Velocity and cluster distributions in a bottleneck system

Vidar Frette, Per C. Hemmer
2009 Physical Review E  
Velocity and cluster distributions for particles with unidirectional motion in one dimension are studied. The particles never pass each other, like cars on a narrow road that does not allow overtaking. As a result, particles cluster behind slow particles ͑queues are formed behind slow cars͒. Thus, the actual velocity of each particle is to a large extent determined by slow particles further ahead. Considering all possible permutations of N particles with initial velocities ͕v i ͖, the average
more » ... i ͖, the average number of particles with actual velocity v i is ͑N +1͒ / ͓i͑i +1͔͒ ͑in the sequence ͕v i ͖, the initial velocities are listed with monotonically increasing values͒. For i large and v i ϰ i the average number of actual velocities is thus a power law in v i , even though the average cluster density is found to be independent of cluster size, L. On the other hand, the cluster density varies significantly with cluster velocity; we obtain The average velocity at a given position in the sequence of N particles, and the average global velocity are determined. Explicit results for several distributions of the initial velocities show that the global velocity depends sensitively on the form of this distribution.
doi:10.1103/physreve.80.051115 pmid:20364955 fatcat:2uvdmgpw5fhmjphbvrosmiilie