Exact solutions for mass-dependent irreversible aggregations.

  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={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={84 4 Pt 1},
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… 

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