Dresden 2017 – scientific programme
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O: Fachverband Oberflächenphysik
O 53: Nanostructures at Surfaces: Other Aspects
O 53.9: Poster
Tuesday, March 21, 2017, 18:30–20:30, P1C
Hyperuniformisation by Lloyd’s algorithm for Centroidal Voronoi diagrams — •Jakov Lovrić1,2, Philipp Schoenhoefer3,4, Sebastian Kapfer3, Fabian Schaller3, Michael Klatt5, Bruce Gardiner4, Ana-Sunčana Smith1,2, and Gerd Schröder-Turk4 — 1Institute Ruđer Bošković, Division of Physical Chemistry, Group for Computational Biosciencies, Zagreb, Croatia — 2Institute for Theoretical Physics, PULS Group and Cluster of Excellence: EAM, FAU Erlangen-Nürnberg, Germany — 3Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany — 4School of Engineering and Information Technology, Murdoch University, Western Australia 6150, Australia — 5Karlsruhe Institute of Technology (KIT), Institute of Stochastics, Karlsruhe, Germany
We study an application of centroidal Voronoi diagrams and Lloyds algorithm. The simple idea is that the evolution of points under Lloyd’s algorithm leads to more uniform structures, in a loose sense. We investigated, and found an initial positive result, that Lloyd’s algorithm can be used to achieve hyper-uniform structures when starting from several types of disordered point patterns. We havn’t found a point pattern where Lloyd’s algorithm does not lead to a hyper-uniform structure. An important question is whether Lloyd’s algorithm induces crystalisation of the point configuration; one may have thought this possible, given that the body-centered cubic lattice is considered the configuration with lowest energy w.r.t. the functional used in Lloyd’s algorithm.