STATISTICAL FIELD THEORY OF HIERARCHICAL AVALANCHE ENSEMBLE

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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