102 research outputs found
Tracer Dispersion in a Self-Organized Critical System
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 cellular automaton modeling the experiment.Comment: 4 pages, RevTex, 1 Encapsulated PostScript and 4 PostScript available
upon request, Submitted to Phys. Rev. Let
Long-range effects in granular avalanching
We introduce a model for granular flow in a one-dimensional rice pile that
incorporates rolling effects through a long-range rolling probability for the
individual rice grains proportional to , being the distance
traveled by a grain in a single topling event. The exponent controls the
average rolling distance. We have shown that the crossover from power law to
stretched exponential behaviors observed experimentally in the granular
dynamics of rice piles can be well described as a long-range effect resulting
from a change in the transport properties of individual grains. We showed that
stretched exponential avalanche distributions can be associated with a
long-range regime for where the average rolling distance grows as a
power law with the system size, while power law distributions are associated
with a short range regime for , where the average rolling distance is
independent of the system size.Comment: 5 pages, 3 figure
Stretched exponentials and power laws in granular avalanching
We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion.
Comment: 8 pages, more concise and some points clarified
Avalanche statistics of sand heaps
Large scale computer simulations are presented to investigate the avalanche
statistics of sand piles using molecular dynamics. We could show that different
methods of measurement lead to contradicting conclusions, presumably due to
avalanches not reaching the end of the experimental table.Comment: 6 pages, 4 figure
Self-organized criticality in a rice-pile model
We present a new model for relaxations in piles of granular material. The
relaxations are determined by a stochastic rule which models the effect of
friction between the grains. We find power-law distributions for avalanche
sizes and lifetimes characterized by the exponents and
, respectively. For the discharge events, we find a
characteristic size that scales with the system size as , with . We also find that the frequency of the discharge events
decrease with the system size as with .Comment: 4 pages, RevTex, multicol, epsf, rotate (sty files provided). To
appear Phys. Rev. E Rapid Communication (Nov or Dec 96
Stability of Monomer-Dimer Piles
We measure how strong, localized contact adhesion between grains affects the
maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer
grains, each consisting of two spheres that have been rigidly bonded together,
with simple spherical monomer grains, we create sandpiles that contain strong
localized adhesion between a given particle and at most one of its neighbors.
We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing
fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number
fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the
increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the
surface, which reduces the density of monomers that need to be accomodated in
the most stable surface traps. A full characterization and geometrical
stability analysis of surface traps provides a good quantitative agreement
between experiment and theory over a wide range of nu_d, without any fitting
parameters.Comment: 11 pages, 12 figures consisting of 21 eps files, submitted to PR
A simple deterministic self-organized critical system
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 universality class as the Oslo rice pile system, boundary driven interface
depinning and the train model for earthquakes. Although the system is chaotic,
in the thermodynamic limit chaos occurs only in a microscopic level.Comment: System slightly modified. New results on Liapunov exponents.
Submitted for publication (8 pages
Rain: Relaxations in the sky
We demonstrate how, from the point of view of energy flow through an open
system, rain is analogous to many other relaxational processes in Nature such
as earthquakes. By identifying rain events as the basic entities of the
phenomenon, we show that the number density of rain events per year is
inversely proportional to the released water column raised to the power 1.4.
This is the rain-equivalent of the Gutenberg-Richter law for earthquakes. The
event durations and the waiting times between events are also characterised by
scaling regions, where no typical time scale exists. The Hurst exponent of the
rain intensity signal . It is valid in the temporal range from
minutes up to the full duration of the signal of half a year. All of our
findings are consistent with the concept of self-organised criticality, which
refers to the tendency of slowly driven non-equilibrium systems towards a state
of scale free behaviour.Comment: 9 pages, 8 figures, submitted to PR
Avalanche Merging and Continuous Flow in a Sandpile Model
A dynamical transition separating intermittent and continuous flow is
observed in a sandpile model, with scaling functions relating the transport
behaviors between both regimes. The width of the active zone diverges with
system size in the avalanche regime but becomes very narrow for continuous
flow. The change of the mean slope, Delta z, on increasing the driving rate, r,
obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the
continuous flow phase with an exponent theta given, paradoxically, only in
terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).Comment: Explanations added; relation to other model
Self-Structuring of Granular Media under Internal Avalanches
We study the phenomenon of internal avalanching within the context of
recently proposed ``Tetris'' lattice models for granular media. We define a
recycling dynamics under which the system reaches a steady state which is
self-structured, i.e. it shows a complex interplay between textured internal
structures and critical avalanche behavior. Furthermore we develop a general
mean-field theory for this class of systems and discuss possible scenarios for
the breakdown of universality.Comment: 4 pages RevTex, 3 eps figures, revised version to appear in Phys.
Rev. Let
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