Workshop on Spatial Organisation of Convection, Clouds and Precipitation

Scale-free distributions in nature: an overview of self-organized criticality

5 May 2021, 16:00

1h 45m

virtual

Interactive presentation Modelling and Parameterising Deep Convective Organisation Modelling and Parameterising Deep Convective Organisation

Speaker

Ronald Dickman (UFMG)

Description

Power-law distributions in nature pose a challenge for statistical physics. The paradigm of self-organized criticality (SOC), introduced by Per Bak and coworkers [1], might resolve this puzzle. SOC shows how scale-free event-size and duration distributions can arise in the apparent absence of tuning parameters, in a system of many interacting entities, each having a threshold for relaxation, under a slow external drive. This paradigm may underly phenomena such as power-law distributions in meteorology [2,3] and neuronal activity [4]. SOC in its most familiar context, the "sandpile" models, is related to a continuous phase transition to an absorbing state [5]. Together, relaxation and slow drive restrict the system to the neighborhood of the critical point, yielding power-law scaling without parameter tuning [5,6].

1. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
2. O. Peters et al., Phys. Rev. Lett. 88,
   018701 (2002); O. Peters and K. Christensen, Phys. Rev. E 66, 036120
   (2002).
3. J. D. Neelin et al., J. Atmos. Sci. 66, 2367 (2009).
4. J. M. Beggs and D. Plenz, J. Neurosci. 23, 11167 (2003).
5. R. Dickman et al, Braz. J. Phys. 30, (2000) 27.
6. G. Pruessner, Self-Organised Criticality (CUP, Cambridge, 2012).

Presentation materials

DickmanPoster.png