title: Analytical approach to directed sandpile models on the Apollonian network.
abstract: 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.
authors.affiliation: Departamento de Engenharia Metalúrgica e de Materiais, Universidade Federal do Ceará, Campus do Pici, 60455-760 Fortaleza, Brazil.
authors.forename: André P
authors.initials: AP
authors.lastname: Vieira
authors.forename: José S
authors.initials: JS
authors.lastname: Andrade
authors.forename: Hans J
authors.initials: HJ
authors.lastname: Herrmann
authors.forename: Roberto F S
authors.initials: RF
authors.lastname: Andrade