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

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 $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.Comment: Four pages, our figure

Randmoness and Step-like Distribution of Pile Heights in Avalanche Models

The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the pile is destined to describe the crossover. The height's densities corresponding to the models with relaxation of the both types tend one to another as the parameter increases. These densities follow a step-like behaviour in contrast to the peaked shape found in the models with the local loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149, (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure

Turbulent self-organized criticality

In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and global simple scaling regimes analogous to those holding for velocity structure functions in fluid turbulence. The correspondence involves identity of a basic scaling relation and of the form of relevant probability distributions. The sandpile provides a qualitative analog of many features of turbulent phenomena.Comment: Revised version. 5 RevTex pages and 4 postscript 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.

Driven Diffusive Systems with Disorder

We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial distribution of transition rates, both with a single easy direction and with random reversals of the easy direction; dynamical disorder, where particles move in a disordered landscape which itself evolves in time. In every case, the system exhibits phase separation; in some cases, it is of an unusual sort. The time-dependent properties of density fluctuations are in accord with the kinematic wave criterion that the dynamical universality class is unaffected by disorder if the kinematic wave velocity is nonzero.Comment: To appear in Physica A, Proc. of International Workshop on Common Trends in Traffic Systems (IIT, Kanpur,2006

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

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