Ballistic Coalescence Model

TL;DR

This paper investigates a one-dimensional coalescing particle system with particles moving at constant velocities, proposing a mean-field theory that explains the observed $t^{-1}$ decay in particle concentration and describes gap densities.

Contribution

It introduces a mean-field theoretical framework for a coalescing particle system with constant velocities, confirming simulation results and providing qualitative insights into gap distributions.

Findings

Particle concentration decays as $t^{-1}$ over time.

Mean-field theory aligns with simulation results.

Provides qualitative descriptions of gap densities.

Abstract

We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory that confirms a $t^{-1}$ concentration decay obtained in simulations and provides qualitative description for the densities of growing, constant, and shrinking inter-particle gaps.