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arXiv · 1012.4809

Effect of Noise on Patterns Formed by Growing Sandpiles

Tridib Sadhu·Deepak Dhar
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Abstract

We consider patterns generated by adding large number 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, \textit{viz.}, 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 in growing abelian sandpiles.

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Tridib Sadhu, Deepak Dhar. 2010-12-20. Effect of Noise on Patterns Formed by Growing Sandpiles. https://doi.org/10.1088/1742-5468%2F2011%2F03%2Fp03001

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