title: Scaling of the Euler characteristic, surface area, and curvatures in the phase separating or ordering systems.
abstract: We present robust scaling laws for the Euler characteristic and curvatures applicable to any symmetric system undergoing phase separating or ordering kinetics. We apply it to the phase ordering in a system of the nonconserved scalar order parameter and find three scaling regimes. The appearance of the preferred nonzero curvature of an interface separating +/- domains marks the crossover to the late stage regime characterized by the Lifshitz-Cahn-Allen scaling.
authors.affiliation: Institute of Physical Chemistry PAS and College of Science, Department III, Warsaw, Poland.
authors.forename: M
authors.initials: M
authors.lastname: Fialkowski
authors.forename: A
authors.initials: A
authors.lastname: Aksimentiev
authors.forename: R
authors.initials: R
authors.lastname: Hołyst