Persistence in Cluster-Cluster Aggregation

E.K.O. Hellén, M.J. Alava

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
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Persistence is considered in one-dimensional diffusion-limited cluster-cluster aggregation when the diffusion coefficient of a cluster depends on its size s as D(s)∼sγ. The probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences. The cluster persistence gives the probability of a cluster remaining intact. The empty site and cluster persistences are universal whereas the filled site depends on the initial concentration. For γ>0 the universal persistences decay algebraically with the exponent 2/(2−γ). For the empty site case the exponent remains the same for γ<0 but the cluster persistence shows a stretched exponential behavior as it is related to the small s behavior of the cluster size distribution. The scaling of the intervals between persistent regions demonstrates the presence of two length scales: the one related to the distances between clusters and that between the persistent regions.
Original languageEnglish
Article number026120
Pages (from-to)1-9
JournalPhysical Review E
Issue number2
Publication statusPublished - 2002
MoE publication typeA1 Journal article-refereed


  • aggregation
  • persistence
  • universality

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