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Size effects of slope dynamics in a 2-dimensional sandpile

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  • Ruskin, H.J.
  • McCarren, A.L.

Abstract

We study a two-dimensional sandpile automaton model under the so-called critical slope dynamics where the stability depends upon the first derivative of the sand height, i.e. height difference. For fixed critical slope we investigate systems of increasing linear dimension L on the square lattice for both randomly and systematically built piles. Statistics are presented for the size and duration of the avalanches produced. For excess grains distributed with equal probability to nearest neighbours, the average cluster size tends to a fixed limit which is dependent on the size of the initial perturbation. Furthermore, stable behaviour appears to be reached for relatively low values of the linear dimension L ∼ 250. The average time taken for avalanches of all sizes to die away stabilizes less readily within the system sizes considered. No evidence is found in support of a scaling law of the usual type.

Suggested Citation

  • Ruskin, H.J. & McCarren, A.L., 1994. "Size effects of slope dynamics in a 2-dimensional sandpile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(4), pages 477-482.
    • Handle: RePEc:eee:phsmap:v:207:y:1994:i:4:p:477-482
    DOI: 10.1016/0378-4371(94)90204-6
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    References listed on IDEAS

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    1. Hong, D.C. & McLennan, J.A., 1992. "Molecular dynamics simulations of hard sphere granular particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 187(1), pages 159-171.
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