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.

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Received 2 September 2011

DOI:https://doi.org/10.1103/PhysRevE.85.021109

Authors & Affiliations

Jiantong Li¹, Biswajit Ray², Muhammad A. Alam^2,*, and Mikael Östling¹

¹KTH Royal Institute of Technology, School of Information and Communication Technology, Electrum 229, SE-164 40 Kista, Sweden
²School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907-1285, USA

^*alam@purdue.edu

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Vol. 85, Iss. 2 — February 2012

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics