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… 

Figures from this paper

How initial condition impacts aggregation -- a systematic numerical study
In a process of aggregation, a finite number of particles merge irreversibly to create growing clusters. In this work, impact of particular initial conditions: monodisperse, power–law, exponential,
Agglomerative percolation on the Bethe lattice and the triangular cactus
Agglomerative percolation (AP) on the Bethe lattice and the triangular cactus is studied to establish the exact mean-field theory for AP. Using the self-consistent simulation method based on the
THE MANY FACES OF PERCOLATION
The theory of percolation deals with the appearance of large connected domains between randomly interlinked nodes and with the spreading of non-conserved ‘agents’ over these domains. Near threshold,
Discontinuous percolation transitions in growing networks