How initial condition impacts aggregation -- a systematic numerical study

TL;DR

This study systematically investigates how different initial conditions influence the aggregation process across various kernels, revealing similarities, unexpected behaviors, and questioning the possibility of phase transitions triggered solely by initial states.

Contribution

It provides a comprehensive numerical analysis of initial condition effects on diverse aggregation kernels, highlighting new behaviors and challenging assumptions about phase transitions.

Findings

Strong correspondence between constant and Brownian kernels

Unexpected behavior of the product kernel with condensation nuclei initial conditions

Initial conditions alone are unlikely to trigger phase transitions

Abstract

In a process of aggregation, a finite number of particles merge irreversibly to create growing clusters. In this work, impact of particular initial conditions: monodisperse, power-law, exponential, and inspired by condensation nuclei was tested against several aggregation processes: constant, additive, product, electrorheological, anti-social, Berry's, Brownian, shear, and gravitational kernels. Coagulating systems consisting of a thousand monomers were observed in the late time of the evolution, for the moment when only fifty clusters were left in the system. In this way, the impact of particular initial condition was revealed in relation to other initial conditions. Several similarities between different kernels were observed, among others, strong correspondence between the constant and the Brownian kernel was confirmed. In case of the product kernel, unexpected behaviour related to the condensation nuclei initial conditions was revealed and explained. According to the results, it is doubtful that a phase transition can be triggered by appropriate setting of initial condition.