Research PapersNo Access

THE AVERAGE AVALANCHE SIZE IN THE MANNA MODEL AND OTHER MODELS OF SELF-ORGANIZED CRITICALITY

GUNNAR PRUESSNER

Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom

https://doi.org/10.1142/S0217979213500094Cited by:7 (Source: Crossref)

Abstract

The average avalanche size can be calculated exactly in a number of models of self-organized criticality (SOC). While the calculation is straight-forward in one dimension, it is more involved in higher dimensions and further complicated by the presence of different boundary conditions and different forms of external driving. Amplitudes of the leading order are determined analytically and evaluated to obtain analytical references for numerical work. A subtle link exists between the procedure to calculate the average avalanche size and the field theory of SOC.

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