Sandpile on Scale-Free Networks
K.-I. Goh, D.-S. Lee, B. Kahng, D. Kim

TL;DR
This paper studies avalanche dynamics in the sandpile model on scale-free networks, deriving critical exponents analytically and numerically, revealing how network heterogeneity influences avalanche behavior.
Contribution
It provides an analytical framework for understanding avalanche size distributions on scale-free networks, extending the BTW model to heterogeneous thresholds.
Findings
Avalanche size distribution follows a power law with exponents depending on network degree exponent.
Analytic expressions for exponents $ au$ and $z$ as functions of $eta$ are derived.
Numerical simulations confirm the theoretical predictions.
Abstract
We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model on scale-free (SF) networks, where threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent . Applying the theory of multiplicative branching process, we obtain the exponent and the dynamic exponent as a function of the degree exponent of SF networks as and in the range and the mean field values and for , with a logarithmic correction at . The analytic solution supports our numerical simulation results. We also consider the case of uniform threshold, finding that the two exponents reduce to the mean field ones.
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