Aging and SOC in driven dissipative systems (original) (raw)

Aging and self-organized criticality in driven dissipative systems

Physical Review E, 2001

We study the noisy dynamics of a close relative to the original sandpile model. Depending on the type of noise and the time scale of observation, we find stationary fluctuations ͑similar to self-organized criticality͒ or an aging dynamics with punctuated equilibria, a decreasing rate of events and reset properties qualitatively similar to those of glassy systems, evolution models, and vibrated granular media.

Driving, Conservation, and Absorbing States in Sandpiles

Physical Review Letters, 1998

We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension d c = 4. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions. PACS numbers: 64.60.Lx, 05.40.+j, 05.70.Ln Typeset using REVT E X 1 A wide variety of nonequilibrium systems display transitions between "active" and "absorbing" states: examples are epidemic processes [1] catalysis [2], directed percolation (DP) [3], and the depinning of interfaces in quenched disorder [4]. When driven continuously, such systems may exhibit stick-slip instabilities, or broadly distributed avalanches, commonly associated with self-organized criticality (SOC) [5,6]. SOC sandpiles [5] possess an infinite number of absorbing configurations (i.e., from which the system cannot escape), and are placed, by definition, at the critical point in a twodimensional parameter space [7,8] resembling that of directed percolation (DP) [3] or contact processes [9-11].

Critical states in a dissipative sandpile model

Physical Review E, 1999

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.

Large Fluctuations in Driven Dissipative Media

Physical Review Letters, 2011

We analyze the fluctuations of the dissipated energy in a simple and general model where dissipation, diffusion and driving are the key ingredients. The full dissipation distribution, which follows from hydrodynamic fluctuation theory, shows non-Gaussian tails and no negative branch, thus violating the fluctuation theorem as expected from the irreversibility of the dynamics. It exhibits simple scaling forms in the weak-and strong-dissipation limits, with large fluctuations favored in the former case but strongly suppressed in the latter. The typical path associated to a given dissipation fluctuation is also analyzed in detail. Our results, confirmed in extensive simulations, strongly support the validity of hydrodynamic fluctuation theory to describe fluctuating behavior in driven dissipative media.

Slow Dynamics, Aging and History-Dependent Effects in the Parking-Lot Model

Fractals, 2003

We review the properties of the Parking Lot Model and their connection with the phenomenology of vibrated granular materials. New simulation results concerning the out-of-equilibrium, aging behavior of the model are presented. We investigate in particular the relation between two-time response and correlation functions and the so-called violation of the fluctuation-dissipation theorem.

Surface fluctuations in a slowly driven granular system

Physica A: Statistical Mechanics and its Applications, 2000

We report an experiment on a granular packing: a box ÿlled with glass beads is tilted very slowly up to the maximum angle of stability where a big avalanche is produced. During the build-up period many rearrangements occur on the free surface of the packing. Digital imaging was used to study these rearrangements. The probability distribution of sizes for the observed mass uctuations follow a power-law behavior, which is the signature of self-organized criticality. However, this description breaks down in the limit of big rearrangements where inertia e ects are not negligible.

Continuously varying exponents in a sandpile model with dissipation near surface

arXiv (Cornell University), 2000

We consider the directed Abelian sandpile model in the presence of sink sites whose density f t at depth t below the top surface varies as c t −χ. For χ > 1 the disorder is irrelevant. For χ < 1, it is relevant and the model is no longer critical for any nonzero c. For χ = 1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this dependence exactly, and verify the results with simulations.

Noise Activated Granular Dynamics

Physical Review Letters, 2003

We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized "phase" one encounters two different scenarios: for moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously. PACS numbers: 02.50.Ey, 05.20.Dd, 81.05.Rm Granular gases [1], i.e. assemblies of inelastic particles losing a little kinetic energy at each collision, exhibit a variety of complex behaviors, such as clustering [2], spontaneous formation of vortices [3], lack of energy equipartition [4], non-Maxwellian velocity distributions [5]

Self-organised criticality in some dissipative sandpile models

Physica A: Statistical Mechanics and its Applications, 1997

We investigate here self-organised criticality (SOC) in two-dimensional dissipative sandpile models without the local conservation law. Both dissipative cellular automata and dissipative coupled map lattice models with open boundary conditions are considered. There appears to be no evidence for the existence of SOC in the former models. In 2he CML models, scale-invariant avalanches are observed to occur for some specific local dynamical rules. This suggests that the occurrence of SOC depends, at least in part, on the nature of the dissipative dynamics.