100 research outputs found
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
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
Universality classes for rice-pile models
We investigate sandpile models where the updating of unstable columns is done
according to a stochastic rule. We examine the effect of introducing nonlocal
relaxation mechanisms. We find that the models self-organize into critical
states that belong to three different universality classes. The models with
local relaxation rules belong to a known universality class that is
characterized by an avalanche exponent , whereas the models
with nonlocal relaxation rules belong to new universality classes characterized
by exponents and . We discuss the values
of the exponents in terms of scaling relations and a mapping of the sandpile
models to interface models.Comment: 4 pages, including 3 figure
Coiling Instabilities in Multilamellar Tubes
Myelin figures are densely packed stacks of coaxial cylindrical bilayers that
are unstable to the formation of coils or double helices. These myelin figures
appear to have no intrinsic chirality. We show that such cylindrical membrane
stacks can develop an instability when they acquire a spontaneous curvature or
when the equilibrium distance between membranes is decreased. This instability
breaks the chiral symmetry of the stack and may result in coiling. A
unilamellar cylindrical vesicle, on the other hand, will develop an
axisymmetric instability, possibly related to the pearling instability.Comment: 6 pages, 2 figure
Breakdown of self-organized criticality
We introduce two sandpile models which show the same behavior of real
sandpiles, that is, an almost self-organized critical behavior for small
systems and the dominance of large avalanches as the system size increases. The
systems become fully self-organized critical, with the critical exponents of
the Bak, Tang and Wiesenfeld model, as the system parameters are changed,
showing that these systems can make a bridge between the well known theoretical
and numerical results and what is observed in real experiments. We find that a
simple mechanism determines the boundary where self-organized can or cannot
exist, which is the presence of local chaos.Comment: 3 pages, 4 figure
Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile
We investigate the formation processes of a sandpile using numerical
simulation. We find a new relation between the fluctuation of the motion of the
top and the surface state of a sandpile. The top moves frequently as particles
are fed one by one every time interval T. The time series of the top location
has the power spectrum which obeys a power law, S(f)~f^{\alpha}, and its
exponent \alpha depends on T and the system size w. The surface state is
characterized by two time scales; the lifetime of an avalanche, T_{a}, and the
time required to cause an avalanche, T_{s}. The surface state is fluid-like
when T_{a}~T_{s}, and it is solid-like when T_{a}<<T_{s}. Our numerical results
show that \alpha is a function of T_{s}/T_{a}.Comment: 15 pages, 13 figure
Avalanche Dynamics in Wet Granular Materials
We have studied the dynamics of avalanching wet granular media in a rotating
drum apparatus. Quantitative measurements of the flow velocity and the granular
flux during avalanches allow us to characterize novel avalanche types unique to
wet media. We also explore the details of viscoplastic flow (observed at the
highest liquid contents) in which there are lasting contacts during flow,
leading to coherence across the entire sample. This coherence leads to a
velocity independent flow depth at high rotation rates and novel robust pattern
formation in the granular surface.Comment: 5 pages, 3 figures in color, REVTeX4, for smaller pdfs see
http://angel.elte.hu/~tegzes/condmat.htm
Renormalization group approach to an Abelian sandpile model on planar lattices
One important step in the renormalization group (RG) approach to a lattice
sandpile model is the exact enumeration of all possible toppling processes of
sandpile dynamics inside a cell for RG transformations. Here we propose a
computer algorithm to carry out such exact enumeration for cells of planar
lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett.
{\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed
by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690
(1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev.
Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG
transformations more quickly with large cell size, e.g. cell for
the square (sq) lattice in PVZ RG equations, which is the largest cell size at
the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51},
1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only
attractive fixed point for each lattice and calculate the avalanche exponent
and the dynamical exponent . Our results suggest that the increase of
the cell size in the PVZ RG transformation does not lead to more accurate
results. The implication of such result is discussed.Comment: 29 pages, 6 figure
Avalanche Statistics of Driven Granular Slides in a Miniature Mound
We examine avalanche statistics of rain- and vibration-driven granular slides
in miniature sand mounds. A crossover from power-law to non power-law
avalanche-size statistics is demonstrated as a generic driving rate is
increased. For slowly-driven mounds, the tail of the avalanche-size
distribution is a power-law with exponent , reasonably close to
the value previously reported for landslide volumes. The interevent occurrence
times are also analyzed for slowly-driven mounds; its distribution exhibits a
power-law with exponent .Comment: 4 pages, 3 figures, 1 tabl
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