• DOI:10.1103/PhysRevE.84.040102
• Corpus ID: 13573339

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
        }
}

• S. Son, C. Christensen, +2 authors M. Paczuski
• Published 31 August 2011
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics

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.