# Critical Fragmentation Properties of Random Drilling: How Many Holes Need to Be Drilled to Collapse a Wooden Cube?

@article{Schrenk2016CriticalFP, title={Critical Fragmentation Properties of Random Drilling: How Many Holes Need to Be Drilled to Collapse a Wooden Cube?}, author={K. Julian Schrenk and Marcelo R. Hilario and Vladas Sidoravicius and Nuno A. M. Ara{\'u}jo and Hans J. Herrmann and Marcel Thielmann and Amaral Teixeira}, journal={Physical review letters}, year={2016}, volume={116 5}, pages={ 055701 } }

A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical and probabilistic behavior that is discussed here. Combining numerical simulations and rigorous results, we find off-critical scale-free behavior and a continuous transition at a critical density of holes that significantly differs from classical percolation.

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This work systematically explore dependence of the probability Π_{d}(L,u) of percolation (existence of a spanning cluster) of sites not removed by the RW on L and u, which shows the concentration of unvisited sites decays exponentially with increasing u, while the visited sites are highly correlated.

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