Eulerian Walkers as a Model of Self-Organized Criticality
- 16 December 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 77 (25) , 5079-5082
- https://doi.org/10.1103/physrevlett.77.5079
Abstract
We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an Abelian group, same as the group for the Abelian sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.Keywords
All Related Versions
This publication has 10 references indexed in Scilit:
- Formation of Avalanches and Critical Exponents in an Abelian Sandpile ModelPhysical Review Letters, 1996
- Simplest Possible Self-Organized Critical SystemPhysical Review Letters, 1996
- Punctuated equilibrium and criticality in a simple model of evolutionPhysical Review Letters, 1993
- Toppling distributions in one-dimensional Abelian sandpilesJournal of Physics A: General Physics, 1992
- Self-organized critical forest-fire modelPhysical Review Letters, 1992
- Self-organized criticality in a crack-propagation model of earthquakesPhysical Review A, 1991
- Self-organized critical state of sandpile automaton modelsPhysical Review Letters, 1990
- Self-Organized Criticality and EarthquakesEurophysics Letters, 1989
- Self-organized criticality: An explanation of the 1/fnoisePhysical Review Letters, 1987
- GRAPH THEORYPublished by Defense Technical Information Center (DTIC) ,1969