arXiv subjects

F. Daerden

Publications and source records attributed to F. Daerden.

4 recordsLinked to original sources

arXiv2001

Dissipative Abelian Sandpiles and Random Walks

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles' correlation length exponent νalways equals 1/d_w, where d_w is the fractal dimension of the random walker. This leads to a new understanding of the known results that ν=1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions.

cond-mat.stat-mech↗

arXiv2000

Distribution of consecutive waves in the sandpile model on the Sierpinski gasket

The scaling properties of waves of topplings in the sandpile model on the Sierpinski gasket are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is found. Predictions for scaling exponents in the forward and backward conditional probabilites for two consecutive waves are given. All predictions were examined by numerical simulations and were found to be in reasonable agreement with the obtained data.

cond-mat.stat-mech↗

arXiv1997

Sandpiles on the Sierpinski gasket

We perform extensive simulations of the sandpile model on a Sierpinski gasket. Critical exponents for waves and avalanches are determined. We extend the existing theory of waves to the present case. This leads to an exact value for the exponent $τ_w$ which describes the distribution of wave sizes: $τ_w = \ln{(9/5)}/\ln{3}$. Numerically, it is found that the number of waves in an avalanche is proportional to the number of distinct sites toppled in the avalanche. This leads to a conjecture for the exponent $τ$ that determines the distribution of avalanche sizes: $τ=1+τ_w = \ln{(27/5)}/\ln{3}$. Our predictions are in good agreement with the numerical results.

cond-mat.stat-mech↗

arXiv1995

1/f-noise in the Bak-Sneppen model

We calculate time correlation functions in the Bak-Sneppen model (Phys. Rev. Lett. {\bf 71} 4083 (1993)), a model showing self-organised criticality. For a random neighbour version of the model, analytical results are presented, while on a one dimensional lattice we give numerical results. The power spectrum of these correlation functions shows $1/f$- behaviour in both cases.

cond-mat↗