Mathematics Colloquia and Seminars

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The Voronoi tessellation has applications in many scientific fields, for problems where space must be allocated between a group of objects or points. The talk will begin by describing a free software library, Voro++, which has been developed to carry out three-dimensional Voronoi computations. A distinguishing feature of the library is that it computes the Voronoi cell for each point individually, allowing the computation to be tailored to handle complex boundary conditions, and making it particularly suited for problems in physics and materials science.

Two applications of the library will be presented. In the study of dense granular materials, the Voronoi tessellation can be used to examine small changes in local packing density that occur as grains flow past each other. By analyzing these changes within large-scale simulations, the rheology of granular materials can be investigated.

The library has also been used in the analysis of crystalline porous materials, such as zeolites, which contain complex networks of void channels that are exploited in many industrial applications. For a given application, it is important to select a material with the optimal void topology, but this is often a difficult task, since the number of possible topologies is extremely large: thousands of materials have been already been synthesized, and databases of millions of hypothetical structures are available. The Voronoi tessellation provides a map of the void topology and can be used to rapidly screen these large databases to select materials that may be the most appropriate for a given application.