Chen, Chien-Chih; Lee, Ya-Ting; Chiao, Ling-Yun Intermittent criticality in the long-range connective sandpile (LRCS) model. (English) Zbl 1221.05286 Phys. Lett., A 372, No. 24, 4340-4343 (2008). Summary: We here propose a long-range connective sandpile model with variable connection probability \(P_{c}\) which has an important impact on the slope of the power-law frequency-size distribution of avalanches. The long-range connection probability \(P_{c}\) is changed according to an explicit function of the size of the latest event, although the evolution rule of \(P_{c}\) may be different in various physical systems. Such version of the sandpile model demonstrates large fluctuations in the dynamical variable \(\overline{Z}(t)\) (the spatially averaged amount of grains retained within the grid at each time step), indicating the state of intermittent criticality in the system. Many researches have suggested that the earthquake fault system is an intermittent criticality system, which would imply some level of statistical predictability of great events. Our modified sandpile model thus provides a testing ground for many proposed precursory measures related to great earthquakes. MSC: 05C82 Small world graphs, complex networks (graph-theoretic aspects) 37B15 Dynamical aspects of cellular automata 86A15 Seismology (including tsunami modeling), earthquakes 82C35 Irreversible thermodynamics, including Onsager-Machlup theory 82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics 82C27 Dynamic critical phenomena in statistical mechanics 68M10 Network design and communication in computer systems 35B38 Critical points of functionals in context of PDEs (e.g., energy functionals) 76T25 Granular flows 74E20 Granularity Keywords:sandpile model; self-organized criticality; small-world network; long-range connection; seismicity PDFBibTeX XMLCite \textit{C.-C. Chen} et al., Phys. Lett., A 372, No. 24, 4340--4343 (2008; Zbl 1221.05286) Full Text: DOI Link References: [1] Sornette, A.; Sornette, D., Tectonophysics, 179, 327 (1990) [2] Main, I., Rev. Geophys., 34, 433 (1996) [3] Rundle, J. B.; Klein, W.; Turcotte, D. L.; Malamud, B. D., Pure Appl. Geophys., 157, 2165 (2000) [4] Zoller, G.; Hainzl, S.; Kurths, J., J. Geophys. Res. B, 106, 2167 (2001) [5] Rundle, J. B.; Turcotte, D. L.; Shcherbakov, R.; Klein, W.; Sammis, C., Rev. Geophys., 41 (2003) [6] Chen, C. C.; Rundle, J. B.; Li, H. C.; Holliday, J. R.; Turcotte, D. L.; Tiampo, K. F., Geophys. Res. Lett., 33 (2006) [7] Bak, P.; Tang, C.; Wiesenfeld, K., Phys. Rev. Lett., 59, 381 (1987) [8] Bak, P.; Tang, C., J. Geophys. Res., 94, 15635 (1989) [9] Sornette, A.; Sornette, D., Europhys. Lett., 9, 197 (1989) [10] Ito, K.; Matsuzaki, M., J. Geophys. Res., 95, 6853 (1990) [11] Sammis, C. G.; Smith, S. W., Pure Appl. Geophys., 155, 307 (1999) [12] Rundle, J. B.; Klein, W.; Gross, S., Pure Appl. Geophys., 155, 575 (1999) [13] Castellaro, S.; Mulargia, F., Geophys. J. Int., 150, 483 (2002) [14] Main, I. G.; Al-Kindy, F. H., Geophys. Res. Lett., 29 (2002) [15] Bowman, D. D.; Sammis, C. G., Pure Appl. Geophys., 161, 1945 (2004) [16] Ben-Zion, Y.; Eneva, M.; Liu, Y., J. Geophys. Res. B, 108 (2003) [17] C.C. Chen, L.Y. Chiao, Y.T. Lee, H.W. Cheng, Y.M. Wu, Tectonophysics (2008), 10.1016/j.tecto.2008.04.004; C.C. Chen, L.Y. Chiao, Y.T. Lee, H.W. Cheng, Y.M. Wu, Tectonophysics (2008), 10.1016/j.tecto.2008.04.004 [18] Watts, D. J.; Strogatz, S. H., Nature, 393, 440 (1998) [19] Bak, P., How Nature Works: The Science of Self-Organized Criticality (1996), Springer: Springer New York · Zbl 0894.00007 [20] Jensen, H. J., Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems (1998), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0945.70001 [21] Lomnitz-Adler, J., J. Geophys. Res. B, 98, 17745 (1993) [22] Castellaro, S.; Mulargia, F., Geophys. J. Int., 150, 483 (2001) [23] Weatherley, D.; Mora, P.; Xia, M. F., Pure Appl. Geophys., 159, 2469 (2002) [24] Shimazaki, K.; Nakata, T., Geophys. Res. Lett., 7, 279 (1980) [25] Lomnitz, C., Fundamentals of Earthquake Prediction (1994), Wiley: Wiley New York [26] Mulargia, F.; Gasperini, P., Geophys. J. Int., 120, 453 (1995) [27] Kanamori, H.; Brodsky, E. E., Rep. Prog. Phys., 67, 1429 (2004) [28] Goltz, C.; Bose, M., Geophys. Res. Lett., 29 (2002) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.