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2015-01

Modeling of the material structure using Voronoi diagrams and tessellation methods

by Burtseva, L.; Werner, F.; Salas, B. V.; Pestryakov, A.; Romero, R.; Petranovski, V..


Series: 2015-01, Preprints

MSC:
11H31 Lattice packing and covering
05B45 Tessellation and tiling problems

Abstract:
Tessellation methods are a relatively new approach for modeling the structure of a material. In this paper, such structures are interpreted as sphere packing models, where molecules and atoms represent spheres of equal or different size. Based on the review of the literature, it is shown that the tessellation approach is a powerful method for modeling and simulating such structures with desirable metric and topological properties. Two basic tessellation methods are considered more in detail: the Delaunay tessellation and the Voronoi diagram in Laguerre geometry, as well as some of their generalizations. The principal concepts of both tessellation methods are briefly explained for a better understanding of the application details. It is noted that packing models created by tessellation methods are not based on the use of the gravity camp effect, which is a difference to numerical and mathematic programming modeling approaches. Therefore, tessellation methods permit the development of structures without taking into account the gravitation, what is important for modeling the structure on the microscopic and nano levels, where the influence of the gravitation is studied insufficiently. A review of the related literature is given, focusing on the details of the tessellation method and the particle size distribution.

Keywords:
Voronoi diagram, Delaunay tessellation, Laguerre geometry, Voronoi statistics, material structure, packing