Pattern formation and a clustering transition in power-law sequential adsorption

Ofer Biham, Ofer Malcai, Daniel A. Lidar Hamburger, David Avnir

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We present a model that describes adsorption and clustering of particles on a surface. A clustering transition is found that separates between a phase of weakly correlated particle distributions and a phase of strongly correlated distributions in which the particles form localized fractal clusters. The order parameter of the transition is identified and the fractal nature of both phases is examined. The model is relevant to a large class of clustering phenomena such as aggregation and growth on surfaces, population distribution in cities, and plant and bacterial colonies, as well as gravitational clustering.

Original languageAmerican English
Pages (from-to)R4713-R4716
JournalPhysical Review E
Issue number5
StatePublished - 1999


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