Alexander Olemskoi

Institute of Applied Physics, National Academy of Sciences of Ukraine
In recent years considerable study has been given to the theory of self-organized criticality (SOC) that explains avalanche dynamics in a variety of systems such as ensemble of grains of sand moving along increasingly tilted surface (sandpile model [1]), intermittency in biological evolution [2], earthquakes and propagation of forest-fires, depinning transitions in random medium and so on (see [3]). The above models had been mostly studied by making use of scaling{type arguments supplemented with extensive computer simulations [4]. By contrast, in this work we put forward the related statistical theory that deals with avalanche ensemble in the course of SOC progressing.
[1] P. Bak, C. Tang, K. Wiesenfeld. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59 (1987) 381.
[2] P. Bak, K. Sneppen. Punctuated equilibrium and criticality in a simple model of evolution. Phys. Rev. Lett. 71 (1993) 4083.
[3] T. Halpin-Healy, Y.C. Zhang. Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Phys. Rep. 254 (1995) 215.
[4] M. Parzuski, S. Maslov, P. Bak. Avalanche dynamics in evolution, growth, and depinning models. Phys. Rev. E, 53 (1996) 414.
[5] P. Bak.How nature works: the science of self-organised criticality. Oxford University Press, 1997.
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