Ballistic aggregation: a solvable model of irreversible many particles dynamics
- Resource Type
- Working Paper
- Authors
- Frachebourg, L.; Martin, Ph. A.; Piasecki, ; J.
- Source
- Subject
- Condensed Matter - Statistical Mechanics
- Language
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.
Comment: 23 pages, 6 figures included