Analytical approach to directed sandpile models on the Apollonian network.
We investigate a set of directed sandpile models on the Apollonian network, which are inspired by the work of Dhar and Ramaswamy [Phys. Rev. Lett. 63, 1659 (1989)] on Euclidian lattices. They are characterized by a single parameter q , which restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two- and three-point correlation functions are amenable to exact treatment, leading to analytical results for avalanche distributions in the limit of an infinite system for q=1,2 . The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite-size systems when larger values of q are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.
Vieira
André P
AP
Departamento de Engenharia Metalúrgica e de Materiais, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Brazil.
Andrade
José S
JS
Herrmann
Hans J
HJ
Andrade
Roberto F S
RF