Exact solutions for mass-dependent irreversible aggregations

Details Exact solutions for mass-dependent irreversible aggregations Exact solutions for mass-dependent irreversible aggregations

2011-08-31

arxiv.org/abs/1109.0045v1

Phys. Rev. E 84, 040102(R) (2011)

Physics

Data Analysis, Statistics and Probability

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.84.040102

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.

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