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arXiv · 1306.0311

Bak-Tang-Wiesenfeld Model in the Finite Range Random Link Lattice

M. N. Najafi
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Abstract

We consider the BTW model in random link lattices with finite range interaction (RLFRI). The degree distribution for nodes is considered to be uniform in the interval $(0,n_0)$. We numerically calculate the exponents of the distribution functions in terms of $(n_0,R)$ in which $R$ is the range of interactions. Dijkstra radius is utilized to calculate the fractal dimension of the avalanches. Our analysis shows that there is, at least one length scale ($r_0(n_0,R)$) in which the fractal dimension is changed. We find that for the scales smaller than $r_0(n_0,R)$, which is typically one decade, the fractal dimension is nearly independent of $n_0$ and $R$ and is equal to $1.4$, i.e. close to that of the BTW in the regular lattice ($1.25$). Using this fact and other analysis, we conclude that the BTW-type behaviors are dominant for small values of $n_0$ and $R$, whereas for large values of these parameters a new regime is seen in which the exponent of distribution function of avalanche masses is nearly $1.4$. We also numerically calculate the explicit form of the \textit{number of unstable nodes} (NUN) as a time dependent process and show that for regular lattice it is (up to a normalization) proportional to a one dimensional Weiner process and for RLFRI it acquires a drift term. Using this dynamical variable it is numerically shown that we can not continuously approach the regular lattice limit by decreasing $R$.

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BibTeXRIS

M. N. Najafi. 2013-11-21. Bak-Tang-Wiesenfeld Model in the Finite Range Random Link Lattice. https://doi.org/10.1016/j.physleta.2014.05.051

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