Models of defects in atomistic systems

We analyze the overall behavior of discrete systems in the presence of defects (modeled by truncated quadratic potentials for some of the interactions) by exhibiting approximate free-discontinuity continuous energies. We give bounds on the limit surface energy densities, and we prove that these bounds are sharp in the classes of energy densities depending only on the normal to the discontinuity set, or concave and depending only on the jump across the interface. As a preliminary result we give a continuous descriptions of the 'discrete Neumann sieve'. © 2010 Springer-Verlag.