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.
Barre, C., Talbot, J., Viot, P., Angelani, L., Gabrielli, A. (2015). Generalized model of blockage in particulate flow limited by channel carrying capacity. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 92(3), 032141 [10.1103/PhysRevE.92.032141].
Generalized model of blockage in particulate flow limited by channel carrying capacity
Gabrielli A.
2015-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
