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

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

Keywords

double-level percolation, doped polymer

DOI

10.1103/PhysRevE.85.021109

Citation

Threshold of hierarchical percolating systems Jiantong Li, Biswajit Ray, Muhammad A. Alam, and Mikael Östling Phys. Rev. E 85, 021109 – Published 7 February 2012

Date of this Version

2-6-2012

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