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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

- VACF within the AR model
- Density of states within the AR model
- Discrete memory function of the VACF within the AR model
- MSD within the AR model
- Friction coefficient within the AR model

Next: VACF within the AR Up: Auto-Regressive Analysis Previous: Auto-Regressive Analysis Contents