Critical Bottleneck Size for Jamless Particle Flows in Two Dimensions
  We propose a simple microscopic model for arching phenomena at bottlenecks. The dynamics of particles in front of a bottleneck is described by a one-dimensional stochastic cellular automaton on a semicircular geometry. The model reproduces oscillation phenomena due to formation and collapsing of arches. It predicts the existence of a critical bottleneck size for continuous particle flows. The dependence of the jamming probability on the system size is approximated by the Gompertz function. The analytical results are in good agreement with simulations. 
Takumi Masuda, Katsuhiro Nishinari, and Andreas Schadschneider
cond-mat.stat-mech nlin.CG physics.comp-ph