Dresden 2017 – wissenschaftliches Programm

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O: Fachverband Oberflächenphysik

O 53: Nanostructures at Surfaces: Other Aspects

O 53.9: Poster

Dienstag, 21. März 2017, 18:30–20:30, P1C

Hyperuniformisation by Lloyd’s algorithm for Centroidal Voronoi diagrams — •Jakov Lovrić^1,2, Philipp Schoenhoefer^3,4, Sebastian Kapfer³, Fabian Schaller³, Michael Klatt⁵, Bruce Gardiner⁴, Ana-Sunčana Smith^1,2, 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.