1995
DOI: 10.1103/physreve.51.1711
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Renormalization approach to the self-organized critical behavior of sandpile models

Abstract: We introduce a renormalization scheme of a type that is able to describe the self-organized critical state (SOC) of sandpile models. We have defined a characterization of the phase space that allows us to study the evolution of the dynamics under change of scale. In addition, a stationarity condition provides a feedback mechanism that drives the system to its critical state. We obtain an attractive fixed point in the phase space of the parameters that clarifies the self-organized critical nature of these syste… Show more

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Cited by 84 publications
(67 citation statements)
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References 37 publications
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“…However, if we use an approximation for the steady state P (σ), such as a mean field approximation, then equation (10) provides a well defined RG transformation W → W from the old W to the new W transition probability. It is interesting to write equation (10) in the form…”
Section: Rg Transformationmentioning
confidence: 99%
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“…However, if we use an approximation for the steady state P (σ), such as a mean field approximation, then equation (10) provides a well defined RG transformation W → W from the old W to the new W transition probability. It is interesting to write equation (10) in the form…”
Section: Rg Transformationmentioning
confidence: 99%
“…The last step is an approximation which we call the one-site independence approximation. In this manner we obtain a renormalized probabilistic cellular automaton, with the property of one-site independence, whose one-site transition probability w(τ i |τ ′ ) is obtained from the original one w(σ i |σ ′ ) through equations (14), (10), and (1). Thus we understand the present renormalization as the transformation w(σ i |σ ′ ) → w(τ i |τ ′ ).…”
Section: Rg Transformationmentioning
confidence: 99%
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“…These may include: (i) the temperature profiles for the convection dominated thermoconduction and turbulent convection [9] (as in the convective zone of the sun and stars), (ii) stability and average profiles of granular materials (e.g., the sand pile profiles) and granular flows [2,3], (iii) equilibrium and steady state profiles of plasma pressure and temperature in fusion devices [8,10], etc. Despite its importance, the problem of spatial structure and characteristics of the SO steady states has received minor attention [7,[11][12][13]. In this Letter, we propose a method which is equally applicable to any CA provided its rules are rather simple.…”
mentioning
confidence: 99%
“…In particular, CA models are useful to study traffic jams [1], granular material dynamics [2], and selforganization [3,4]. The transport properties of systems the, especially in the Self-Organized (SO) critical regime were extensively studied (cf., [4][5][6][7][8]). However, for many applications, one needs to know an entire structure of the SO states.…”
mentioning
confidence: 99%