Jc. Bonvin et al., STATISTICS OF MASS AGGREGATION IN A SELF-GRAVITATING ONE-DIMENSIONAL GAS, Journal of statistical physics, 91(1-2), 1998, pp. 177-197
We study at the microscopic level the dynamics of a one-dimensional, g
ravitationally interacting sticky gas. Initially, N identical particle
s of mass m with uncorrelated, randomly distributed Velocities fill ho
mogeneously a finite region of space. It is proved that at a character
istic time a single macroscopic mass is formed with certainty, surroun
ded by a dust of nonextensive fragments. In the continuum limit this c
orresponds to a single shock creating a singular mass density. The sta
tistics of the remaining fragments obeys the Poisson law at all times
following the shock. Numerical simulations indicate that up to the mom
ent of macroscopic aggregation the system remains internally homogeneo
us. At the short time scale a rapid decrease in the kinetic energy is
observed, accompanied by the formation of a number similar to root N o
f aggregates with masses similar to m root N.