Dimension of branching processes and self-organized criticality
- 1 June 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 49 (6) , 4903-4906
- https://doi.org/10.1103/physreve.49.4903
Abstract
Branching processes and their application as a model of self-organized criticality are briefly reviewed. The critical dimension for this model is calculated. The differences between our result and similar ones on polymers and percolation are explained. We discuss semiquantitatively why the critical dimension of a model of self-organized criticality that includes the oscillation of the sandpile around its critical value would be different, perhaps even infinite. Finally, we conjecture that our mathematical results are more general than they seem.Keywords
This publication has 8 references indexed in Scilit:
- A branching process model for sand avalanchesJournal of Statistical Physics, 1993
- Critical phase transitions made self-organized : a dynamical system feedback mechanism for self-organized criticalityJournal de Physique I, 1992
- I.J. Bienaymé: Family Information and Proof of the Criticality TheoremInternational Statistical Review, 1992
- Dynamical and spatial aspects of sandpile cellular automataJournal of Statistical Physics, 1991
- Self-organized criticality: An explanation of the 1/fnoisePhysical Review Letters, 1987
- The Dimensions of Chain Molecules Containing Branches and RingsThe Journal of Chemical Physics, 1949
- On the Generalized "Birth-and-Death" ProcessThe Annals of Mathematical Statistics, 1948
- On the Probability of the Extinction of Families.The Journal of the Anthropological Institute of Great Britain and Ireland, 1875