On power law scaling dynamics for time-fractional phase field models during coarsening

Abstract

In this paper, the energy scaling behavior of the time-fractional phase field models is investigated. We report a seminal observation that the effective free energy of the time-fractional phase field models obeys a general power-law scaling dynamics during coarsening. Mainly, the effective free energy and roughness in the time-fractional phase field models scale by following a similar power law as the integer phase field models, where the power is linearly proportional to the fractional order. This general scaling law is verified numerically against several classes of phase field models, including the Cahn–Hilliard equation with different types of variable mobilities and the molecular beam epitaxy models. This new finding opens potential paths of applying time-fractional phase field models in studying anomalous coarsening dynamics.