MONTE-CARLO AS BROWNIAN DYNAMICS

A study is reported of the relationship between Metropolis Monte Carlo (MC), smart Monte Carlo (SMC), and Brownian dynamics (BD) as invented by Ermak. SMC and ED are shown to be formally equivalent in the limit of zero timestep (i.e., Delta t --> 0). However it is not easy to pro ve the equivalence between MC and ED beyond the trivial zeroth-order t erm (i.e., not at the order of the mean-square systematic force contri bution to the mean-square displacement). Test calculations on model hi gh volume fraction colloidal systems reveal that SMC gives the same dy namics as ED and, in addition, can be employed I,vith larger timesteps than the ED method without any noticeable loss of accuracy or systema tic displacement of the averages and time autocorrelation functions (f orce and sheer stress). (The importance sampling in the SMC method fil ters out statistically unrepresentative trajectories that lead to algo rithmic breakdown with large timesteps in ED.) The gain in efficiency resulting from an increased timestep is reduced somewhat by the increa sing rejection rate found with increasing timestep (accumulated time i s equal to NT Delta tf where NT is the number of attempted moves, Delt a t is the equivalent timestep and f is the fraction of attempted move s accepted). Nevertheless the lack of timestep drift in thermodynamic properties seen in SMC when compared with ED does offer significant ad vantages in the simulation of model colloidal liquids. The use of MC a s a substitute for ED is not so advantageous as the rejection rate inc reases more dramatically with timestep than SMC. Also its formal relat ionship with BD/SMC for finite timesteps is not so clear.