a general feature
of models with infinitely many absorbing configurations, when they are subject
to slow driving at the critical point. Our assertions are supported by
simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive,
periodic boundaries), and of the slowly-driven pair contact process. We
formulate a field theory for the sandpile model, in which the order parameter
is coupled to a conserved energy density, which plays the role of an effective
creation rate.Comment: 19 pages, 9 figure
Critical exponents in stochastic sandpile models
We present large scale simulations of a stochastic sandpile model in two
dimensions. We use moments analysis to evaluate critical exponents and finite
size scaling method to consistently test the obtained results. The general
picture resulting from our analysis allows us to characterize the large scale
behavior of the present model with great accuracy.Comment: 6 pages, 4 figures. Invited talk presented at CCP9
Dynamical and correlation properties of the Internet
The description of the Internet topology is an important open problem,
recently tackled with the introduction of scale-free networks. In this paper we
focus on the topological and dynamical properties of real Internet maps in a
three years time interval. We study higher order correlation functions as well
as the dynamics of several quantities. We find that the Internet is
characterized by non-trivial correlations among nodes and different dynamical
regimes. We point out the importance of node hierarchy and aging in the
Internet structure and growth. Our results provide hints towards the realistic
modeling of the Internet evolution.Comment: 4 pages, 4 EPS figure
- …