Ballistic aggregation: a solvable model of irreversible many particles dynamics

Details Ballistic aggregation: a solvable model of irreversible many particles dynamics Ballistic aggregation: a solvable model of irreversible many particles dynamics

1999-11-22

arxiv.org/abs/cond-mat/9911346v1

Physics

Condensed Matter

Statistical Mechanics

23 pages, 6 figures included

Scientific paper

10.1016/S0378-4371(99)00585-3

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.

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