Efficient representation of Laguerre mosaics with an application to microstructure simulation of complex ore

Laguerre mosaics have been an important modeling approach in astronomy, physics, crystallography, geology and mathematics for several decades. In material sciences 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 studies 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. Lower dimensional components such as cells, facets, edges and vertices can be accessed directly which allows to efficiently create the mosaics, derive statistics, plane sections and new mosaic models by intersection. Furthermore, it allows to easily deduce the dual mosaic and efficient storage.
The mineral microstructure of complex ore can be very complicated and often shows a highly fractal structure. Therefore, numerical modeling and representation of these microstructures are challenging. The presented approach for La-guerre mosaic creation and representation is applied successfully to the modeling of mineral microstructures and particles. These microstructure models are used for mineral processing simulations in in order to find optimal processing strategies to save valuable resources.