  Mesoscale phenomena -- involving a level of description between the finest
atomistic scale and the macroscopic continuum -- can be studied by a variation
on the usual atomistic-level molecular dynamics (MD) simulation technique. In
mesodynamics, the mass points, rather than being atoms, are mesoscopic in size,
for instance representing the centers of mass of polycrystalline grains or
molecules. In order to reproduce many of the overall features of fully
atomistic MD, which is inherently more expensive, the equations of motion in
mesodynamics must be derivable from an interaction potential that is faithful
to the compressive equation of state, as well as to tensile de-cohesion that
occurs along the boundaries of the mesoscale units. Moreover, mesodynamics
diffrers from Newton's equations of motion in that dissipation -- the exchange
of energy between mesoparticles and their internal degrees of freedom (DoFs) --
must be described, and so should the transfer of energy between the internal
modes of neighboring mesoparticles. We present a formulation where energy
transfer between the internal modes of a mesoparticle and its external
center-of-mass DoFs occurs in the phase space of mesoparticle coordinates,
rather than momenta, resulting in a Galilean invariant formulation that
conserves total linear momentum and energy (including the energy internal to
the mesoparticles). We show that this approach can be used to describe, in
addition to mesoscale problems, conduction electrons in atomic-level
simulations of metals, and we demonstrate applications of mesodynamics to
shockwave propagation and thermal transport.
