Kinetics of Aggregation with Choice

TL;DR

This paper explores a generalized aggregation process with choice, revealing novel scaling behaviors and tail overpopulation in cluster size distributions, extending understanding of aggregation dynamics.

Contribution

It introduces a new aggregation model with choice, analyzing its asymptotic behavior and uncovering unique scaling and distribution features not seen in ordinary aggregation.

Findings

Small cluster density exhibits anomalous scaling.

Overpopulation of small and large cluster tails.

Moderate clusters are abundant at the expense of small and large ones.

Abstract

We generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly selected, and the target cluster merges with the larger of the two candidate clusters. We study the long-time asymptotic behavior, and find that as in ordinary aggregation, the size density adheres to the standard scaling form. However, aggregation with choice exhibits a number of novel features. First, the density of the smallest clusters exhibits anomalous scaling. Second, both the small-size and the large-size tails of the density are overpopulated, at the expense of the density moderate-size clusters. We also study the complementary case where the smaller candidate clusters participates in the aggregation process, and find abundance of moderate clusters at the expense of small and large clusters. Additionally, we investigate aggregation processes with choice among multiple candidate clusters, and a symmetric implementation where the choice is between two pairs of clusters.