5.3 Autocorrelation Functions

is the velocity autocorrelation in fluids

(5.2) |

This has profound consequences. The diffusion constant of a liquid is given by

Due to the

The reason for the long time tail in was later explained as a
collective dynamical effect: part of the momentum of a particle
is stored in a microscopic vortex that dies off very slowly.[DORFMAN 72]

Procedure for calculating autocorrelation functions :

- At regular intervals of time steps, mark starting values . Since in the further process only the preceding starting values are required, it is best to store them in registers that are cyclically overwritten.
- At each time , compute the products

and relate them to the (discrete) time displacements ; a particular defines a channel number

indicating the particular histogram channel to be incremented by . To simplify the final normalization it is recommended to count the number of times each channel is incremented.

Plot the ACF and see whether it resembles the one given in
Figure 5.2.

F. J. Vesely / University of Vienna