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Intermittent criticality in the long-range connective sandpile (LRCS) model. (English) Zbl 1221.05286

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
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