Self-organized branching process for a one-dimensional ricepile model

A self-organized branching process is introduced to describe one-dimensional ricepile model with stochastic topplings. Although the branching processes are generally supposed to describe well highdimensional systems, our modification grasps some of the peculiarities present in one dimension. We find analytically the crossover behavior from the trivial one-dimensional BTW behaviour to self-organized criticality characterised by power-law distribution of avalanches. The finite-size effects, which are crucial in the crossover, are calculated. PACS. 05.65.+b Self-organized systems – 05.70.Jk Critical point phenomena – 45.70.-n Granular systems