@article{ref1,
title="Abelian deterministic self-organized-criticality model: Complex dynamics of avalanche waves",
journal="Physical review E: Statistical, nonlinear, and soft matter physics",
year="2010",
author="Cernák, Jozef",
volume="82",
number="6 Pt 1",
pages="061116-061116",
abstract="The aim of this study is to investigate a wave dynamics and a size scaling of avalanches which were created by the mathematical model [J. Černák, Phys. Rev. E 65, 046141 (2002)10.1103/PhysRevE.65.046141]. Numerical simulations were carried out on a two-dimensional lattice L×L in which two constant thresholds E_{c}^{I}=4 and E_{c}^{II}>E_{c}^{I} were randomly distributed. The density of sites c of the thresholds E_{c}^{II} and threshold E_{c}^{II} are parameters of the model. Autocorrelations of avalanche size waves, Hurst exponents, avalanche structures, and avalanche size moments were determined for several densities c and thresholds E_{c}^{II} . The results show correlated avalanche size waves and multifractal scaling of avalanche sizes not only for specific conditions, densities c=0.0,1.0 and thresholds 8≤E_{c}^{II}≤32 , in which relaxation rules were precisely balanced, but also for more general conditions, densities 0.0<c<1.0 and thresholds 8≤E_{c}^{II}≤32 , in which relaxation rules were unbalanced. The results suggest that the hypothesis of a precise relaxation balance could be a specific case of a more general rule.<p /> <p>Language: en</p>",
language="en",
issn="1539-3755",
doi="",
url="http://dx.doi.org/"
}