engleski

Hyperuniformisation by Lloyd’s algorithm for Centroidal Voronoi diagrams

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 therefore 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 have not found a point pattern where Lloyd’s algorithm does not lead to a hyper-uniform structure. A related, and important, question is whether Lloyd’s algorithm induces crystallisation (i.e. ordering into at least locally crystalline structures) of the point configuration ; one may have thought this possible, given that the body-centered cubic Bravais lattice is considered the configuration with lowest energy w.r.t. the functional used in Lloyd’s algorithm.

Lloyds algorithm ; optimization ; hyperuniform

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