Emergent Spatial Structures in Critical Sandpiles

作者: Bosiljka Tadić , Deepak Dhar

DOI: 10.1103/PHYSREVLETT.79.1519

关键词: PhysicsCritical exponentPower lawSteady stateConservation lawScalingPercolation critical exponentsAbelian sandpile modelDirected percolationStatistical physics

摘要: We introduce and study a new directed sandpile model with threshold dynamics stochastic toppling rules. show that particle conservation law the percolation-like local evolution of avalanches lead to formation spatial structure in steady state, density developing power tail away from top. determine scaling exponents characterizing avalanche distributions terms critical percolation all dimensions.

参考文章(21)
Per Bak, Chao Tang, Kurt Wiesenfeld, Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters. ,vol. 59, pp. 381- 384 ,(1987) , 10.1103/PHYSREVLETT.59.381
Leo P. Kadanoff, Sidney R. Nagel, Lei Wu, Su-min Zhou, Scaling and universality in avalanches. Physical Review A. ,vol. 39, pp. 6524- 6537 ,(1989) , 10.1103/PHYSREVA.39.6524
S.S. Manna, Critical exponents of the sand pile models in two dimensions Physica A-statistical Mechanics and Its Applications. ,vol. 179, pp. 249- 268 ,(1991) , 10.1016/0378-4371(91)90063-I
Ashvin B. Chhabra, Mitchell J. Feigenbaum, Leo P. Kadanoff, Amy J. Kolan, Itamar Procaccia, Sandpiles, avalanches, and the statistical mechanics of nonequilibrium stationary states Physical Review E. ,vol. 47, pp. 3099- 3121 ,(1993) , 10.1103/PHYSREVE.47.3099
Bosiljka Tadić, Ramakrishna Ramaswamy, Defects in self-organized criticality: A directed coupled map lattice model Physical Review E. ,vol. 54, pp. 3157- 3164 ,(1996) , 10.1103/PHYSREVE.54.3157
Deepak Dhar, Self-organized critical state of sandpile automaton models. Physical Review Letters. ,vol. 64, pp. 1613- 1616 ,(1990) , 10.1103/PHYSREVLETT.64.1613
S.N. Majumdar, Deepak Dhar, Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model Physica A-statistical Mechanics and Its Applications. ,vol. 185, pp. 129- 145 ,(1992) , 10.1016/0378-4371(92)90447-X
Deepak Dhar, S. S. Manna, Inverse avalanches in the Abelian sandpile model. Physical Review E. ,vol. 49, pp. 2684- 2687 ,(1994) , 10.1103/PHYSREVE.49.2684
Yi-Cheng Zhang, Scaling theory of self-organized criticality. Physical Review Letters. ,vol. 63, pp. 470- 473 ,(1989) , 10.1103/PHYSREVLETT.63.470
S S Manna, Two-state model of self-organized criticality Journal of Physics A. ,vol. 24, ,(1991) , 10.1088/0305-4470/24/7/009