Exact solutions for mass-dependent irreversible aggregations
Data Analysis, Statistics and Probability
2011-11-02 v1 Disordered Systems and Neural Networks
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.
Cite
@article{arxiv.1109.0045,
title = {Exact solutions for mass-dependent irreversible aggregations},
author = {Seung-Woo Son and Claire Christensen and Golnoosh Bizhani and Peter Grassberger and Maya Paczuski},
journal= {arXiv preprint arXiv:1109.0045},
year = {2011}
}
Comments
4 pages, 4 figures