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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References

SHOWING 1-10 OF 12 REFERENCES

Introduction To Percolation Theory

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in

Percolation ?

572 NOTICES OF THE AMS VOLUME 53, NUMBER 5 Percolation is a simple probabilistic model which exhibits a phase transition (as we explain below). The simplest version takes place on Z2, which we view

Proceedings of the International Congress of Mathematicians

ALGEBRAIC VARIETIES By ALEXANDER GROTHENDIEGK It is less than four years since eohomologieal methods (i.e. methods of Homologieal Algebra) were introduced into Algebraic Geometry in Serre's

“Model”

Tiki is the Free/Open Source Web Application with the most built-in features and is a community recursively developing a community management system.

Mechanik

Coordinate Percolation on Z 3

We consider the following percolation process defined on the Z-lattice: For each column that is parallel to one of the coordinate axis we decide whether to remove it or not with a probability (or

Commun

  • Math. Phys. 108, 489
  • 1987

Physica A 262

  • 251
  • 1999

Probab

  • Theory Relat. Fields 154, 165
  • 2012

Fractals 21

  • 1350021
  • 2013