Dynamic condensates in aggregation processes with mass injection

TL;DR

This paper studies dynamic condensates in a one-dimensional aggregation model with mass injection, revealing how large mass clusters form and evolve, significantly impacting the mass distribution over time.

Contribution

It introduces the concept of dynamic condensates in the Takayasu aggregation model and analyzes their growth and statistical properties over time.

Findings

Dynamic condensates hold about 80% of the mass when injection and diffusion are equal.

The largest mass grows as a power law in time with multiplicative logarithmic corrections.

At long times, a condensate's mass increases linearly with time, atop a power-law background.

Abstract

The Takayasu aggregation model is a paradigmatic model of aggregation with mass injection, known to exhibit a power law distribution of mass over a range which grows in time. Working in one dimension we find that the mass profile in addition shows distinctive {\it dynamic condensates} which collectively hold a substantial portion of the mass (approximately $80\%$ when injection and diffusion rates are equal) and lead to a substantial hump in the scaled distribution. To track these, we monitor the largest mass within a growing coarsening length. An interesting outcome of extremal statistics is that the mean of the globally largest mass in a finite system grows as a power law in time, modulated by strong multiplicative logarithms in both time and system size. At very long times in a finite system, the state consists of a power-law-distributed background with a condensate whose mass increases linearly with time.