Plato's cube and the natural geometry of fragmentation.
Gömböc
fracture mechanics
pattern formation
statistical physics
Journal
Proceedings of the National Academy of Sciences of the United States of America
ISSN: 1091-6490
Titre abrégé: Proc Natl Acad Sci U S A
Pays: United States
ID NLM: 7505876
Informations de publication
Date de publication:
04 08 2020
04 08 2020
Historique:
pubmed:
19
7
2020
medline:
19
7
2020
entrez:
19
7
2020
Statut:
ppublish
Résumé
Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra-shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.
Identifiants
pubmed: 32680966
pii: 2001037117
doi: 10.1073/pnas.2001037117
pmc: PMC7414180
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.
Langues
eng
Sous-ensembles de citation
IM
Pagination
18178-18185Déclaration de conflit d'intérêts
The authors declare no competing interests.
Références
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Aug;76(2 Pt 2):026112
pubmed: 17930109
Phys Rev Lett. 2006 Jan 20;96(2):025504
pubmed: 16486594
Science. 2010 Mar 19;327(5972):1470-5
pubmed: 20299586
Phys Rev Lett. 1993 Nov 8;71(19):3107-3110
pubmed: 10054859
Phys Rev Lett. 2015 Oct 9;115(15):154301
pubmed: 26550724
Sci Rep. 2015 Mar 16;5:9147
pubmed: 25772300
Science. 1988 Jan 29;239(4839):471-6
pubmed: 17838884
Phys Rev Lett. 2004 Jul 16;93(3):035504
pubmed: 15323834
Proc Natl Acad Sci U S A. 2015 Aug 4;112(31):9536-41
pubmed: 26183228
Soft Matter. 2019 Jun 12;15(23):4689-4702
pubmed: 31119245
Science. 2015 Oct 30;350(6260):534-8
pubmed: 26516279
Nature. 2016 Jun 01;534(7605):79-81
pubmed: 27251278
Nat Commun. 2018 Apr 12;9(1):1432
pubmed: 29650990
Phys Rev Lett. 2010 Mar 5;104(9):095502
pubmed: 20366993
Nat Commun. 2015 Oct 13;6:8366
pubmed: 26460507
Sci Adv. 2018 Mar 28;4(3):eaao4946
pubmed: 29670937
Phys Rev E. 2019 Jan;99(1-1):012802
pubmed: 30780299
Phys Rev Lett. 2004 Jun 18;92(24):245506
pubmed: 15245098
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Feb;65(2 Pt 2):026203
pubmed: 11863628
Nature. 2016 Jul 7;535(7610):140-3
pubmed: 27309815
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Apr;71(4 Pt 2):046214
pubmed: 15903777
Philos Trans A Math Phys Eng Sci. 2013 Nov 04;371(2004):20120353
pubmed: 24191108