Finite Size Effects in Addition and Chipping Processes

TL;DR

This paper analyzes how finite size effects influence the dynamics of cluster systems undergoing addition and chipping processes, revealing different scaling behaviors and states depending on process probabilities.

Contribution

It provides an analytical and numerical study of finite size effects in cluster evolution with addition and chipping, highlighting distinct behaviors based on process dominance.

Findings

Monomers disappear in a time scaling as ln N when addition prevails.

System reaches a jammed state with addition dominance.

In chipping dominance, the system remains quasi-stationary for exponential time in N.

Abstract

We investigate analytically and numerically a system of clusters evolving via collisions with clusters of minimal mass (monomers). Each collision either leads to the addition of the monomer to the cluster or the chipping of a monomer from the cluster, and emerging behaviors depend on which of the two processes is more probable. If addition prevails, monomers disappear in a time that scales as $\ln N$ with the total mass $N\gg 1$, and the system reaches a jammed state. When chipping prevails, the system remains in a quasi-stationary state for a time that scales exponentially with $N$, but eventually, a giant fluctuation leads to the disappearance of monomers. In the marginal case, monomers disappear in a time that scales linearly with $N$, and the final supercluster state is a peculiar jammed state, viz., it is not extensive.