Deriving coarse grained descriptions of particle based simulations

In the field of molecular simulations, the long standing aim has been to study mechanisms that cannot easily be observed in experiments or understood in terms of more abstract models. Fully detailed molecular dynamics simulations can be extremely successful in many areas, but when applied to mesoscopic systems with a large number of molecules, the time and length scales on which important phenomena take place are often far beyond what is feasible to simulate with modern computers. To overcome this issue, several different coarse graining schemes have been developed, resulting in effective dynamics evolving on larger length and time scales than the fully detailed microscopic systems. A simulation technique that has received increasing interest in the last decade is Dissipative Particle Dynamics (DPD), but despite its popularity, the physical interpretation of DPD is not fully satisfying. In particular, no clear explanation has been given concerning the connection between the mesoscopic DPD technique and the assumed microscopic systems from which the mesoscopic dynamics originates. In paper I a bottom-up method is presented for deriving effective interaction parameters for coarse grained representations of microscopic simulations. The method relies on the DPD ansatz for the coarse grained dynamics. We apply the method to a projection where several particles are clustered together into larger, mesoscopic, particles and derive effective coarse grained equations of motion for the mesoscopic particles. Conservative interactions are recreated using the well known inverse Monte Carlo (IMC) technique, whereas dissipative and stochastic interactions are derived using a newly introduced quantity termed the force covariance. Paper II concerns the use of DPD as a thermostat for coarse grained simulations of liquid water. We systematically test how the functional form of the DPD interactions affect transport properties. The main result is that with a hard core potential derived using the IMC technique, it is possible to resolve the so called Schmidt number problem of DPD, i.e. to find a functional form of the stochastic and dissipative interactions such that the diffusion and the viscosity of the underlying system is simultaneously retained on the coarse grained level of description, something that is not possible with classical united atoms simulations