J. Phys. I France
Volume 4, Numéro 2, February 1994
Page(s) 209 - 221
DOI: 10.1051/jp1:1994133
J. Phys. I France 4 (1994) 209-221

Sweeping of an instability : an alternative to self-organized criticality to get powerlaws without parameter tuning

Didier Sornette

Laboratoire de Physique de la Matière Condensée, Université de Nice-Sophia Antipolis, B.P. 71, Parc Valrose, 06108 Nice Cedex 2, France

(Received 3 September 1993, received in final form 27 September 1993, accepted 8 November 1993)

We show that a notable fraction of numerical and experimental works claiming the observation of self-organized criticality (SOC) rely in fact on a different physical mechanism, which involves the slow sweeping of a control parameter towards a global instability. This slow sweeping (which does not apparently involve a parameter tuning) has been the cause for the confusion with the characteristic SOC situation presenting truly no parameter tuning and functioning persistently in a marginal stability condition due to the operation of a feedback mechanism that ensures a steady state in which the system is marginally stable against a disturbance. The observation of power law distributions of events, often believed to be the hallmark of SOC, can be traced back to the cumulative measurements of fluctuations diverging on the approach of the critical instability. For non-critical instabilities such as first-order transitions, the power law distribution exists on a limiting size range up to a maximum value which is an increasing function of the range of interaction. We discuss the relevance of these ideas on the onset of spinodal decomposition, off-threshold multifractality, an exactly soluble model of rupture, the Burridge-Knopoff model of earthquakes, foreshocks and acoustic emissions, impact ionization breakdown in semiconductors, the Barkhausen effect, charge density waves, pinned flux lattices, elastic string in random potentials and real sandpiles.

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