Combined micro--macro integration scheme from an invariance principle:   application to ferrofluid dynamics
  A method for the combination of microscopic and macroscopic simulations is developed which is based on the invariance of the macroscopic relative to the microscopic dynamics. The method recognizes the onset and breakdown of the macroscopic description during the integration. We apply this method to the case of ferrofluid dynamics, where it switches between direct Brownian dynamics simulations and integration of the constitutive equation. 
Patrick Ilg, Iliya V. Karlin