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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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Abstract
Granular materials display a variety of behaviors that are in many ways different from those of other substances. They cannot be easily classified as either solids or liquids. This has prompted the generation of analogies between the physics found in a simple sandpile and that found in complicated microscopic systems, such as flux motion in superconductors or spin glasses. Recently, the unusual behavior of granular systems has led to a number of new theories and to a new era of experimentation on granular systems.
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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