Stochastic models of multi-channel particulate transport with blockage
| Autor: | Pascal Viot, Gregory Page, Chloé Barré, Julian Talbot |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Steady state Statistical Mechanics (cond-mat.stat-mech) Stochastic modelling Mathematical analysis Flux FOS: Physical sciences Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Open-channel flow Cascade Bundle 0103 physical sciences Particle General Materials Science 010306 general physics Condensed Matter - Statistical Mechanics Communication channel Computer Science::Information Theory |
| DOI: | 10.48550/arxiv.1803.09629 |
| Popis: | Networks of channels conveying particles are often subject to blockages due to the limited carrying capacity of the individual channels. If the channels are coupled, blockage of one causes an increase in the flux entering the remaining open channels leading to a cascade of failures. Once all channels are blocked no additional particle can enter the system. If the blockages are of finite duration, however, the system reaches a steady state with an exiting flux that is reduced compared to the incoming one. We propose a stochastic model consisting of $N_c$ channels each with a blocking threshold of $N$ particles. Particles enter the system according to a Poisson process with the entering flux of intensity $\Lambda$ equally distributed over the open channels. Any particle in an open channel exits at a rate $\mu$ and a blocked channel unblocks at a rate $\mu^*$. We present a method to obtain the exiting flux in the steady state, and other properties, for arbitrary $N_c$ and $N$ and we present explicit solutions for $N_c=2,3$. We apply these results to compare the efficiency of conveying a particulate stream of intensity $\Lambda$ using different channel configurations. We compare a single "robust" channel with a large capacity with multiple "fragile" channels with a proportionately reduced capacity. The "robust" channel is more efficient at low intensity, while multiple, "fragile" channels have a higher throughput at large intensity. We also compare $N_c$ coupled channels with $N_c$ independent channels, both with threshold $N=2$. For $N_c=2$ if $\mu^*/\mu>1/4$, the coupled channels are always more efficient. Otherwise the independent channels are more efficient for sufficiently large $\Lambda$. Comment: 13 pages submitted to J. Phys. Cond. Matter |
| Databáze: | OpenAIRE |
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