Issue |
Europhys. Lett.
Volume 58, Number 2, April 2002
|
|
---|---|---|
Page(s) | 250 - 256 | |
Section | Condensed matter: structure, mechanical and thermal properties | |
DOI | https://doi.org/10.1209/epl/i2002-00630-6 | |
Published online | 01 August 2002 |
A solvable non-conservative model of Self-Organised Criticality
Department of Mathematics, Imperial College
180 Queen's
Gate, London SW7 2BZ, UK
Corresponding authors: gunnar.pruessner@physics.org h.jensen@ic.ac.uk
Received:
19
September
2001
Accepted:
25
January
2002
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
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