Tracer Dispersion in a Self-Organized Critical System

Abstract

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a $1D$ cellular automaton modeling the experiment.

4 pages, RevTex, 1 Encapsulated PostScript and 4 PostScript available upon request, Submitted to Phys. Rev. Lett

References in corpus (1)

• Transport in Sand Piles, Interface Depinning, and Earthquake Models

Cited by in corpus (82)

• Colloquium: Criticality and dynamical scaling in living systems
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• The universality class of absorbing phase transitions with a conserved field
• Self-diffusion in dense granular shear flows
• Transport in Sand Piles, Interface Depinning, and Earthquake Models
• Self-organization without conservation: true or just apparent scale-invariance?
• Superconducting vortex avalanches, voltage bursts, and vortex plastic flow: Effect of the microscopic pinning landscape on the macroscopic properties
• Avalanches, Scaling and Coherent Noise
• A Simple Model of Superconducting Vortex Avalanches
• Self-Organized Bistability Associated With First-Order Phase Transitions
• Feedback mechanisms for self-organization to the edge of a phase transition
• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
• Long-Tailed Trapping Times and Levy Flights in a Self-Organized Critical Granular System
• Self-organized criticality in a rice-pile model
• Some Results and a Conjecture for Manna's Stochastic Sandpile Model
• The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
• Avalanche Merging and Continuous Flow in a Sandpile Model
• Aging in a Model of Self-Organized Criticality
• Confirming and extending the hypothesis of universality in sandpiles
• Theoretical Results for Sandpile Models of SOC with Multiple Topplings
• Self-organized bistability and its possible relevance for brain dynamics
• Exact solution of stochastic directed sandpile model
• Abelian Manna model on various lattices in one and two dimensions
• The Oslo rice pile model is a quenched Edwards-Wilkinson equation
• Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality
• A simple deterministic self-organized critical system
• Cusps, self-organization, and absorbing states
• Sandpile formation by revolving rivers
• Multifractal properties of power-law time sequences; application to ricepiles
• Universality classes for rice-pile models
• Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality
• Energy avalanches in a rice-pile model
• Criticality and self-organization in branching processes: application to natural hazards
• Correlations and hyperuniformity in the avalanche size of the Oslo Model
• How to discriminate easily between Directed-percolation and Manna scaling
• Anisotropy and universality: the Oslo model, the rice pile experiment and the quenched Edwards-Wilkinson equation
• One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve
• Probability distribution of residence times of grains in models of ricepiles
• Linking space-time correlations for a class of self-organized critical systems
• Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
• Renormalization group approach to an Abelian sandpile model on planar lattices
• Steady State and Relaxation Spectrum of the Oslo Rice-pile
• Exact solution of the totally asymmetric Oslo model
• Avalanches in Tip-Driven Interfaces in Random Media
• Avalanche Behavior in an Absorbing State Oslo Model
• Directed abelian algebras and their applications to stochastic models
• Aging Exponents in Self-Organized Criticality
• Probability distribution of residence-times of grains in sandpile models
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• $1/f^{\alpha }$ fluctuations in a ricepile model
• Temporally disordered granular flow: A model of landslides
• Stretched exponentials and power laws in granular avalanching
• Disorder-induced phase transition in a one-dimensional model of rice pile
• Breakdown of self-organized criticality
• Mapping the train model for earthquakes onto the stochastic sandpile model
• Calculation of the transition matrix and of the occupation probabilities for the states of the Oslo sandpile model
• Correlations of triggering noise in driven magnetic clusters
• Connecting the Micro-dynamics to the Emergent Macro-variables: Self-Organized Criticality and Absorbing Phase Transitions in the Deterministic Lattice Gas
• Energy fluctuations in one dimensional Zhang sandpile model
• Dynamic roughening of the magnetic flux landscape in YBa${}_2$Cu${}_3$O${}_{7-x}$
• Avalanche Mixing of Granular Solids
• Anomalous Transport in Conical Granular Piles
• Scale-free energy dissipation and dynamic phase transition in stochastic sandpiles
• Finite-size scaling of critical avalanches
• Long-range effects in granular avalanching
• One-dimensional general forest fire processes
• Anchored advected interfaces, Oslo model, and roughness at depinning
• Fine Structure of Avalanches in the Abelian Sandpile Model
• Sampling rare fluctuations of height in the Oslo ricepile model
• Universality Class of One-Dimensional Directed Sandpile Models
• Self-organised criticality in stochastic sandpiles: Connection to directed percolation
• Exponential and power law distribution of mass clusters in a (magnetic-like) deposition model of elongated grains in 2D piles
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Hyperuniformity in Ashkin-Teller model
• Cohesion induced deepening transition of avalanches
• Assortative Exchange Processes
• Depinning as a coagulation process
• Generic power laws in higher-dimensional lattice models with multidirectional hopping
• Critical Density of the Abelian Manna Model via a Multi-type Branching Process
• Absorbing phase transitions with memory in critical scaling
• Residence Time Distribution of Sand Grains in the 1-Dimensional Abelian Sandpile Model