DOI: 10.1209/epl/i2002-00630-6


Europhys. Lett., 58 (2) , pp. 250-256 (2002)

A solvable non-conservative model of Self-Organised Criticality

G. Pruessner and H. Jeldtoft Jensen

Department of Mathematics, Imperial College 180 Queen's Gate, London SW7 2BZ, UK

gunnar.pruessner@physics.org
h.jensen@ic.ac.uk

(Received 19 September 2001; accepted in final form 25 January 2002)

Abstract
We present the first solvable non-conservative sandpile-like critical model of Self-Organised Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi (VESPIGNANI A. and ZAPPERI S., Phys. Rev. E, 57 (1998) 6345) that a lack of conservation in the microscopic dynamics of an SOC model can be compensated by introducing an external drive and thereby re-establishing criticality. The model shown is critical for all values of the conservation parameter. The analytical derivation follows the lines of Bröker and Grassberger (BRÖKER H.-M. and GRASSBERGER P., Phys. Rev. E, 56 (1997) 3944) and is supported by numerical simulation. In the limit of vanishing conservation the Random Neighbour Drossel Schwabl Forest Fire Model (R-DS-FFM) is recovered.

PACS
64.60.Ht - Dynamic critical phenomena.
05.65.+b - Self-organized systems.
02.50.-r - Probability theory, stochastic processes, and statistics.


© EDP Sciences 2002