منابع مشابه
Pattern Formation in Growing Sandpiles
The topic of Pattern Formation in Growing Sandpiles was first looked at in the 1980’s through a model of sand being added to a two dimensional system at a constant rate.[1] How this sand creates patterns of inactivity and unpredictability is an interesting natural phenomena. The Abelian Sandpile model is one model created to model these patterns, showing that the ending stable state of the mode...
متن کاملFast/slow Diffusion and Collapsing Sandpiles
We regard the limit as p ! 1 of the ow governed by the p-Laplacian as providing a simplistic model for the \collapse of an initially unstable sandpile." Upon rescaling to stretch out the initial layer we obtain some simple dynamics and provide fairly explicit solutions in certain cases. In particular we note that such models entail \instanta-neous" mass transfer governed by Monge-Kantorovich th...
متن کاملPattern formation in growing sandpiles with multiple sources or sinks
Adding sand grains at a single site in Abelian sandpile models produces beautiful but complex patterns. We study the effect of sink sites on such patterns. Sinks change the scaling of the diameter of the pattern with the number N of sand grains added. For example, in two dimensions, in presence of a sink site, the diameter of the pattern grows as √ (N/ logN) for large N , whereas it grows as √ ...
متن کاملEffect of Noise on Patterns Formed by Growing Sandpiles
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, viz., randomness in the point of addition, disorder in the initial periodic configuration, and disorder in the co...
متن کاملLadder Sandpiles
We study Abelian sandpiles on graphs of the form G×I, where G is an arbitrary finite connected graph, and I ⊂ Z is a finite interval. We show that for any fixed G with at least two vertices, the stationary measures μI = μG×I have two extremal weak limit points as I ↑ Z. The extremal limits are the only ergodic measures of maximum entropy on the set of infinite recurrent configurations. We show ...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1996
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0166