Long-range topological correlations of real polycrystalline grains in two dimensions

Study on topological properties in two-dimensional grain networks via large-scale Monte Carlo simulation

“…This result provides sound evidence for the generalized Aboav-Weaire relationship on the basis of a large dataset. It is consistent with the experimental observation in a single-phase polycrystalline steel [23]. There also exists a relation between grain edges n and the number of grains in its jth nearest neighbor layer, q j (n).…”

Ring correlations in random networks

“…For this reason, m t (n) approaches 6 as t −1 (since K t (n) ∼ t) which is sometimes interpreted as a long-range correlation [48,49]. However this should be regarded as an artifact because the shells are defined in such a way (topologically) which results(unfortunately) in the topological charge never going to zero, even at very large distances, and in fact approaching a constant as shown here.…”

Texture Controlled Grain Growth in Thin Films Studied by 3D Potts Model

“…Further investigations took the average number of edges of all grains of the ensemble, , as well as the corresponding second moment of the neighbor distribution, μ 2 , into account resulting in what is well‐known today also beyond polycrystalline metals and alloys as the Aboav–Weaire law where the geometrical constant α has been introduced to describe different types of polycrystalline respectively cellular pattern. In particular, for normal grain growth or ideal coarsening holds …”