### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities.** / Lega, Joceline C; Sethuraman, Sunder; Young, Alexander L.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 170, no. 6, pp. 1088-1122. https://doi.org/10.1007/s10955-018-1974-4

}

TY - JOUR

T1 - On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities

AU - Lega, Joceline C

AU - Sethuraman, Sunder

AU - Young, Alexander L.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - Binary collisions

KW - Collision times

KW - Exchangeable arrays

KW - Interacting particles

KW - Maximal order statistics

KW - Molecular dynamics

UR - http://www.scopus.com/inward/record.url?scp=85042565547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042565547&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-1974-4

DO - 10.1007/s10955-018-1974-4

M3 - Article

AN - SCOPUS:85042565547

VL - 170

SP - 1088

EP - 1122

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -