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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

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.

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Verlagsausgabe §
DOI: 10.5445/IR/1000091855
Veröffentlicht am 05.03.2019
DOI: 10.1038/s41467-019-08360-5
Zitationen: 1
Web of Science
Zitationen: 1
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2019
Sprache Englisch
Identifikator ISSN: 2041-1723
KITopen-ID: 1000091855
Erschienen in Nature Communications
Band 10
Heft 1
Seiten Article: 811
Bemerkung zur Veröffentlichung Gefördert durch den KIT-Publikationsfonds
Vorab online veröffentlicht am 18.02.2019
Nachgewiesen in Web of Science
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