On energy and clusters in stochastic systems of sticky gravitating particles

V. V. Vysotsky

doi:10.1137/S0040585X97981639

On energy and clusters in stochastic systems of sticky gravitating particles

V. V. Vysotsky

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider a one-dimensional model of a gravitational gas. The gas consists of n particles whose initial positions and speeds are random. At collisions particles stick together, forming "clusters." Our main goal is to study the properties of the gas as n → ∞. We separately consider "cold gas" (each particle has zero initial speed) and "warm gas" (each particle has nonzero initial speed). For the cold gas, the asymptotics of the number of clusters K_n(t) is studied. We also explore the kinetic energy E_n(t). It is proved that the warm gas instantly "cools," i.e., E_n(+0) → 0 as n → ∞.

Original language	English (US)
Pages (from-to)	265-283
Number of pages	19
Journal	Theory of Probability and its Applications
Volume	50
Issue number	2
DOIs	https://doi.org/10.1137/S0040585X97981639
State	Published - Jul 24 2006

Keywords

Energy
Gravitational gas
Nonelastic collisions
Number of clusters
Sticky particles
System of particles

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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AB - We consider a one-dimensional model of a gravitational gas. The gas consists of n particles whose initial positions and speeds are random. At collisions particles stick together, forming "clusters." Our main goal is to study the properties of the gas as n → ∞. We separately consider "cold gas" (each particle has zero initial speed) and "warm gas" (each particle has nonzero initial speed). For the cold gas, the asymptotics of the number of clusters Kn(t) is studied. We also explore the kinetic energy En(t). It is proved that the warm gas instantly "cools," i.e., En(+0) → 0 as n → ∞.

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KW - System of particles

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On energy and clusters in stochastic systems of sticky gravitating particles

Abstract

Keywords

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