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

K J Schrenk; M R Hilário; V Sidoravicius; N A M Araújo; H J Herrmann; M Thielmann; A Teixeira

doi:10.1103/PhysRevLett.116.055701

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

Phys Rev Lett. 2016 Feb 5;116(5):055701. doi: 10.1103/PhysRevLett.116.055701. Epub 2016 Feb 2.

Authors

K J Schrenk^{1

2}, M R Hilário^{3

4}, V Sidoravicius^{5

6

7}, N A M Araújo⁸, H J Herrmann^{1

9}, M Thielmann¹⁰, A Teixeira¹¹

Affiliations

¹ Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
² Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
³ Departamento de Matemática, Universidade Federal de Minas Gerais, Avenida Antonio Carlos, 6627-P.O. Box 702-30161-970, Belo Horizonte, Minas Gerais, Brazil.
⁴ Section de Mathématiques, Université de Genève, 2-4 Rue du Lièvre, 1211 Genève, Switzerland.
⁵ Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.
⁶ New York University-Shanghai, 1555 Century Avenue, Pudong New Area, Shanghai 200122, China.
⁷ CEMADEN, Avenida Doutor Altino Bondensan, 500, São José dos Campos, São Paulo 12247-016, Brazil.
⁸ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal and Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal.
⁹ Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
¹⁰ Bayerisches Geoinstitut, University of Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany.
¹¹ Instituto Nacional de Matemática Pura e Aplicada, Est. Dona Castorina, 110, 22460-320 Rio de Janeiro, Rio de Janeiro, Brazil.

PMID: 26894717
DOI: 10.1103/PhysRevLett.116.055701

Abstract

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.