title: Generalized model of blockage in particulate flow limited by channel carrying capacity.
abstract: We investigate stochastic models of particles entering a channel with a random time distribution. When the number of particles present in the channel exceeds a critical value N, a blockage occurs and the particle flux is definitively interrupted. By introducing an integral representation of the n-particle survival probabilities, we obtain exact expressions for the survival probability, the distribution of the number of particles that pass before failure, the instantaneous flux of exiting particles, and their time correlation. We generalize previous results for N=2 to an arbitrary distribution of entry times and obtain exact solutions for N=3 for a Poisson distribution and partial results for N≥4.
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France.
authors.forename: C
authors.initials: C
authors.lastname: Barré
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France.
authors.forename: J
authors.initials: J
authors.lastname: Talbot
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France.
authors.forename: P
authors.initials: P
authors.lastname: Viot
authors.affiliation: Istituto dei Sistemi Complessi (ISC) - CNR, UOS "Sapienza," Department of Physics, University "Sapienza" of Rome, Piazzale Aldo Moro 2, 00185 Rome, Italy.
authors.forename: L
authors.initials: L
authors.lastname: Angelani
authors.affiliation: Istituto dei Sistemi Complessi (ISC) - CNR, UOS "Sapienza," Department of Physics, University "Sapienza" of Rome, Piazzale Aldo Moro 2, 00185 Rome, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Gabrielli