Universal hidden order in amorphous cellular geometries

• DOI: 10.1038/s41467-019-08360-5
• Publication Date: 2019-02-18T11:03:22Z
• Authors: Michael A. Klatt; Jakov Lovrić; Duyu Chen; Sebastian C. Kapfer; Fabian M. Schaller; Philipp W. A. Sch...; Bruce S. Gardiner; Ana-Sunčana Smith; Gerd E. Schröder-...; Salvatore Torquato
• Keywords: Maxima and minima; Polyhedron; Degeneracy (biology)

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 optimisation moment inertia Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile are preferred. We employ Lloyd’s centroidal diagram algorithm to solve this find it converges disordered states associated deep local minima. These universal sense their structure factors characterised by complete independence wide class initial conditions they evolved from. They moreover exhibit an anomalous suppression long-wavelength density fluctuations quickly become effectively hyperuniform. Our findings warrant search for novel amorphous hyperuniform phases cellular materials unique physical properties.