Exact solutions for mass-dependent irreversible aggregations

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 p...

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Bibliographic Details
Published in:arXiv.org 2011-08
Main Authors: Seung-Woo, Son, Christensen, Claire, Bizhani, Golnoosh, Grassberger, Peter, Paczuski, Maya
Format: Article
Language:English
Subjects:
Agglomeration
Clusters
Combinatorial analysis
Exact solutions
Mass distribution
Mathematical analysis
Scaling laws
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1109.0045