2015/05/14 by C. Barré, J. Talbot, P. Viot L. Angelani +4
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Channel (broadcasting) #Computer science #Diffusion and Search Dynamics #Distribution (mathematics) #Flow (mathematics) #Flux (metallurgy) #Materials science #Mathematical analysis #Mathematics #Mechanics #Particle (ecology) #Particle number #Physics #Poisson distribution #Representation (politics) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Telecommunications #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.92.032141
published as Phys. Rev. E 92, 032141 (2015) · 13 pages, 9 figures
arxiv created 2015/05/14 · openalex publication_date 2015/09/29 · arxiv updated 2015/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.