Correlator tutorial

Observables and correlations tutorial

In this tutorial we demonstrate the usage of the new concept of observables and correlations of Espresso 3.1.

As an example we simulate a single polymer chain diffusing in the implicit solvent (Langevin thermostat). We add a few non-interacting freely diffusing particles which are used as a benchmark for comparison (free diffusion). During the simulation, we compute the mean-square displacement (msd) and the velocity autocorrelation function (vacf).

In the msd we can observe the ballistic motion due to the Langevin thermostat (msd(t)~t^2) which crosses over to the normal diffusion for the freely diffusing particles (msd(t)=6Dt). The diffusion of monomers goes from ballistic through subdiffusive regime related to internal polymer dynamics (Rouse dynamics) at intermediate times and finally reach diffusive motion with D=1/N where N is the polymer chain length. This can be compared to the diffusion of the centre of mass of the polymer with D=1/N for all time scales. Depending on the chain length, the transition from Rouse-like to diffusive dynamics in the polymer can span many decades in lag times.

The velocity autocorrelation funcion of the freely diffusing particles displays much slower decay than that of the polymer. In the free particle case, it is only the thermostat which causes the vacf to decay on a characteristic time scale t~1/Gamma where Gamma is he thermostat friction coefficient. Note that the vacf fully decays only at t>10/Gamma. In the polymer case, the vacf of the polymer decays much faster. Note the different spacing between data points as a consequence of different correlator settings.


 * The containing
 * The simulation script
 * Gnuplot scripts to quickly plot the results (processed files)
 * The