35 research outputs found
Particle-hole symmetry in a sandpile model
In a sandpile model addition of a hole is defined as the removal of a grain
from the sandpile. We show that hole avalanches can be defined very similar to
particle avalanches. A combined particle-hole sandpile model is then defined
where particle avalanches are created with probability and hole avalanches
are created with the probability . It is observed that the system is
critical with respect to either particle or hole avalanches for all values of
except at the symmetric point of . However at the
fluctuating mass density is having non-trivial correlations characterized by
type of power spectrum.Comment: Four pages, our figure
From waves to avalanches: two different mechanisms of sandpile dynamics
Time series resulting from wave decomposition show the existence of different
correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld
model, long range correlations determine a modification of the wave size
distribution under coarse graining in time, and multifractal scaling for
avalanches. In the Manna model, the distribution of avalanches coincides with
that of waves, which are uncorrelated and obey finite size scaling, a result
expected also for the d=3 Bak et al. model.Comment: 5 pages, 4 figure
On the scaling behavior of the abelian sandpile model
The abelian sandpile model in two dimensions does not show the type of
critical behavior familar from equilibrium systems. Rather, the properties of
the stationary state follow from the condition that an avalanche started at a
distance r from the system boundary has a probability proportional to 1/sqrt(r)
to reach the boundary. As a consequence, the scaling behavior of the model can
be obtained from evaluating dissipative avalanches alone, allowing not only to
determine the values of all exponents, but showing also the breakdown of
finite-size scaling.Comment: 4 pages, 5 figures; the new version takes into account that the
radius distribution of avalanches cannot become steeper than a certain power
la
Non conservative Abelian sandpile model with BTW toppling rule
A non conservative Abelian sandpile model with BTW toppling rule introduced
in [Tsuchiya and Katori, Phys. Rev. E {\bf 61}, 1183 (2000)] is studied. Using
a scaling analysis of the different energy scales involved in the model and
numerical simulations it is shown that this model belong to a universality
class different from that of previous models considered in the literature.Comment: RevTex, 5 pages, 6 ps figs, Minor change
Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
We study probability distributions of waves of topplings in the
Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves
represent relaxation processes which do not contain multiple toppling events.
We investigate bulk and boundary waves by means of their correspondence to
spanning trees, and by extensive numerical simulations. While the scaling
behavior of avalanches is complex and usually not governed by simple scaling
laws, we show that the probability distributions for waves display clear power
law asymptotic behavior in perfect agreement with the analytical predictions.
Critical exponents are obtained for the distributions of radius, area, and
duration, of bulk and boundary waves. Relations between them and fractal
dimensions of waves are derived. We confirm that the upper critical dimension
D_u of the model is 4, and calculate logarithmic corrections to the scaling
behavior of waves in D=4. In addition we present analytical estimates for bulk
avalanches in dimensions D>=4 and simulation data for avalanches in D<=3. For
D=2 they seem not easy to interpret.Comment: 12 pages, 17 figures, submitted to Phys. Rev.
Probability distribution of the sizes of largest erased-loops in loop-erased random walks
We have studied the probability distribution of the perimeter and the area of
the k-th largest erased-loop in loop-erased random walks in two-dimensions for
k = 1 to 3. For a random walk of N steps, for large N, the average value of the
k-th largest perimeter and area scales as N^{5/8} and N respectively. The
behavior of the scaled distribution functions is determined for very large and
very small arguments. We have used exact enumeration for N <= 20 to determine
the probability that no loop of size greater than l (ell) is erased. We show
that correlations between loops have to be taken into account to describe the
average size of the k-th largest erased-loops. We propose a one-dimensional
Levy walk model which takes care of these correlations. The simulations of this
simpler model compare very well with the simulations of the original problem.Comment: 11 pages, 1 table, 10 included figures, revte
Avalanche Polynomials of some Families of Graphs
We study the abelian sandpile model on different families of graphs. We introduced the avalanche polynomial which enumerates the size of the avalanches triggered by the addition of a particle on a recurrent configuration. This polynomial is calculated for several families of graphs. In the case of the complete graph, the result involves some known result on Parking function
Two-lane traffic rules for cellular automata: A systematic approach
Microscopic modeling of multi-lane traffic is usually done by applying
heuristic lane changing rules, and often with unsatisfying results. Recently, a
cellular automaton model for two-lane traffic was able to overcome some of
these problems and to produce a correct density inversion at densities somewhat
below the maximum flow density. In this paper, we summarize different
approaches to lane changing and their results, and propose a general scheme,
according to which realistic lane changing rules can be developed. We test this
scheme by applying it to several different lane changing rules, which, in spite
of their differences, generate similar and realistic results. We thus conclude
that, for producing realistic results, the logical structure of the lane
changing rules, as proposed here, is at least as important as the microscopic
details of the rules
Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events
An analysis of moments and spectra shows that, while the distribution of
avalanche areas obeys finite size scaling, that of toppling numbers is
universally characterized by a full, nonlinear multifractal spectrum. Rare,
large avalanches dissipating at the border influence the statistics very
sensibly. Only once they are excluded from the sample, the conditional toppling
distribution for given area simplifies enough to show also a well defined,
multifractal scaling. The resulting picture brings to light unsuspected, novel
physics in the model.Comment: 5 pages, 4 figure
Segregation of granular binary mixtures by a ratchet mechanism
We report on a segregation scheme for granular binary mixtures, where the
segregation is performed by a ratchet mechanism realized by a vertically shaken
asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied
this system by computer simulations and found that most binary mixtures can be
segregated using an appropriately chosen ratchet, even when the particles in
the two components have the same size, and differ only in their normal
restitution coefficient or friction coefficient. These results suggest that the
components of otherwise non-segregating granular mixtures may be separated
using our method.Comment: revtex, 4 pages, 4 figures, submitte