ABSTRACT
The ability to replace an atomistic system with a lower-resolution representation which retains important physical aspects, in a simplified form, of the original system has been the focus of coarse graining. Coarse-graining methods often derive effective potentials between a reduced number of coarse-grained particles to simulate systems at the mesoscale, where fully atomistic simulations are unfeasible and classical continuum models are not suitable. In computational biology, for instance, it is common to group atoms into coarse-grained sites or beads and describe the internal forces of a given system as effective interactions between beads. Examples of coarse-graining approaches in the literature include the elastic network model [38], the MARTINI force field [19], a force-matching approach [13], a reverse Monte Carlo approach [18], and the direct Boltzmann inversion approach [39], among many others. Reviews of coarse-grained models can be found in, e.g., [25, 4]. In contrast to those approaches, we attempt to replace atomistic models by a generalized nonlocal continuum formulation, rather than by a reduced discrete representation. We restrict our discussion to crystalline structures at zero temperature.
