  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 a simple energy, 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 large, accurate
simulations of isotropic grain growth.
