Spatial updating of grand canonical Monte Carlo algorithms: Generalization to soft-core potentials, binary fluids, and parallel implementation

Monte Carlo simulations have become more widely used recently due to their relatively inexpensive nature. This increase has allowed Monte Carlo simulations to be applied to many different disciplines. However, the basic simulation methods have remained largely unchanged. In general, Monte Carlo simulation methods are based on strict detailed balance. This condition was shown to be sufficient, but not necessary. The less strict local balance condition was shown to guarantee convergence and will provide the starting point for this work. Monte Carlo algorithms will be developed based on this local balance condition with the intention of finding more efficient, general simulation methods. These new methods will be proven to be mathematically valid and demonstrated for two different ensembles, the grand canonical and canonical ensembles. For the grand canonical ensemble, the spatial updating technique will be defined and demonstrated to provide a significant improvement over the standard methods at every system density tested, with the efficiency increasing by up to 40%. When this method is utilized in parallel, the efficiency can improve by up to 80%. The spatial method is then extended to binary systems in order to demonstrate its generality. Strong improvements in efficiency are again seen, with efficiencies improving by almost 70%. Finally, canonical systems will be investigated sequentially. The serial efficiencies are seen to be virtually identical to the random method, but a large improvement is demonstrated when the new sequential method is conducted in parallel, with systems demonstrating nearly ideal performance. Ideas for future work will then be provided, including directly applicable, practical uses for the algorithms derived in this work.