N-fold symmetric two-dimensional shapes evolving by surface diffusion

Abstract

We present theoretical and numerical results concerning the surface-diffusion-driven evolution of closed 2D interfaces having n-fold rotational symmetry such as gear- and star-type shapes. We find a family of approximate solutions depending on a few parameters; by solving the time dependence of such parameters, we can predict the evolution of interface morphology in close agreement with numerical results. Finally, we show how our findings can be applied in some practical cases to get a mathematical description of interface morphology just by determining a few characteristic features.