Scaling behavior in disordered sandpile automata

Tadić, Bosiljka; Nowak, Ulrich; Usadel, Klaus-Dieter; Ramaswamy, R.; Padlewski, S.

Scaling behavior in disordered sandpile automata

Dateien

Tadic_1992_ScalingBehavior.pdfGröße: 1.39 MBDownloads: 288

Datum

1992

Autor:innen

Tadić, Bosiljka

Nowak, Ulrich

Usadel, Klaus-Dieter

Ramaswamy, R.

Padlewski, S.

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Physik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Physical Review A. 1992, 45(12), pp. 8536-8545. Available under: doi: 10.1103/PhysRevA.45.8536

Zusammenfassung

We study numerically the scaling behavior of disordered sandpile automata with preferred direction on a two-dimensional square lattice. We consider two types of bulk defects that modify locally the dynamic rule: (i) a random distribution of holes, through which sand grains may leave the system, and (ii) several models with a random distribution of critical heights. We find that at large time and length scales the self-organized critical behavior, proved exactly in the pure model, is lost for any finite concentration of defects both in the model of random holes and in those models of random critical heights in which the dynamic rule violates the height conservation law. In the case of the random critical height model with the height-conserving dynamics, we find that self-organized criticality holds for the entire range of concentrations of defects, and it belongs to the same universality class as the pure model. In the case of random holes we analyze the scaling properties of the probability distributions P(T,p,L) and D(s,p,L) of avalanches of duration larger than T and size larger than s, respectively, at lattices with linear size L and concentration of defect sites p. We find that in general the following scaling forms apply: P(T)=T-αscrP(T/x,T/L) and D(s)=s-τscrD(s/m,s/Lν), where x≡x(p) and m≡m(p) are the characteristic duration (length) and the characteristic size (mass) of avalanches for a given concentration of defects. The power-law behavior of the distributions still persists for length scales T

Fachgebiet (DDC)

530 Physik

Zitieren

ISO 690

TADIĆ, Bosiljka, Ulrich NOWAK, Klaus-Dieter USADEL, R. RAMASWAMY, S. PADLEWSKI, 1992. Scaling behavior in disordered sandpile automata. In: Physical Review A. 1992, 45(12), pp. 8536-8545. Available under: doi: 10.1103/PhysRevA.45.8536

BibTex

@article{Tadic1992Scali-9372,
  year={1992},
  doi={10.1103/PhysRevA.45.8536},
  title={Scaling behavior in disordered sandpile automata},
  number={12},
  volume={45},
  journal={Physical Review A},
  pages={8536--8545},
  author={Tadić, Bosiljka and Nowak, Ulrich and Usadel, Klaus-Dieter and Ramaswamy, R. and Padlewski, S.}
}

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    <dcterms:abstract xml:lang="eng">We study numerically the scaling behavior of disordered sandpile automata with preferred direction on a two-dimensional square lattice. We consider two types of bulk defects that modify locally the dynamic rule: (i) a random distribution of holes, through which sand grains may leave the system, and (ii) several models with a random distribution of critical heights. We find that at large time and length scales the self-organized critical behavior, proved exactly in the pure model, is lost for any finite concentration of defects both in the model of random holes and in those models of random critical heights in which the dynamic rule violates the height conservation law. In the case of the random critical height model with the height-conserving dynamics, we find that self-organized criticality holds for the entire range of concentrations of defects, and it belongs to the same universality class as the pure model. In the case of random holes we analyze the scaling properties of the probability distributions P(T,p,L) and D(s,p,L) of avalanches of duration larger than T and size larger than s, respectively, at lattices with linear size L and concentration of defect sites p. We find that in general the following scaling forms apply: P(T)=T-αscrP(T/x,T/L) and D(s)=s-τscrD(s/m,s/Lν), where x≡x(p) and m≡m(p) are the characteristic duration (length) and the characteristic size (mass) of avalanches for a given concentration of defects. The power-law behavior of the distributions still persists for length scales T</dcterms:abstract>
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