On the avalanche-finiteness of Abelian Sandpiles

  title={On the avalanche-finiteness of Abelian Sandpiles},
  author={Shing-wai Chan and Hf Chau},
  journal={Physica A-statistical Mechanics and Its Applications},
  • S. ChanH. Chau
  • Published 17 October 1994
  • Mathematics, Geology
  • Physica A-statistical Mechanics and Its Applications
2 Citations

Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above

We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We perform an exact analysis of the spherical model in any dimension D>2 and numerical



Abelian sandpile model.

  • Chau
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1993
A systematic and simple method to find the correlation function of the Abelian sandpile model up to any finite order is developed. In addition, an algorithm for evaluating the distribution function

Inverse avalanches on Abelian sandpiles.

  • Chau
  • Geology, Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be

Self-organized critical state of sandpile automaton models.

  • Dhar
  • Computer Science, Physics
    Physical review letters
  • 1990
The critical state is characterized, and its entropy for an arbitrary finite lattice in any dimension is determined, and the two-point correlation function is shown to satisfy a linear equation.

Generalized Abelian sandpile model

A sufficient condition is presented herein for which the particle addition operations commute in the eventual phase space of a general cellular automata‐type of sandpile model. The commutative nature

Abelian sandpile model on the bethe lattice

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It is proved that all bounded subsets of Rn with nonempty interior are cutable. Also found is an if and only if classification of when a nontrivial absolute steady state (ASS) of the sandpile‐type

Structure of two-dimensional sandpile. I. Height probabilities

The height probabilities of the two-dimensional Abelian sandpile model are the fractionial numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these

Self-organized criticality.