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

Joceline C Lega, Sunder Sethuraman, Alexander L. Young

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1088-1122
Number of pages35
JournalJournal of Statistical Physics
Volume170
Issue number6
DOIs
StatePublished - Mar 1 2018

Fingerprint

classifying
Sorting
One Dimension
Collision
collisions
Conserve
One-dimensional System
infinity
Numerical Investigation
elastic scattering
Asymptotic distribution
Momentum
momentum
Infinity
Binary
Energy

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

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

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