Friction dominated dynamics of interacting particles locally close to a crystallographic lattice

A system of particles, in general d‐dimensional space, that interact by means of pair potentials and adjust their positions according to the gradient flow dynamics induced by the total energy of the system is studied. The case when the range of the interaction is of the same order as the mean interparticle distance is considered. It is also assumed that particles, locally, are located close to some crystallographic lattice. An appropriate system of equations that describes the evolution of macroscopic deformation of the crystallographic lattice, as well as the system that describes the evolution of the main crystallographic directions is derived. Well‐posedness of the derived system is studied as well as the stability of the particle system. Same examples of potentials that yield stable and unstable systems are given. Copyright © 2012 John Wiley & Sons, Ltd.