Geodesic
Energy and number of clusters in stochastic systems of sticky gravitating particles
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 241-265

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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 $n\to\infty$. 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., $E_n(+0)\to 0$ as $n\to\infty$.
Mots-clés : gravitational gas
Keywords: sticky particles, nonelastic collisions, system of particles, number of clusters, energy. 
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     author = {V. V. Vysotsky},
     title = {Energy and number of clusters in stochastic systems of sticky gravitating particles},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {241--265},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a2/}
}
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V. V. Vysotsky. Energy and number of clusters in stochastic systems of sticky gravitating particles. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 241-265. http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a2/