Threshold of hierarchical percolating systems
Date of this Version
2-6-2012Citation
Threshold of hierarchical percolating systems Jiantong Li, Biswajit Ray, Muhammad A. Alam, and Mikael Östling Phys. Rev. E 85, 021109 – Published 7 February 2012
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
Discipline(s)
Electronic Devices and Semiconductor Manufacturing
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Comments
This is the published version of Jiantong Li, Biswajit Ray, Muhammad A. Alam, and Mikael Östling. (7 February 2012). Threshold of hierarchical percolating systems. First published in the Physical Review E Vol. 85, Iss. 2 and is available online at: http://dx.doi.org/10.1103/PhysRevE.85.021109