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


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. A. Martin and J. Piasecki,J. Stat. Phys. 76:447 (1994).Google Scholar
  2. 2.
    W. Feller,An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968).Google Scholar
  3. 3.
    J. E. Robinson,Phys. Rev. 83:678 (1951).Google Scholar
  4. 4.
    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

Personalised recommendations