Ballistic aggregation: a solvable model of irreversible many particles dynamics
Statistical Mechanics
2009-10-31 v1
Abstract
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system of two coupled equations for a large class of initial conditions. The solution to these nonlinear equations is found by a direct construction of the relevant probability distributions in the limit of a continuous initial mass distribution. We show that those limiting distributions are identical to those of the statistics of shocks in the Burgers turbulence. The analysis relies on a mapping on a Brownian motion problem with parabolic constraints.
Cite
@article{arxiv.cond-mat/9911346,
title = {Ballistic aggregation: a solvable model of irreversible many particles dynamics},
author = {L. Frachebourg and Ph. A. Martin and ; J. Piasecki},
journal= {arXiv preprint arXiv:cond-mat/9911346},
year = {2009}
}
Comments
23 pages, 6 figures included