Control parameters in turbulence, Self Organized Criticality and ecosystems

dc.creatorChapman, S. C.
dc.creatorRowlands, G.
dc.creatorWatkins, N. W.
dc.date2007-07-26
dc.date2008-02-21
dc.date.accessioned2026-07-07T09:21:50Z
dc.date.available2026-07-07T09:21:50Z
dc.descriptionFrom the starting point of the well known Reynolds number of fluid turbulence we propose a control parameter $R$ for a wider class of systems including avalanche models that show Self Organized Criticality (SOC) and ecosystems. $R$ is related to the driving and dissipation rates and from similarity analysis we obtain a relationship $R\sim N^{β_N}$ where $N$ is the number of degrees of freedom. The value of the exponent $β_N$ is determined by detailed phenomenology but its sign follows from our similarity analysis. For SOC, $R=h/ε$ and we show that $β_N<0$ hence we show independent of the details that the transition to SOC is when $R \to 0$, in contrast to fluid turbulence, formalizing the relationship between turbulence (since $β_N >0$, $R \to \infty$) and SOC ($R=h/ε\to 0$). A corollary is that SOC phenomenology, that is, power law scaling of avalanches, can persist for finite $R$ with unchanged exponent if the system supports a sufficiently large range of lengthscales; necessary for SOC to be a candidate for physical systems. We propose a conceptual model ecosystem where $R$ is an observable parameter which depends on the rate of throughput of biomass or energy; we show this has $β_N>0$, so that increasing $R$ increases the abundance of species, pointing to a critical value for species 'explosion'.
dc.description1 manuscript file (Revtex), 2 figure files (.eps). Revised and resubmitted to J. Phys. A
dc.identifierhttps://arxiv.org/abs/0707.3958
dc.identifierhttp://arxiv.org/abs/0707.3958
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155169
dc.subjectBiological Physics
dc.subjectGeneral Physics
dc.titleControl parameters in turbulence, Self Organized Criticality and ecosystems
dc.typetext

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