Efficient Representation of Laguerre Mosaics with an Application to Microstructure Simulation of Complex Ore

Abstract

Laguerre mosaics have been an important modeling approach in astronomy, physics, crystallography, geology and mathematics for several decades. In materials science, they are used as models for cellular and polycrystalline materials, networks and cell foams. In this study, Laguerre mosaics are used to model the three-dimensional internal mineral microstructure of complex ores. Here, the difficulties arise in representing and simulating these microstructure mosaics for dimensions larger than two. Therefore, this manuscript introduces a general workflow for the representation in arbitrary dimensions and presents a realization of this workflow using generalized maps for representation in two and three dimensions. With this approach, lower-dimensional components such as cells, facets, edges and vertices can be accessed directly, which enables us to efficiently create the mosaics and derive statistics, plane sections and new mosaic models by intersection. Furthermore, it allows for easy deduction of the dual mosaic and efficient storage. The mineral microstructure of complex ores can be very complicated and often shows a highly fractal structure. Therefore, numerical modeling and representation of these microstructures is challenging. The proposed approach for Laguerre mosaic creation and representation is successfully applied to the modeling of mineral microstructures and particles. These microstructure models are used for mineral processing simulations in order to determine optimal processing strategies to conserve valuable resources.