  Based on a novel concept of multiplicative multiscale decomposition, we have
derived a multiscale micromorphic molecular dynamics (MMMD)to extent the
(Andersen)-Parrinello-Rahman molecular dynamics to mesoscale and macroscale.
The multiscale micromorphic molecular dynamics is a con-current three-scale
particle dynamics that couples a fine scale molecular dynamics, a mesoscale
particle dynamics of micromorphic medium, and a coarse scale nonlocal particle
dynamics of nonlinear continuum. By choosing proper statistical closure
conditions, we have shown that the original Andersen-Parrinello-Rahman
molecular dynamics can be rigorously formulated and justified from first
principle, and it is a special case of the proposed multiscale micromorphic
molecular dynamics. The discovered mutiscale structure and the corresponding
multiscale dynamics reveal a seamless transition channel from atomistic scale
to continuum scale and the intrinsic coupling relation among them, and it can
be used to solve finite size nanoscale science and engineering problems with
arbitrary boundary conditions.
