Dimension Dependence of Clustering Dynamics in Models of Ballistic Aggregation and Freely Cooling Granular Gas

TL;DR

This study uses simulations to analyze how clustering dynamics in inelastic particle systems depend on spatial dimension, revealing distinct behaviors and scaling relations in ballistic aggregation and granular gas models.

Contribution

It provides a comparative analysis of clustering kinetics across dimensions in two models, highlighting dimension-dependent exponents and scaling behaviors.

Findings

BAM exponents strongly depend on dimension and follow hyperscaling.

In high packing fractions, BAM behavior aligns with a scaling theory predicting inverse energy-mass relation.

GGM shows dimension-insensitive mass growth and energy decay, differing from BAM patterns.

Abstract

Via event-driven molecular dynamics simulations we study kinetics of clustering in assemblies of inelastic particles in various space dimensions. We consider two models, viz., the ballistic aggregation model (BAM) and the freely cooling granular gas model (GGM), for each of which we quantify the time dependence of kinetic energy and average mass of clusters (that form due to inelastic collisions). These quantities, for both the models, exhibit power-law behavior, at least in the long time limit. For the BAM, corresponding exponents exhibit strong dimension dependence and follow a hyperscaling relation. In addition, in the high packing fraction limit the behavior of these quantities become consistent with a scaling theory that predicts an inverse relation between energy and mass. On the other hand, in the case of the GGM we do not find any evidence for such a picture. In this case, even though the energy decay, irrespective of packing fraction, matches quantitatively with that for the high packing fraction picture of the BAM, it is inversely proportional to the growth of mass only in one dimension, and the growth appears to be rather insensitive to the choice of the dimension, unlike the BAM.