Control parameters in turbulence, Self Organized Criticality and ecosystems
| dc.creator | Chapman, S. C. | |
| dc.creator | Rowlands, G. | |
| dc.creator | Watkins, N. W. | |
| dc.date | 2007-07-26 | |
| dc.date | 2008-02-21 | |
| dc.date.accessioned | 2026-07-07T09:21:50Z | |
| dc.date.available | 2026-07-07T09:21:50Z | |
| dc.description | From 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.description | 1 manuscript file (Revtex), 2 figure files (.eps). Revised and resubmitted to J. Phys. A | |
| dc.identifier | https://arxiv.org/abs/0707.3958 | |
| dc.identifier | http://arxiv.org/abs/0707.3958 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155169 | |
| dc.subject | Biological Physics | |
| dc.subject | General Physics | |
| dc.title | Control parameters in turbulence, Self Organized Criticality and ecosystems | |
| dc.type | text |