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18 February 2025
 
  » arxiv » 1109.0045

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Exact solutions for mass-dependent irreversible aggregations
Seung-Woo Son ; Claire Christensen ; Golnoosh Bizhani ; Peter Grassberger ; Maya Paczuski ;
Date 1 Sep 2011
AbstractWe 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.
Source arXiv, 1109.0045
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