Convergence of MSD of soft-sphere particles

In the figure above the x-axis is sampling time while the y-axis is the variance of the MSD of 111 plane computed at a particular timestep. The distribution of MSD of the ordered system must go to a delta function as we sample longer. The variance must go like ~ 1/N (where N=number of independent samples). The measured exponent of the power-law decay in the variance of the ordered system's MSD is ~= 1, in accord with expectation. The disordered system's MSD distribution must have an intrinsic variance which is exhibited by the plateauing of the variance.