Aggregation with Multiple Conservation Laws

TL;DR

This paper analyzes aggregation processes with multiple conserved quantities, deriving exact mean-field solutions and revealing complex scaling behaviors, including an additional diffusion-like scale in systems with multiple conservation laws.

Contribution

It provides an exact mean-field solution for aggregation with multiple conservation laws and uncovers novel double scaling phenomena.

Findings

Exact size distribution solution for multiple conserved quantities

Identification of double scaling behavior in asymptotic solutions

Application to ballistic and diffusive aggregation processes

Abstract

Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double'' scaling. While processes with one conserved quantity are governed by a single scale, processes with multiple conservation laws exhibit an additional diffusion-like scale. The theory is applied to ballistic aggregation with mass and momentum conserving collisions and to diffusive aggregation with multiple species.