2012/05/08 by H. J. Hilhorst, H J Hilhorst, C. Appert-Rolland +1 · 3 citations
Mathematics · Physics and Astronomy · #Core (optical fiber) #Hard core #Intersection (aeronautics) #Jamming #Lattice (music) #Markov Chains and Monte Carlo Methods #Obstacle #Range (aeronautics) #Square lattice #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Unit square #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2012/06/p06009
published as J. Stat. Mech. (2012) P06009 · 30 pages, 9 figures
arxiv created 2012/05/08 · openalex publication_date 2012/06/19 · openalex created_date 2016/06/24 · arxiv updated 2017/09/20 · openalex updated_date 2026/08/05
A one-way street of width M is modeled as a set of M parallel one-dimensional TASEPs. The intersection of two perpendicular streets is a square lattice of size M × M . We consider hard core particles entering each street with an injection probability α. On the intersection square the hard core exclusion creates a many-body problem of strongly interacting TASEPs and we study the collective dynamics that arises. We construct an efficient algorithm that allows for the simulation of streets of infinite length, which have sharply defined critical jamming points. The algorithm employs the ‘frozen shuffle update’, in which the randomly arriving particles have fully deterministic bulk dynamics. High precision simulations for street widths up to M = 24 show that when α increases, there occur jamming transitions at a sequence of M critical values . As M grows, the principal transition point α M M decreases roughly as ∼ (log M ) −1 in the range of M values studied. We show that a suitable order parameter is provided by a reflection coefficient associated with the particle current in each TASEP.