Percolation of overlapping squares or cubes on a lattice

@article{Koza2014PercolationOO,
  title={Percolation of overlapping squares or cubes on a lattice},
  author={Zbigniew Koza and Grzegorz Kondrat and Karol Suszczy'nski},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2014},
  volume={2014}
}
Porous media are often modeled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other for the void space. Here we investigate these percolation thresholds in the model of overlapping squares or cubes of linear size k > 1 randomly distributed on a regular lattice. We find that the percolation threshold of obstacles is a nonmonotonic function of k, whereas the percolation threshold of the void space is… 

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