### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1088-1122 |

Number of pages | 35 |

Journal | Journal of Statistical Physics |

Volume | 170 |

Issue number | 6 |

DOIs | |

State | Published - Mar 1 2018 |

### Keywords

- Binary collisions
- Collision times
- Exchangeable arrays
- Interacting particles
- Maximal order statistics
- Molecular dynamics

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics