https://doi.org/10.1140/epjb/e20020023
Self-organized branching process for a one-dimensional rice-pile model
Institute of Physics,
Academy of Sciences of the Czech Republic,
Na Slovance 2, 18221 Praha,
Czech Republic
Corresponding author: a slanina@fzu.cz
Received:
21
June
2001
Revised:
14
November
2001
Published online: 15 January 2002
A self-organized branching process is introduced to describe one-dimensional rice-pile model with stochastic topplings. Although the branching processes are generally expected to describe well high-dimensional systems, our modification highlights some of the peculiarities present in one dimension. We find analytically that the crossover behavior from the trivial one-dimensional BTW behaviour to self-organized criticality is characterised by a power-law distribution of avalanches. The finite-size effects, which are crucial to the crossover, are calculated.
PACS: 05.65.+b – Self-organized systems / 05.70.Jk – Critical point phenomena / 45.70.-n – Granular systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002