Related papers: Self-Organized Criticality in a Bulk Driven One-Di…
We introduce a new continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any kind of embedded randomness, not even in the initial conditions. This system is in the same…
Using the Bak-Sneppen model of biological evolution as our paradigm, we investigate in which cases noise can be substituted with a deterministic signal without destroying Self-Organized Criticality (SOC). If the deterministic signal is…
The train model which is a variant of the Burridge-Knopoff earthquake model is investigated for a velocity-strengthening friction law. It shows self-organized criticality with complex scaling exponents. That is, the probability density…
We identify a new universality class in one-dimensional driven open quantum systems with a dark state. Salient features are the persistence of both the microscopic non-equilibrium conditions as well as the quantum coherence of dynamics…
A simple model economy with locally interacting producers and consumers is introduced. When driven by extremal dynamics, the model self-organizes {\em not} to an attractor state, but to an asymptote, on which the economy has a constant rate…
We have investigated the essential ingredients allowing a system to show Self Organized Criticality (SOC) in its collective behavior. Using the Bak-Sneppen model of biological evolution as our paradigm, we show that the random microscopic…
In this work, we explore an unconventional class of problems in the study of (quantum) critical phenomena, termed ''deep boundary criticality''. Traditionally, critical systems are analyzed with two types of perturbations: those uniformly…
We make an extensive numerical study of a two dimensional nonconservative model proposed by Olami-Feder-Christensen to describe earthquake behavior. By analyzing the distribution of earthquake sizes using a multiscaling method, we find…
Models of self-organized criticality, which can be described as singular diffusions with or without (multiplicative) Wiener forcing term (as e.g. the Bak/Tang/Wiesenfeld- and Zhang-models), are analyzed. Existence and uniqueness of…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…
The dynamics of critical slope self-organized critical models is studied, using a previous mapping into a linear interface depinning model dragged at one end. The model is solved obtaining the complete set of scaling exponents. Some results…
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…
A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities…
Self-Organized Criticality is the emergence of long-ranged spatio-temporal correlations in non-equilibrium steady states of slowly driven systems without fine tuning of any control parameter. Sandpiles were proposed as prototypical examples…
We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical…
We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory…