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Journal of Statistical Physics

, Volume 84, Issue 3–4, pp 837–857 | Cite as

Aggregation dynamics in a self-gravitating one-dimensional gas

  • Philippe A. Martin
  • Jarosław Piasecki
Articles

Abstract

Aggregation of mass by perfectly inelastic collisions in a one-dimensional self-gravitating gas is studied. The binary collisions are subject to the laws of mass and momentum conservation. A method to obtain an exact probabilistic description of aggregation is presented. Since the one-dimensional gravitational attraction is confining, all particles will eventually form a single body. The detailed analysis of the probabilityP n (t) of such a complete merging before timet is performed for initial states ofn equidistant identical particles with uncorrelated velocities. It is found that for a macroscopic amount of matter (n→∞), this probability vanishes before a characteristic timet*. In the limit of a continuous initial mass distribution the exact analytic form ofP n (t) is derived. The analysis of collisions leading to the time-variation ofP n (t), reveals that in fact the merging into macroscopic bodies always occurs in the immediate vicinity oft*. Fort>t*, andn large,P n (t) describes events corresponding to the final aggregation of remaining microscopic fragments.

Key Words

Inelastic collisions gravitational forces aggregation of mass 

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References

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    P. A. Martin and J. Piasecki,J. Stat. Phys. 76:447 (1994).Google Scholar
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    W. C. Saslaw,Gravitational Physics of Stellar and Galactic Systems (Cambridge University Press, Cambridge, 1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Philippe A. Martin
    • 1
  • Jarosław Piasecki
    • 2
  1. 1.Institut de Physique ThéoriqueEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Institute of Theoretical PhysicsUniversity of WarsawWarsawPoland

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