Macro state Markov chain model for computer simulation of grand canonical ensemble

Abstract

The existing Monte Carlo simulation models for the grand canonical ensemble proposed by many researchers to date use sequential state-generating schemes which require large amounts of computational time. In this study, a new Monte Carlo simulation model based on the stochastic Markov process theory for computer simulation of the grand canonical ensemble is developed. Essentially, in this new model the states in the grand canonical ensemble are grouped into macro states of the canonical ensembles, and a macro state Markov chain is established by a Monte Carlo sampling technique. This macro state Markov chain is then solved for a stationary solution. A prominent advantage of this new macro state Markov chain model is that it is suitable for massively parallel implementation, and hence the computational time required for the computer experiments can be reduced greatly. A massively parallel scheme for gas adsorption in zeolite 5A based on this model has been implemented on the Connection Machine CM2. A preliminary study shows that results are in good agreement with the experimental data available in the literature, and the simulation time is dramatically reduced in comparison with conventional sequential schemes.