Kinetics of self-induced aggregation in Brownian particles

TL;DR

This paper investigates a model of Brownian particles that self-organize into clusters through local interactions, revealing power-law growth and scaling behaviors in aggregation dynamics.

Contribution

It introduces a simple interaction mechanism leading to self-induced aggregation in Brownian particles, with analysis of the resulting nonlinear dynamics and scaling laws.

Findings

Clusters grow with a power law in time

Scaling properties of stochastic aggregation are verified

Low randomness favors coalescence behavior

Abstract

We study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in group of individuals. Each individual, represented by a Brownian particle, experiences an interaction produced by the local unbalance in the spatial distribution of the other individuals. This interaction results in a nonlinear velocity driving the particle trajectories in the direction of the nearest more crowded regions; the competition among different aggregating centers generates nontrivial dynamical regimes. Our simulations show that for sufficiently low randomness, the system evolves through a coalescence behavior characterized by clusters of particles growing with a power law in time. In addition, the typical scaling properties of the general theory of stochastic aggregation processes are verified.