title: Complete topology of cells, grains, and bubbles in three-dimensional microstructures.
abstract: We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of three-dimensional microstructures that are often regarded as close analogues in the literature: one resulting from normal grain growth (mean curvature flow) and another resulting from a random Poisson-Voronoi tessellation of space. Grain growth strongly favors particular grain topologies, compared with the Poisson-Voronoi model. Moreover, the frequencies of highly symmetric grains are orders of magnitude higher in the grain growth microstructure than they are in the Poisson-Voronoi one. Grain topology statistics provide a strong, robust differentiator of different cellular microstructures and provide hints to the processes that drive different classes of microstructure evolution.
authors.affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, USA.
authors.forename: Emanuel A
authors.initials: EA
authors.lastname: Lazar
authors.forename: Jeremy K
authors.initials: JK
authors.lastname: Mason
authors.forename: Robert D
authors.initials: RD
authors.lastname: MacPherson
authors.forename: David J
authors.initials: DJ
authors.lastname: Srolovitz
mesh_terms: D002477:Cells / Q000648:ultrastructure*; D003460:Crystallization; D008954:Models, Biological; D008956:Models, Chemical; D008962:Models, Theoretical; D010316:Particle Size; D016012:Poisson Distribution