On 2D interface networks that are translation-invariant under curvature-driven migration

Abstract

The issue of constructing interface networks translating under curvature-driven migration is addressed. The translating networks are the main accessory for testing capillarity driven migration mode in grain growth simulations. They also arise in experimental studies of boundary mobility and junction drag. The networks are constructed of pieces of simple translating curves—lines and grim reapers (GRs)—meeting at triple junctions. The primary method of building the networks relies on a certain property of GRs which reduces the construction to simple algebraic operations. At the outset, networks of interfaces having different tensions are considered. More detailed discussion concerns a restricted model in which the migration speed does not depend on the tensions. In this second case, the networks have noteworthy properties: some cell dimensions are directly related to angles at triple junctions, there are simple expressions for area sweeping rates, and there is a convenient and elegant alternative way of constructing these particular networks.