The effect of noise on patterns formed by growing sandpiles

Sadhu, Tridib ; Dhar, Deepak (2011) The effect of noise on patterns formed by growing sandpiles Journal of Statistical Mechanics: Theory and Experiment, 2011 (3). P03001. ISSN 1742-5468

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We consider patterns generated by adding large numbers of sand grains at a single site in an Abelian sandpile model with a periodic initial configuration, and relaxing. The patterns show proportionate growth. We study the robustness of these patterns against different types of noise, namely, randomness in the point of addition, disorder in the initial periodic configuration, and disorder in the connectivity of the underlying lattice. We find that the patterns show a varying degree of robustness to addition of a small amount of noise in each case. However, introducing stochasticity in the toppling rules seems to destroy the asymptotic patterns completely, even for a weak noise. We also discuss a variational formulation of the pattern selection problem for growing Abelian sandpiles.

Item Type:Article
Source:Copyright of this article belongs to Institute of Physics.
Keywords:Pattern Formation (theory); Self-organized Criticality (theory); Patterns; Sandpile Models (theory)
ID Code:82200
Deposited On:10 Feb 2012 04:18
Last Modified:10 Feb 2012 04:18

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