Exact solutions for mass-dependent irreversible aggregations.
@article{Son2011ExactSF, 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}, year={2011}, volume={84 4 Pt 1}, pages={ 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…
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