title: Exact solutions for mass-dependent irreversible aggregations.
abstract: We consider the mass-dependent aggregation process (k+1)X→X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with k neighbors in one dimension, or--in the well-mixed case--with k other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite-size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed.
authors.affiliation: Complexity Science Group, University of Calgary, Calgary T2N 1N4, Canada.
authors.forename: Seung-Woo
authors.initials: SW
authors.lastname: Son
authors.forename: Claire
authors.initials: C
authors.lastname: Christensen
authors.forename: Golnoosh
authors.initials: G
authors.lastname: Bizhani
authors.forename: Peter
authors.initials: P
authors.lastname: Grassberger
authors.forename: Maya
authors.initials: M
authors.lastname: Paczuski