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

Ronald Dickman
Federal University of Minas Gerais

Following a brief review of power-law distributions in nature, I shall explain why such observations pose a challenge for statistical physics, and the paradigm of self-organized criticality (SOC), introduced by Per Bak and coworkers [1]. SOC shows how scale-free event 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. A similar mechanism has been suggested to underly power-law distributions of rain and drought [2]. SOC in its most familiar context, the "sandpile" models, is connected with a phase transition to an absorbing state [3]. I shall also discuss the generation of apparent power-law distributions via chaotic advection [4].




1. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).

2. O. Peters, C. Hertlein, and K. Christensen, Phys. Rev. Lett. 88,
018701 (2002); O. Peters and K. Christensen, Phys. Rev. E 66, 036120
(2002).

3. R. Dickman, M. A. Muñoz, A. Vespignani, and S. Zapperi, Braz. J. Phys.
30, (2000) 27.

4. R. Dickman, Phys. Rev. Lett. 90, 108701 (2003).

Presentation (PDF File)

Back to Workshop III: Simulation Hierarchies for Climate Modeling