Sandpile on scale-free networks.
We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the 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 tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic exponent z as a function of the degree exponent gamma of SF networks as tau=gamma divided by (gamma-1) and z=(gamma-1) divided by (gamma-2) in the range 2<gamma<3 and the mean-field values tau=1.5 and z=2.0 for gamma>3, with a logarithmic correction at gamma=3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.
Goh
K-I
KI
School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.
Lee
D-S
DS
Kahng
B
B
Kim
D
D