  The present work is essentially concerned with the development of statistical
theory for the low temperature dislocation glide in concentrated solid
solutions where atom-sized obstacles impede plastic flow. In connection with
such a problem, we compute analytically the external force required to drag an
elastic string along a discrete two-dimensional square lattice, where some
obstacles have been randomly distributed. The corresponding numerical
simulations allow us to demonstrate a remarkable agreement between simulations
and theory for an obstacle density ranging from 1 to 50 % and for lattices with
different aspect ratios. The theory proves efficient on the condition that the
obstacle-chain interaction remains sufficiently weak compared to the string
stiffness.
