Abstract :
Macroscopic continuum simulations can be based on an unstructured moving spatial grid made up of “smooth particles”. The smooth particles’ equations of motion include interpolated values of the macroscopic stress gradient at each particle’s position. Microscopic solid-state simulations can be based on the motion of “embedded atoms”, with equations of motion based on a physical idea – embedding atoms in the local electronic density. The embedded atoms then move according to Newtonian equations of motion, based on electronic density gradients at each particle position. I show here that these two descriptions, macroscopic smooth particles and microscopic embedded atoms, can give identical particle trajectories. This demonstration facilitates the understanding of macroscopic models for surface tension and also suggests that certain macroscopic continuum approaches to smooth particle applied mechanics could have useful analogs in microscopic molecular dynamics.
