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For: Zhang YC. Scaling theory of self-organized criticality. Phys Rev Lett 1989;63:470-473. [PMID: 10041083 DOI: 10.1103/physrevlett.63.470] [Citation(s) in RCA: 53] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Number Cited by Other Article(s)
51
Majumdar SN, Dhar D. Height correlations in the Abelian sandpile model. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/24/7/008] [Citation(s) in RCA: 118] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
52
Dhar D, Majumdar SN. Abelian sandpile model on the Bethe lattice. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/23/19/018] [Citation(s) in RCA: 128] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
53
Somfai E, Czirok A, Vicsek T. Power-law distribution of landslides in an experiment on the erosion of a granular pile. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/27/20/001] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
54
Chen DM, Wu S, Guo A, Yang ZR. Self-organized criticality in a cellular automaton model of pulse-coupled integrate-and-fire neurons. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/28/18/009] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
55
Peng G. Self-organized critical state in a directed sandpile automaton on Bethe lattices: equivalence to site percolation. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/20/010] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
56
Manna SS. Two-state model of self-organized criticality. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/24/7/009] [Citation(s) in RCA: 328] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
57
Grasso JR, Sornette D. Testing self-organized criticality by induced seismicity. ACTA ACUST UNITED AC 1998. [DOI: 10.1029/97jb01344] [Citation(s) in RCA: 72] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
58
Bottani S. Synchronization of integrate and fire oscillators with global coupling. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996;54:2334-2350. [PMID: 9965338 DOI: 10.1103/physreve.54.2334] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
59
Kutnjak-Urbanc B, Zapperi S, Milosevic S, Stanley HE. Sandpile model on the Sierpinski gasket fractal. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996;54:272-277. [PMID: 9965069 DOI: 10.1103/physreve.54.272] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
60
Ivashkevich EV. Critical behavior of the sandpile model as a self-organized branching process. PHYSICAL REVIEW LETTERS 1996;76:3368-3371. [PMID: 10060949 DOI: 10.1103/physrevlett.76.3368] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
61
Priezzhev VB, Ktitarev DV, Ivashkevich EV. Formation of avalanches and critical exponents in an Abelian sandpile model. PHYSICAL REVIEW LETTERS 1996;76:2093-2096. [PMID: 10060604 DOI: 10.1103/physrevlett.76.2093] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
62
Caglioti E, Loreto V. Dynamical properties and predictability of a class of self-organized critical models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996;53:2953-2956. [PMID: 9964584 DOI: 10.1103/physreve.53.2953] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
63
Loreto V, Paladin G, Vulpiani A. Concept of complexity in random dynamical systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996;53:2087-2098. [PMID: 9964486 DOI: 10.1103/physreve.53.2087] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
64
Ben-Hur A, Biham O. Universality in sandpile models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996;53:R1317-R1320. [PMID: 9964475 DOI: 10.1103/physreve.53.r1317] [Citation(s) in RCA: 110] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
65
Maslov S, Zhang YC. Exactly Solved Model of Self-Organized Criticality. PHYSICAL REVIEW LETTERS 1995;75:1550-1553. [PMID: 10060326 DOI: 10.1103/physrevlett.75.1550] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
66
Bottani S. Pulse-coupled relaxation oscillators: From biological synchronization to self-organized criticality. PHYSICAL REVIEW LETTERS 1995;74:4189-4192. [PMID: 10058438 DOI: 10.1103/physrevlett.74.4189] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
67
Vespignani A, Zapperi S, Pietronero L. Renormalization approach to the self-organized critical behavior of sandpile models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995;51:1711-1724. [PMID: 9962830 DOI: 10.1103/physreve.51.1711] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
68
Middleton AA, Tang C. Self-Organized Criticality in Nonconserved Systems. PHYSICAL REVIEW LETTERS 1995;74:742-745. [PMID: 10058836 DOI: 10.1103/physrevlett.74.742] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
69
Corral Á, Pérez CJ, Díaz-Guilera A, Arenas A. Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. PHYSICAL REVIEW LETTERS 1995;74:118-121. [PMID: 10057713 DOI: 10.1103/physrevlett.74.118] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
70
Csilling Á, Jánosi IM, Pásztor G, Scheuring I. Absence of chaos in a self-organized critical coupled map lattice. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994;50:1083-1092. [PMID: 9962066 DOI: 10.1103/physreve.50.1083] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
71
Gabrielov A, Newman WI, Knopoff L. Lattice models of failure: Sensitivity to the local dynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994;50:188-197. [PMID: 9961956 DOI: 10.1103/physreve.50.188] [Citation(s) in RCA: 28] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
72
Robinson PA. Scaling properties of self-organized criticality. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994;49:3919-3926. [PMID: 9961679 DOI: 10.1103/physreve.49.3919] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
73
