LOCAL MOLECULAR FIELD THEORY FOR NON-EQUILIBRIUM SYSTEMS

Abstract

Local Molecular Field (LMF) theory is a framework for modeling the long range forces of a statistical system using a mimic system with a modified Hamiltonian that includes a self consistent molecular potential. This theory was formulated in the equilibrium context, being an extension of the Weeks Chandler Andersen (WCA) theory to inhomogeneous systems. This thesis extends the framework further into the nonequilibrium regime. It is first shown that the equilibrium derivation can be generalized readily by using a nonequilibrium ensemble average and its relevant equations of motion. Specifically, the equations of interest are fluid dynamics equations which can be generated as moments of the BBGKY hierarchy. Although this approach works well, for the application to simulations it is desirable to approximate the LMF potential dynamically during a single simulation, instead of a nonequilibrium ensemble. This goal was pursued with a variety of techniques, the most promising of which is a nonequilibrium force balance approach to dynamically approximate the relevant ensemble averages. This method views a quantity such as the particle density as a field, and uses the statistical equations of motion to propagate the field, with the forces in the equations computed from simulation. These results should help LMF theory become more useful in practice, in addition to furthering the theoretical understanding of near equilibrium molecular fluids.