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Volumn 57, Issue 6, 1998, Pages 6345-6362

How self-organized criticality works: A unified mean-field picture

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EID: 4243736448     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.6345     Document Type: Article
Times cited : (227)

References (103)
  • 7
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    • for a review, see M. Sahimi, Rev. Mod. Phys. 65, 1393 (1993).RMPHAT
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 1393
    • Sahimi, M.1
  • 64
    • 0001894848 scopus 로고
    • T. Tomé, Physica A 212, 99 (1994).PHYADX
    • (1994) Physica A , vol.212 , pp. 99
    • Tomé, T.1
  • 82
    • 85036336017 scopus 로고    scopus 로고
    • [formula presented] In fact, energy is not usually added on top of already active sites. This makes the energy addiction [formula presented]. Also, the energy balance in the stationary state is changed accordingly, thus obtaining [formula presented]. The latter immediately gives the stationary density of active sites as [formula presented]. For [formula presented], we recover the first order result presented in the text. However, higher order corrections can be considered, obtaining consistency relations useful for a higher order treatment of the MF equations., [formula presented] is the average energy added considering just first order contributions in [formula presented]
    • Jin=hLd is the average energy added considering just first order contributions in h and ρa. In fact, energy is not usually added on top of already active sites. This makes the energy addiction Jin=h(1-ρa)Ld. Also, the energy balance in the stationary state is changed accordingly, thus obtaining h(1-ρa)Ld=ερaLd. The latter immediately gives the stationary density of active sites as ρa=h/(h+ε). For ε≫h, we recover the first order result presented in the text. However, higher order corrections can be considered, obtaining consistency relations useful for a higher order treatment of the MF equations.
  • 87
    • 85036375630 scopus 로고    scopus 로고
    • our notation, [formula presented]
    • In our notation, α≡(1-ε)/(2d).
  • 100
    • 85036285262 scopus 로고    scopus 로고
    • [formula presented]. In the MF description, where no anomalous dimension appears, [formula presented] , The pair connectedness function is given by the percolation properties of tree sites in the presence of a characteristic length defined by the dynamical process. The general form of the pair connectedness is [formula presented]
    • The pair connectedness function is given by the percolation properties of tree sites in the presence of a characteristic length defined by the dynamical process. The general form of the pair connectedness is r2-d-ηocc Γ(r/ξ). In the MF description, where no anomalous dimension appears, ηocc=0.
  • 101
  • 103
    • 85036350929 scopus 로고    scopus 로고
    • It is easy to recognize that, in a dissipative model, each active particle can wander only a finite number of steps. Each toppling process loses on average an amount [formula presented] of energy. The energy unit needed to sustain the activity (the wandering of the active site) is therefore dissipated after [formula presented] toppling events (wandering steps). This indeed recovers the result obtained for the average avalanche size in our MF approach
    • It is easy to recognize that, in a dissipative model, each active particle can wander only a finite number of steps. Each toppling process loses on average an amount ε of energy. The energy unit needed to sustain the activity (the wandering of the active site) is therefore dissipated after ε-1 toppling events (wandering steps). This indeed recovers the result obtained for the average avalanche size in our MF approach.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.