One-dimensional gratings evolving through high-temperature annealing: sine-generated solutions

Abstract

Sine-generated curves (i.e. curves in which the curvature is a sine function of the arc-length parameter) have been used in the past to describe river meanders. Here we show how these curves spontaneously appear during the decay of high-aspect-ratio surfaces mediated by surface diffusion. We obtained analytical results for the kinetic evolution of such processes relevant to a wide class of initial geometries. Our theoretical results were satisfactorily compared with numerical simulations and with results from previous approaches to the same problem, and they can be useful for interpreting and designing experiments related to the technologically important process of high-temperature annealing on nano/micro-structured samples.