Universal hidden order in amorphous cellular geometries

Klatt MA, Lovric J, Chen D, Kapfer S, Schaller FM, Schoenhoefer PWA, Gardiner BS, Smith AS, Schroeder-Turk GE, Torquato S (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Nature Communications Nature Publishing Group: Nature Communications

Book Volume: 10

Article Number: 811

DOI: 10.1038/s41467-019-08360-5

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.

Authors with CRIS profile

Sebastian Kapfer Lehrstuhl für Theoretische Physik Ana-Suncana Smith Physics Underlying Life Science

Involved external institutions

Rudjer Boskovic Institute (RBI) / Institut Ruđer Bošković (IRB) HR Croatia (HR) Murdoch University AU Australia (AU) Princeton University US United States (USA) (US) Karlsruhe Institute of Technology (KIT) DE Germany (DE)

How to cite

APA:

Klatt, M.A., Lovric, J., Chen, D., Kapfer, S., Schaller, F.M., Schoenhoefer, P.W.A.,... Torquato, S. (2019). Universal hidden order in amorphous cellular geometries. Nature Communications, 10. https://dx.doi.org/10.1038/s41467-019-08360-5

MLA:

Klatt, Michael A., et al. "Universal hidden order in amorphous cellular geometries." Nature Communications 10 (2019).

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