Eur. Phys. J. B (2016) 89: 208
https://doi.org/10.1140/epjb/e2016-70411-1

Regular Article

Diminishing blocking interval in particle-conveying channel bundles

Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France

^a e-mail: talbot@lptmc.jussieu.fr

Received: 1 July 2016
Received in final form: 23 July 2016
Published online: 26 September 2016

Abstract

We consider a channel bundle consisting of N_c parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and exit after a fixed transit time, τ. An individual channel blocks if N particles are simultaneously present. When a channel is blocked the flux previously entering it is redistributed evenly over the remaining open channels. We perform event driven simulations to examine the behaviour of an initially empty channel bundle with a total entering flux of intensity Λ. The mean blockage time of the kth channel is denoted by ⟨ t_k ⟩ ,k = 1,...,N_c. For N = 1, as shown previously, the interval between successive blockages is constant, while for N> 1 an accelerating cascade, i.e. one in which the interval between successive blockages decreases, is observed. After an initial transient regime we observe a well-defined universal regime that is characterized by where and denotes the jth order difference.