title: Threshold of hierarchical percolating systems.
abstract: Many modern nanostructured materials and doped polymers are morphologically too complex to be interpreted by classical percolation theory. Here, we develop the concept of a hierarchical percolating (percolation-within-percolation) system to describe such complex materials and illustrate how to generalize the conventional percolation to double-level percolation. Based on Monte Carlo simulations, we find that the double-level percolation threshold is close to, but definitely larger than, the product of the local percolation thresholds for the two enclosed single-level systems. The deviation may offer alternative insights into physics concerning infinite clusters and open up new research directions for percolation theory.
authors.affiliation: KTH Royal Institute of Technology, School of Information and Communication Technology, Electrum 229, SE-164 40 Kista, Sweden.
authors.forename: Jiantong
authors.initials: J
authors.lastname: Li
authors.forename: Biswajit
authors.initials: B
authors.lastname: Ray
authors.forename: Muhammad A
authors.initials: MA
authors.lastname: Alam
authors.forename: Mikael
authors.initials: M
authors.lastname: Östling
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D008958:Models, Molecular; D009010:Monte Carlo Method; D053758:Nanoparticles / Q000737:chemistry* / Q000648:ultrastructure*