Universal hidden order in amorphous cellular geometries

Michael A. Klatt, Jakov Lovrić, Duyu Chen, Sebastian C. Kapfer, Fabian M. Schaller, Philipp W.A. Schönhöfer, Bruce S. Gardiner, Ana Sunčana Smith, Gerd E. Schröder-Turk, Salvatore Torquato

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties.

Original languageEnglish
Article number811
JournalNature Communications
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Dec 2019

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Tile
Physical properties
Voronoi diagrams
Wavelength
Geometry
tiles
moments of inertia
geometry
polyhedrons
cells
foams
counters
physical properties
retarding
Technology
optimization
wavelengths

Cite this

Klatt, M. A., Lovrić, J., Chen, D., Kapfer, S. C., Schaller, F. M., Schönhöfer, P. W. A., ... Torquato, S. (2019). Universal hidden order in amorphous cellular geometries. Nature Communications, 10(1), [811]. https://doi.org/10.1038/s41467-019-08360-5
Klatt, Michael A. ; Lovrić, Jakov ; Chen, Duyu ; Kapfer, Sebastian C. ; Schaller, Fabian M. ; Schönhöfer, Philipp W.A. ; Gardiner, Bruce S. ; Smith, Ana Sunčana ; Schröder-Turk, Gerd E. ; Torquato, Salvatore. / Universal hidden order in amorphous cellular geometries. In: Nature Communications. 2019 ; Vol. 10, No. 1.
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Klatt, MA, Lovrić, J, Chen, D, Kapfer, SC, Schaller, FM, Schönhöfer, PWA, Gardiner, BS, Smith, AS, Schröder-Turk, GE & Torquato, S 2019, 'Universal hidden order in amorphous cellular geometries' Nature Communications, vol. 10, no. 1, 811. https://doi.org/10.1038/s41467-019-08360-5

Universal hidden order in amorphous cellular geometries. / Klatt, Michael A.; Lovrić, Jakov; Chen, Duyu; Kapfer, Sebastian C.; Schaller, Fabian M.; Schönhöfer, Philipp W.A.; Gardiner, Bruce S.; Smith, Ana Sunčana; Schröder-Turk, Gerd E.; Torquato, Salvatore.

In: Nature Communications, Vol. 10, No. 1, 811, 01.12.2019.

Research output: Contribution to journalArticle

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Klatt MA, Lovrić J, Chen D, Kapfer SC, Schaller FM, Schönhöfer PWA et al. Universal hidden order in amorphous cellular geometries. Nature Communications. 2019 Dec 1;10(1). 811. https://doi.org/10.1038/s41467-019-08360-5