NMR diffusion simulation based on conditional random walk

We introduce here a new, very fast, simulation method for free diffusion in a linear magnetic field gradient, which is an extension of the conventional Monte Carlo (MC) method or the convolution method described by Wong et al. In earlier NMR-diffusion simulation methods, such as the finite difference method (FD), the Monte Carlo method, and the deterministic convolution method, the outcome of the calculations depends on the simulation time step. In our method, however, the results are independent of the time step, although, in the convolution method the step size has to be adequate for spins to diffuse to adjacent grid points. By always selecting the largest possible time step the computation time can therefore be reduced. Finally we point out that in simple geometric configurations our simulation algorithm can be used to reduce computation time in the simulation of restricted diffusion.