Sharp fronts in attracting-adatom monolayers

Abstract

The problem of pattern formation by adsorbates undergoing attractive lateral interactions, is described by a parabolic integrodifferential equation having the scaled inverse temperature ε{lunate} and the scaled pressure α of the vapor phase as parameters. A coexistence region of high- and low-coverage stable homogeneous states has been reported in the (ε{lunate}, α) plane. In the small interaction-range limit an effective diffusion coefficient can be defined, which becomes however negative for a coverage range in between the stable homogeneous ones. A novel free-energy-like Lyapunov functional is found here for this problem. When evaluated on the homogeneous states, it leads to a Maxwell-like construction which selects essentially the same value α(ε{lunate} as the originally posited zero front-velocity condition. Moreover, its value on static fronts at this particular α(ε{lunate} coincides with those of the homogeneous states. This article is dedicated to Prof. Helmut Brand with occasion of his 60th birthday. © 2014 EDP Sciences and Springer.