Numéro |
J. Phys. I France
Volume 4, Numéro 2, February 1994
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Page(s) | 209 - 221 | |
DOI | https://doi.org/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 SornetteLaboratoire 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)
Abstract
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.
© Les Editions de Physique 1994