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Universal hidden order in amorphous cellular geometries

Klatt, M.A., Lovrić, J., Chen, D., Kapfer, S.C., Schaller, F.M., Schönhöfer, P.W.A., Gardiner, B.S., Smith, A-S, Schröder-Turk, G.E. and Torquato, S. (2019) Universal hidden order in amorphous cellular geometries. Nature Communications, 10 (1). art. no. 811.

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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.

Item Type: Journal Article
Murdoch Affiliation: School of Engineering and Information Technology
Publisher: Springer Nature
Copyright: © 2019 Springer Nature Publishing AG
URI: http://researchrepository.murdoch.edu.au/id/eprint/43710
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