Transition on the relationship between fractal dimension and Hurst exponent in the long-range connective sandpile models

Abstract The relationships between the Hurst exponent H and the power-law scaling exponent B in a new modification of sandpile models, i.e. the long-range connective sandpile (LRCS) models, exhibit a strong dependence upon the system size L . As L decreases, the LRCS model can demonstrate a transition from the negative to positive correlations between H - and B -values. While the negative and null correlations are associated with the fractional Gaussian noise and generalized Cauchy processes, respectively, the regime with the positive correlation between the Hurst and power-law scaling exponents may suggest an unknown, interesting class of the stochastic processes.

[1]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[2]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[3]  Maya Paczuski,et al.  Large scale structures, symmetry, and universality in sandpiles. , 2002, Physical review letters.

[4]  C. Sammis,et al.  Seismic Cycles and the Evolution of Stress Correlation in Cellular Automaton Models of Finite Fault Networks , 1999 .

[5]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[6]  John B. Rundle,et al.  Physical Basis for Statistical Patterns in Complex Earthquake Populations: Models, Predictions and Tests , 1999 .

[7]  Satya N. Majumdar,et al.  Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model , 1992 .

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  I. Main,et al.  Entropy, energy, and proximity to criticality in global earthquake populations , 2002 .

[10]  B Kahng,et al.  Sandpile on scale-free networks. , 2003, Physical review letters.

[11]  Ling-Yun Chiao,et al.  Intermittent criticality in the long-range connective sandpile (LRCS) model , 2007 .

[12]  F. Mulargia,et al.  What criticality in cellular automata models of earthquakes , 2002 .

[13]  Tilmann Gneiting,et al.  Stochastic Models That Separate Fractal Dimension and the Hurst Effect , 2001, SIAM Rev..

[14]  P. Alstrøm,et al.  COMPLEXITY AND CRITICALITY , 2004 .

[15]  S. S. Manna.  Two-state model of self-organized criticality , 1991 .

[16]  Christensen,et al.  Sandpile models with and without an underlying spatial structure. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Jensen,et al.  Transitions in nonconserving models of self-organized criticality. , 1995, Physical review letters.

[18]  Chien-Chih Chen,et al.  Precursory phenomena associated with large avalanches in the long-range connective sandpile (LRCS) model , 2008 .

[19]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[20]  Maren Böse,et al.  Configurational entropy of critical earthquake populations , 2002 .

[21]  Ming Li,et al.  Modeling network traffic using generalized Cauchy process , 2008 .

[22]  Remo Guidieri.  Res , 1995, RES: Anthropology and Aesthetics.

[23]  V. Uritsky,et al.  Analysis and prediction of high-latitude geomagnetic disturbances based on a self-organized criticality framework , 2006 .

[24]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[25]  Chien-Chih Chen,et al.  Precursory phenomena associated with large avalanches in the long‐range connective sandpile model II: An implication to the relation between the b‐value and the Hurst exponent in seismicity , 2009 .

[26]  Ling-Yun Chiao,et al.  Long-range connective sandpile models and its implication to seismicity evolution , 2008 .

[27]  D. Turcotte,et al.  Precursory Seismic Activation and Critical-point Phenomena , 2000 .

[28]  H. Herrmann,et al.  Self-organized criticality on small world networks , 2001, cond-mat/0110239.

[29]  A. Frankel.  High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults , 1991 .

[30]  R. F. Voss.  Random fractals: self-affinity in noise, music, mountains, and clouds , 1989 .

[31]  G. Paladin,et al.  Earthquake statistics and fractal faults , 1997 .

[32]  Kimmo Kaski,et al.  Sandpiles on Watts-Strogatz type small-worlds , 2005 .

[33]  V. Troyan,et al.  Critical dynamics of fractal fault systems and its role in the generation of pre-seismic electromagnetic emissions , 2004 .