2005/12/16 by Sungchul Kwon, Sungmin Lee, Sung‐Min Lee +1 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.73.056102
6 pages, 6 figures
arxiv created 2005/12/16 · openalex publication_date 2006/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate condensation phase transitions of the symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution P(k)\ensuremath∼k^\ensuremath-\ensuremathγ. In the SCA model, masses diffuse with unit rate, and unit mass chips off from mass with rate \ensuremathω. The dynamics conserves total mass density \ensuremathρ. In the steady state, on RNs and SFNs with \ensuremathγ>3 for \ensuremathω\ensuremath≠\ensuremath∞, we numerically show that the SCA model undergoes the same type of condensation transitions as those on regular lattices. However, the critical line \ensuremathρc(\ensuremathω) depends on network structures. On SFNs with \ensuremathγ\ensuremath\leqslant3, the fluid phase of exponential mass distribution completely disappears and no phase transitions occurs. Instead, the condensation with exponentially decaying background mass distribution always takes place for any nonzero density. For the existence of the condensed phase for \ensuremathγ\ensuremath\leqslant3 at the zero density limit, we investigate one lamb-lion problem on RNs and SFNs. We numerically show that a lamb survives indefinitely with finite survival probability on RNs and SFNs with \ensuremathγ>3, and dies out exponentially on SFNs with \ensuremathγ\ensuremath\leqslant3. The finite lifetime of a lamb on SFNs with \ensuremathγ\ensuremath\leqslant3 ensures the existence of the condensation at the zero density limit on SFNs with \ensuremathγ\ensuremath\leqslant3, at which direct numerical simulations are practically impossible. At \ensuremathω=\ensuremath∞, we numerically confirm that complete condensation takes place for any \ensuremathρ>0 on RNs. Together with the recent study on SFNs, the complete condensation always occurs on both RNs and SFNs in zero range process with constant hopping rate.