  In this paper we use a formal discrete-to-continuum procedure to derive a
continuum variational model for two chains of atoms with slightly
incommensurate lattices. The chains represent a cross-section of a
three-dimensional system consisting of a graphene sheet suspended over a
substrate. The continuum model recovers both qualitatively and quantitatively
the behavior observed in the corresponding discrete model. The numerical
solutions for both models demonstrate the presence of large commensurate
regions separated by localized incommensurate domain walls.
