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Article 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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| http://dx.doi.org/10.1103/PhysRevE.85.021109 | DOI Listing |
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