Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy

Abstract

A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy. The method can also be applied to many-particle dynamics.