Pietronero L, Vespignani A, Zapperi S. Renormalization scheme for self-organized criticality in sandpile models. PHYSICAL REVIEW LETTERS 1994;72:1690-1693. [PMID: 10055676 DOI: 10.1103/physrevlett.72.1690] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
74
Robinson PA. Self-organized criticality involving vector fields and random driving. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994;49:1984-1989. [PMID: 9961438 DOI: 10.1103/physreve.49.1984] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
75
Grassberger P. Efficient large-scale simulations of a uniformly driven system. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994;49:2436-2444. [PMID: 9961487 DOI: 10.1103/physreve.49.2436] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
76
Hu JP, Ding M. Phase representation and its application in the analytical treatment of the theoretical sandpile. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994;49:R5-R7. [PMID: 9961295 DOI: 10.1103/physreve.49.r5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
77
Christensen K, Olami Z. Sandpile models with and without an underlying spatial structure. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993;48:3361-3372. [PMID: 9960993 DOI: 10.1103/physreve.48.3361] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
78
Cagnoli G, Gammaitoni L, Marchesoni F, Segoloni D. On dislocation damping at low frequencies. ACTA ACUST UNITED AC 1993. [DOI: 10.1080/01418619308219371] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
79
Carlson JM, Grannan ER, Singh C, Swindle GH. Fluctuations in self-organizing systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993;48:688-698. [PMID: 9960647 DOI: 10.1103/physreve.48.688] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
80
Carlson JM, Grannan ER, Swindle GH. Self-organizing systems at finite driving rates. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993;47:93-105. [PMID: 9959984 DOI: 10.1103/physreve.47.93] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
81
Chau HF, Cheng KS. Relations of 1/f and 1/f2 power spectra to self-organized criticality. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992;46:R2981-R2983. [PMID: 9908538 DOI: 10.1103/physreva.46.r2981] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
82
Díaz-Guilera A. Noise and dynamics of self-organized critical phenomena. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992;45:8551-8558. [PMID: 9906954 DOI: 10.1103/physreva.45.8551] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
83
Bántay P, Jánosi IM. Avalanche dynamics from anomalous diffusion. PHYSICAL REVIEW LETTERS 1992;68:2058-2061. [PMID: 10045293 DOI: 10.1103/physrevlett.68.2058] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
84
Jaeger HM, Nagel SR. Physics of the Granular State. Science 1992;255:1523-31. [PMID: 17820163 DOI: 10.1126/science.255.5051.1523] [Citation(s) in RCA: 430] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
85
Lomnitz-Adler J, Knopoff L, Martnez-Mekler G. Avalanches and epidemic models of fracturing in earthquakes. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992;45:2211-2221. [PMID: 9907240 DOI: 10.1103/physreva.45.2211] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
86
Creutz M. On self organized criticality. ACTA ACUST UNITED AC 1992. [DOI: 10.1016/0920-5632(92)90245-n] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
87
Chau HF, Cheng KS. Generalized sandpile model and the characterization of the existence of self-organized criticality. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991;44:6233-6240. [PMID: 9905755 DOI: 10.1103/physreva.44.6233] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
88
Fodor Z, Jánosi IM. Results on the continuous-energy self-organized critical model in one dimension. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991;44:1386-1389. [PMID: 9906088 DOI: 10.1103/physreva.44.1386] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
89
Pla O, Guinea F, Louis E. Self-organized criticality in Laplacian growth. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990;42:6270-6273. [PMID: 9903920 DOI: 10.1103/physreva.42.6270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
90
Obukhov SP. Self-organized criticality: Goldstone modes and their interactions. PHYSICAL REVIEW LETTERS 1990;65:1395-1398. [PMID: 10042255 DOI: 10.1103/physrevlett.65.1395] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
91
Wiesenfeld K, Theiler J, McNamara B. Self-organized criticality in a deterministic automaton. PHYSICAL REVIEW LETTERS 1990;65:949-952. [PMID: 10043067 DOI: 10.1103/physrevlett.65.949] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
92
Jánosi IM. Effect of anisotropy on the self-organized critical state. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990;42:769-774. [PMID: 9904087 DOI: 10.1103/physreva.42.769] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
93
Bak P. IS THE WORLD AT THE BORDER OF CHAOS? Ann N Y Acad Sci 1990. [DOI: 10.1111/j.1749-6632.1990.tb22705.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
94
Dhar D. Self-organized critical state of sandpile automaton models. PHYSICAL REVIEW LETTERS 1990;64:1613-1616. [PMID: 10041442 DOI: 10.1103/physrevlett.64.1613] [Citation(s) in RCA: 117] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
95
McNamara B, Wiesenfeld K. Self-organized criticality in vector avalanche automata. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990;41:1867-1873. [PMID: 9903296 DOI: 10.1103/physreva.41.1867] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
96
Meakin P. Fractal structures. PROG SOLID STATE CH 1990. [DOI: 10.1016/0079-6786(90)90001-v] [Citation(s) in RCA: 59] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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