  This paper studies the boundary behaviour at mechanical equilibrium at the
ends of a finite interval of a class of systems of interacting particles with
monotone decreasing repulsive force. Our setting covers pile-ups of
dislocations, dislocation dipoles and dislocation walls. The main challenge is
to control the nonlocal nature of the pairwise particle interactions. Using
matched asymptotic expansions for the particle positions and rigorous
development of an appropriate energy via Gamma-convergence, we obtain the
equilibrium equation solved by the boundary layer correction, associate an
energy with an appropriate scaling to this correction, and provide decay rates
into the bulk.
