On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities


Journal Article

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We investigate a one-dimensional system of N particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the N particles do not interact and become sorted according to their velocities. When the collisions are elastic, we derive asymptotic distributions for the final collision time of a single particle and the final collision time of the system as the number of particles approaches infinity, under different assumptions for the initial distributions of the particles’ positions and velocities. For comparison, a numerical investigation is carried out to determine how a non-elastic collision rule, which conserves neither momentum nor energy, affects the median collision time of a particle and the median final collision time of the system.

Full Text

Cited Authors

  • Lega, J; Sethuraman, S; Young, AL

Published Date

  • March 1, 2018

Published In

Volume / Issue

  • 170 / 6

Start / End Page

  • 1088 - 1122

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-018-1974-4

Citation Source

  • Scopus