Irreversible aggregation and network renormalization
Complexity Science Group, University of Calgary - Calgary T2N 1N4, Canada
2 FZ Jülich - D-52425 Jülich, Germany, EU
Accepted: 22 July 2011
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the complete solution for the probability to find any given state in an aggregation process (k+1)X→X, given a fixed number of unit mass particles in the initial state. Exactly the same probability distributions and scaling are found in one-dimensional systems (a trivial network) and well-mixed solutions. This reveals that scaling laws found in renormalization of complex networks do not prove that they are self-similar.
PACS: 89.75.Hc – Networks and genealogical trees / 02.10.Ox – Combinatorics; graph theory / 05.70.Ln – Nonequilibrium and irreversible thermodynamics
© EPLA, 2011