CROSSOVER PHENOMENON AND UNIVERSALITY: FROM RANDOM WALK TO DETERMINISTIC SAND-PILES THROUGH RANDOM SAND-PILES

Alexander Shapoval and M. G. Shnirman ()
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M. G. Shnirman: International Institute of Earthquake Prediction Theory, Warshavkoye shosse, 79, kor. 2, Moscow, 117556, Russia

International Journal of Modern Physics C (IJMPC), 2005, vol. 16, issue 12, 1893-1907

Abstract: The sand-pile models exhibit a great diversity of behavioral patterns. The average height as a function on time points out the variety of the sand-pile's criticality. We define the classes of universality for the sand-piles in terms of the spectrum of the average height. The definition, in particular, distinguishes two classes with Manna's and Baket al.sand-piles as the typical representatives. The one-parametric family of the models investigated in this paper develops a crossover between the classes and introduces the infinite quantity of other sand-pile's classes. The parameter is the number of grains that any unstable cell transfers to its neighbors. The sand-piles admit a certain normalization generating unified laws. The spectral approach increases the precision of the universalities from our size distribution analysis. The latter describes the sand-piles' typical distribution, sets the correspondence between the sand-piles with small and large parameter values, but fails to determine their diversity.

Keywords: Sand-pile; universality; size distribution; spectrum (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0129183105008412

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