Finite Size Effects in Addition and Chipping Processes

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.

arXiv comment18 pages, 8 figures, 45 references

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Cited by in corpus (4)

• Supercluster states and phase transitions in aggregation-fragmentation processes
• Simple evolving random graphs
• Gelation in input-driven aggregation
• Dynamic Space Filling