Analytical Results for Nontrivial Polydispersity Exponents in Aggregation Models

TL;DR

This paper analyzes a mean-field aggregation model using the Smoluchowski equation, deriving the mass distribution exponent through perturbative methods and discussing potential applications to turbulence.

Contribution

It provides new analytical results for the polydispersity exponents in aggregation models, including both perturbative and non-perturbative approaches.

Findings

Derived the scaling exponent $ au$ for the mass distribution.

Applied perturbative and non-perturbative expansions to the model.

Discussed potential relevance to two-dimensional turbulence.

Abstract

We study a Smoluchowski equation describing a simple mean-field model of particles moving in $d$ dimensions and aggregating with conservation of `mass' $s=R^D$ ($R$ is the particle radius). In the scaling regime the scaled mass distribution $P(s)\sim s^{-\tau}$, and $\tau$ can be computed by perturbative and non perturbative expansions. A possible application to two-dimensional decaying turbulence is briefly discussed.