J. Phys. I France
Volume 3, Numéro 6, June 1993
Page(s) 1377 - 1386
DOI: 10.1051/jp1:1993186
J. Phys. I France 3 (1993) 1377-1386

Critical phase transitions made self-organized: proposed experiments

Nathalie Fraysse1, Anne Sornette2, 3 and Didier Sornette3

1  Department of Chemical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
2  Institut de Géodynamique, CNRS URA 1279, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, and Sophia Antipolis, 1 avenue Albert Einstein, 06560 Valbonne, France
3  Laboratoire de Physique de la Matière Condensée CNRS URA 190, Université de Nice-Sophia Antipolis, B.P. 71, Parc Valrose, 06108 Nice Cedex, France

(Received 27 January 1993, accepted in final form 8 February 1993)

In Sornette, J. Phys. I France 2 (1992) 2065, a scenario for self-organized critically (SOC) has been proposed according to which SOC relies on a non-linear feedback of the order parameter on the control parameter(s), the amplitude of this feedback being tuned by the spatial correlation length $\xi$. Implementing such a feedback mechanism, it is possible in principle to convert standard "unstable" critical phase transitions into self-organized critical dynamics. Here, we analyze this idea in more detail and suggest to couple a standard experiment on critical phenomena with some probing radiation or some electronic feedback using a microprocessor or analog device which pushed the temperature or analog control parameter to that value where the susceptibility, the correlation length or the inverse of the decay rate is maximal. The practical realization of the feedback thus corresponds to an optimization of the response of the system under the action of a probe or a disturbance. We discuss liquid-vapor and binary demixion critical points, and briefly the He4 superfluid transition, magnetic systems, and superfluid transitions.

64.60H - 05.70L - 05.40

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