Non-Markovian Models of Blocking in Concurrent and Countercurrent Flows

Abstract

We investigate models in which blocking can interrupt a particulate flow process at any time. Filtration, and flow in micro/nano-channels and traffic flow are examples of such processes. We first consider concurrent flow models where particles enter a channel randomly. If at any time two particles are simultaneously present in the channel, failure occurs. The key quantities are the survival probability and the distribution of the number of particles that pass before failure. We then 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.

5 pages, 5 figures, to appear in Phys. Rev. Letters

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Cited by in corpus (6)

• Generalized model of blockage in particulate flow limited by channel carrying capacity
• Stochastic models of multi-channel particulate transport with blockage
• Zone clearance in an infinite TASEP with a step initial condition
• Optimizing the Throughput of Particulate Streams Subject to Blocking
• Recurrence dynamics of particulate transport with reversible blockage: from a single channel to a bundle of coupled channels
• Buffon-Laplace Needle Problem as a geometric probabilistic approach to filtration process