title: Geometric and topological properties of the canonical grain-growth microstructure.
abstract: Many physical systems can be modeled as large sets of domains "glued" together along boundaries-biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of an energy that is directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through extensive simulations of isotropic grain growth.
authors.affiliation: Boğaziçi University, Bebek, Istanbul 34342, Turkey.
authors.forename: Jeremy K
authors.initials: JK
authors.lastname: Mason
authors.affiliation: Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Emanuel A
authors.initials: EA
authors.lastname: Lazar
authors.affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, USA.
authors.forename: Robert D
authors.initials: RD
authors.lastname: MacPherson
authors.affiliation: Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: David J
authors.initials: DJ
authors.lastname: Srolovitz