Ballistic aggregation: a solvable model of irreversible many particles dynamics

TL;DR

This paper presents an exactly solvable model of irreversible particle aggregation in one dimension, revealing connections to shock statistics in Burgers turbulence and providing explicit solutions for cluster distributions.

Contribution

It introduces a solvable kinetic model for one-dimensional adhesive particle dynamics and links it to Burgers turbulence shock statistics, offering explicit distribution solutions.

Findings

Distributions of clusters match shock statistics in Burgers turbulence.

The model provides explicit solutions for cluster size distributions.

The approach maps to a Brownian motion problem with constraints.

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.