# Estimating Effective Interactions from Particle Trajectories

[Doktorsavhandling]

The theoretical and practical understanding of molecular systems is strongly dependent on computer simulations. All-atom molecular dynamics techniques are capable of sim- ulating systems on the scale of millions of particles up to about 100 ns. Beyond this scale, into the mesoscopic regime, the all-atom approach is strongly limited by computational complexity. A fundamental challenge in the ﬁeld of molecular computation is to construct coarse-grained models that can bridge the gap between the atomistic and mesoscopic scale. One of the mesoscopic simulation methods that have gained momentum the last decade is dissipative particle dynamics (DPD). The work contained in this thesis mainly concerns two questions: First, how does the dynamics of a DPD system relate to the dynamics of the underlying system? Second, how can the effective interactions on the mesoscale be determined? For coarse-grained systems in general, the ﬁrst question is answered formally by the Mori-Zwanzig ( MZ) theory of projection operators. In our work we establish the link between DPD and the MZ theory, which shows that the dissipative and stochastic forces in the DPD equations are a direct consequence of coarse- graining and must therefore be interpreted as integral parts of the coarse-grained dynamics. We argue that a consistent coarse-graining scheme for molecular systems need to take this into account. Moreover, we design a coarse-graining scheme for deriving the different interaction terms in DPD, based on the theoretical connection between DPD and MZ theory. In Paper II the DPD thermostat is used to represent united atom SPC water. We show that the dynamical properties of the coarse-grained system can be matched with those of the underlying system by heuristically tuning the thermostat. Paper I and Paper III contains the theoretical derivations behind the coarse-graining scheme and discussions on how to practically apply it. Paper IV presents an application of the coarse-graining scheme to united atom SPC water. The resulting effective thermostat is consistent with the results in Paper II. Paper V is an investigation of the so-called ﬂuid particle view of DPD. The study shows that this view is at best uncertain and poses a serious challenge to the mesoscopic simulation community. In Paper VI we deviate from the coarse-graining perspective and propose to use existing techniques from molecular coarse-graining as a platform for testing hypotheses of behavioral rules in animal swarms.

**Nyckelord: **Coarse-graining, Dissipative particle dynamics, Mori-Zwanzig projection, United atoms, Molecular dynamics thermostat, Multi-scale molecular dynamics, Inverse Monte Carlo, Force matching, Swarming

Denna post skapades 2009-05-13. Senast ändrad 2013-09-25.

CPL Pubid: 93930