Randomness and a step-like distribution of pile heights in avalanche models |
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Authors: | A B Shapoval M G Shnirman |
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Institution: | (1) International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Warshavskoye sh. 79, kor. 2, Moscow, 117556, Russia;(2) Finance Academy under the Government of the Russian Federation, Leningradsky pr. 49, 125468 Moscow, Russia;(3) Institut de Physique du Globe de Paris, 4, place Jussieu, 75252 Paris, France |
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Abstract: | This paper considers a one-parameter family of sand-piles.
The family exhibits the crossover
between the models with deterministic and stochastic relaxation.
The mean pile height is used to describe the crossover.
The height densities corresponding to the models with relaxation
of both types approach one another as the parameter increases.
Relaxation is supposed to deal
with the local losses of grains by a fixed amount.
In that case the densities show a step-like behaviour
in contrast to the peaked shape
found in the models with the local loss of grains down
to a fixed level
S. Lübeck, 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 between the two cases for admissible parameter values. |
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Keywords: | 05 70 Jk Critical point phenomena 05 65 +b Self-organized systems |
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