Threshold of hierarchical percolating systems

Jiantong Li, KTH Royal Institute of Technology
Biswajit Ray, Purdue University - Main Campus
Muhammad Alam, Purdue University
Mikael Ostling, KTH Royal Institute of Technology

Date of this Version



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


Electronic Devices and Semiconductor Manufacturing