On Wed, May 22, 2013, Sajeewa Pemasinghe wrote:
>
> In the book 'Molecular modeling principles and applications by Andrew
> Leach" he describes velocity autocorrelations as shown in
> autocorrelation.jpg (please see the attached). I think that amber
> calculates autocorrelation in a similar way.
As noted recently on the list, Amber's analysis routines have no
straightforward way of calculating velocity autocorrelation functions.
>
> I have a question about the normalization in equation 7.79 in
> autocorrealtion.jpg.
>
> If our v(0)= a1 i+ a2 j+ a3 k and
>
> v(t)= b1 i+ b2 j+ b3 k
>
> and v(0).v(0)=a1*a1+a2*a2+a3*a3=norm
>
> Can't there be an instance where v(t).v(0)=a1*b1+a2*b2+a3*b3 >
> a1*a1+a2*a2+a3*a3 ?
>
> If that happens there would be correlation values greater than one. So by
> defining v(0).v(0) as the norm are we assuming that the magnitude of the
> vector v(t) can never go beyond the magnitude of the vector v(0)?
The correlation function is the *average* of <v(0).v(t)> over the whole
ensemble. Individual terms in the average might be greater than 1, but the
average itself is not likely to be -- the assumption is that you have a
stationary ensemble where <v(t).v(t)> is independent of time.
...dac
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Received on Thu May 23 2013 - 05:00:02 PDT
