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Theory and implementation
The concept of Auto-Regressive Analysis (ARA) analysis is intimitely related to the one of memory function. Memory functions have
been used for a long time in theoretical statistical physics to describe the time dependence of autocorrelation
functions. Nevertheless, the use of memory functions in the context of MD simulations has been hindered by the lack of a
suitable numerical algorithm for their calculation. Such an algorithm has been published and is now implemented in
nMOLDYN [57]. The key point is that a reliable estimates for memory functions can be obtained by assuming
an Auto-Regressive (AR) model for the underlying stochastic process and not for the memory function itself.
To compute the memory function
from a discrete time serie
the latter is modelled by an
autoregressive stochastic process of order P [58,59],
 |
(4.68) |
Here
is white noise with zero mean and amplitude
. The coeffients
are fitted to the discrete time serie using Burg's algorithm [60,61],
and
is given by
 |
(4.69) |
where
is the autocorrelation function of
 |
(4.70) |
In all following calculations nMOLDYN works with a set of coefficients
which has been averaged over all
selected atoms and the three Cartesian coordinates.
Subsections
Next: VACF within the AR
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pellegrini eric
2009-10-06