# Deriving effective forces for mesoscopic particle simulations

[Doktorsavhandling]

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. This is hard for systems of mesoscopic size (proteins, membranes etc.) as the time and length scales on which important phenomena take place are often far beyond what is feasible to simulate using an atomistic level of detail. 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 complete. In particular, no strict explanation has been given concerning the connection between the mesoscopic DPD technique and the microscopic systems from which the mesoscopic dynamics originates. This thesis establishes the link between the DPD-representation of a system, and the same system on a fine-grained (microscopic) level. This is achieved by adapting the non-equilibrium statistical mechanics technique of Mori-Zwanzig projections to many-particle systems (Papers I, III), giving a formal footing on which the DPD technique can stand. The theory is also explicitly tested using computer simulations in Paper IV. In that paper, a molecular dynamics simulation of water (using water molecules with one oxygen and two hydrogen atoms) and a DPD representation of the same system with mass-center approximation of the water molecules are compared. The results are compared and contrasted to a DPD-model with parameters manually tuned to give correct transport properties (presented in Paper II). For particle-based coarse-graining of fluids, the particles are often identified with clusters of fluid molecules. In Paper V, the bearings of this view on equilibrium and transport properties of the coarse-grained fluid are investigated. It is shown for the case of coarse-graining through Voronoi tessellation that this representation cannot capture the properties of the microscopic system. Papers VI and VII concern the use of methods from coarse-grained molecular simulations for estimating interactions between flocking animals. In particular, paper VI shows how a force-matching method can be used to faithfully recreate all interactions in a simulated bird flock, and paper VII contains a comment stating that interaction rules used by flocking animals can most likely not be deduced from static photographs.

**Nyckelord: **Coarse graining, Dissipative particle dynamics, Mori-Zwanzig projection, Force matching, Force covariance, Boids, Flocking.

Denna post skapades 2009-09-02. Senast ändrad 2013-09-25.

CPL Pubid: 97055