2008/06/30 by S. C. Chapman, G. Rowlands, N. W. Watkins · 9 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Corollary #Criticality #Dissipation #Exponent #Mechanics #Observable #Physics #Power law #Pure mathematics #Quantum mechanics #Scaling #Self-organized criticality #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Turbulence #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1063/1.3057392
published in Physics of Plasmas 16(1) (American Institute of Physics) · 15 pages plus 4 figures. Developed from part of arXiv:0707.3958v2
openalex publication_date 2009/01/01 · arxiv created 2009/02/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Similarity analysis is used to identify the control parameter RA for the subset of avalanching systems that can exhibit self-organized criticality (SOC). This parameter expresses the ratio of driving to dissipation. The transition to SOC, when the number of excited degrees of freedom is maximal, is found to occur when RA→0. This is in the opposite sense to (Kolmogorov) turbulence, thus identifying a deep distinction between turbulence and SOC and suggesting an observable property that could distinguish them. A corollary of this similarity analysis is that SOC phenomenology, that is, power law scaling of avalanches, can persist for finite RA with the same RA→0 exponent if the system supports a sufficiently large range of lengthscales, necessary for SOC to be a candidate for physical (RA finite) systems.