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Fluctuations in self-organizing systems

J. M. Carlson

E. R. Grannan

C. Singh

G. H. Swindle

  • Department of Physics and Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106

  • Department of Physics, University of California, Irvine, Irvine, California 92717
  • Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106

  • Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106

  • Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, California 93106

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Phys. Rev. E 48, 688 – Published 1 August, 1993

DOI: https://doi.org/10.1103/PhysRevE.48.688

Abstract

Self-organized criticality (SOC) in a wide variety of systems is seen to arise as a consequence of a singularity in the diffusion coefficient of the hydrodynamic limit. We demonstrate that this description is valid for several models on a closed system and observe that it can break down if the driving is sufficiently strong on the open systems where SOC is observed. In this case fluctuations play an important role, and if fluctuations are large enough then pure power laws in event-size distributions are observed. In contrast, when diffusion holds on SOC systems the characteristic event size diverges sublinearly in the system size. We derive an exponent inequality which provides a necessary condition for the singular-diffusion description to hold on the open driven system. The inequality involves the order of the diffusion singularity, the driving rate, and standard critical exponents.

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Outline

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Phys. Rev. E 48, 688– Published 1 August, 1993
  • Received 22 February 1993

© 1993 American Physical Society

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