Stochastic flow models
Pascal Viot (LPTMC, UPMC)
Filtration, and flow in micro/nano-channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. We investigate a concurrent flow model where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, failure occurs. We obtain the exact solution for the survival probability, the distribution of the number of particles that pass before failure, and the instantaneous flux exiting the channel. Several generalizations of this simple model are also studied. We also consider a counterflow model with two opposing Poisson streams. There is no restriction on the number of particles passing in the same direction, but blockage occurs if, at any time, two opposing particles are simultaneously present in the passage. All relevant quantities have been obtained exactly.
[1] Non-Markovian Models of Blocking in Concurrent and Countercurrent Flows, A. Gabrielli, J. Talbot and P. Viot Phys. Rev. Lett, 110, 170601 (2013)
[2] Stochastic model of single-file flow with reversible blockage, Chloé Barré, Julian Talbot and Pascal Viot EPL, 104 60005 (2013)
[3] Irreversible Blocking in Single-File Concurrent and Countercurrent Particulate Flows, J. Talbot, A. Gabrielli and P. Viot J Stat Mech to be published (2015)