Subject: Re: CCL:summary: diffusion coefficient from MSD

From: Konrad Hinsen <[email-masked]>
Date: 31 May 2002 13:40:12 +0200

Hannes Loeffler <[email-masked]> writes:

> 2) Statistics is considerably improved if multiple time origins are
> taken into account.

Here's a trick that is not as widely known as it should be: You can do
an average over all possible time origins with little effort by

1) Expanding the square in the MSD expression.

2) Calculate the correlation function term in the expansion by
   Fourier transforms (FFT).

Although an average over all possible time origins is exaggerated (the
corresponding subtrajectories are not all independent), this procedure
is much faster than averaging over a moderate amount of time origins
in the standard way, due to the efficiency of the FFT algorithm.
-- 
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