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Extended instability criteria in isotropic and anisotropic energy avalanches

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  • Georgoulis, M.
  • Kluiving, R.
  • Vlahos, L.

Abstract

We demonstrate that adding extended instability criteria to 3D critical-slope sand-pile models has the effect of considerably enhancing the self-organized critical state displayed by these models. We present two extended models, an isotropic one which displays large energy-avalanches, and an anisotropic one which shows much shorter and much more frequent energy bursts. We illuminate the multifractal nature of the self-organised critical state in both extended models by finding a nontrivial spectrum of generalised correlation dimensions from the time series and by showing that the power-law regions of the distributions functions for different lattice sizes show a scaling behaviour which is ruled by a generalised multifractal scaling transformation.

Suggested Citation

  • Georgoulis, M. & Kluiving, R. & Vlahos, L., 1995. "Extended instability criteria in isotropic and anisotropic energy avalanches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 218(1), pages 191-213.
    • Handle: RePEc:eee:phsmap:v:218:y:1995:i:1:p:191-213
    DOI: 10.1016/0378-4371(95)00056-D
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    1. Hohenberg, Paul M., 1993. "Time and Order in Metropolitan Vienna: A Seizure of Schedule. By Robert Rotenberg. Washington, DC: Smithsonian Institution Press, 1992. Pp. x, 262. $32.50," The Journal of Economic History, Cambridge University Press, vol. 53(3), pages 668-669, September.
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