2011/11/30 by Shu Tanaka, Ryo Tamura · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Directed percolation #Fractal #Fractal dimension #Lattice (music) #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Square lattice #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.7566/jpsj.82.053002
published in Journal of the Physical Society of Japan 82(5), 053002 (Physical Society of Japan) · 4 pages, 5 figures, accepted for publication in Journal of the Physical Society of Japan
arxiv created 2013/04/11 · openalex publication_date 2013/04/23 · arxiv updated 2013/04/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter q and we study the time evolution of the network. The rule we propose includes a rule in which elements are randomly connected step by step and the rule recently proposed by Achlioptas \it et al. [Science \bf 323 (2009) 1453]. We consider the q-dependence of the dynamics of the number of elements in the largest cluster. As q increases, the percolation step is delayed. Moreover, we also study the q-dependence of the roughness and the fractal dimension of the percolation cluster.