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Article Dans Une Revue Complex Systems Année : 1996

Grain Sorting in the One-dimensional Sand Pile Model

Résumé

We study the evolution of a one-dimensional pile, empty at first, which receives a grain in its first stack at each iteration. The final position of grains is singular: grains are sorted according to their parity. They are sorted on trapezoidal areas alternating on both sides of a diagonal line of slope $\sqrt{2}$. This is explained and proved by means of a local study. Each generated pile, encoded in height differences, is the concatenation of four patterns: $22$, $1313$, $0202$, and $11$. The relative length of the first two patterns and the last two patterns converges to $\sqrt{2}$. We make asymptotic expansions and prove that all the lengths of the pile are increasing proportionally to the square root of the number of iterations.
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Dates et versions

hal-03277267 , version 1 (02-07-2021)

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  • HAL Id : hal-03277267 , version 1

Citer

Jérôme Durand-Lose. Grain Sorting in the One-dimensional Sand Pile Model. Complex Systems , 1996, 10 (3), pp.195-206. ⟨hal-03277267⟩

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