calculate_relaxation_time

mdhelper.analysis.polymer.calculate_relaxation_time(time: ndarray[float], acf: ndarray[float]) → float

Calculates the orientational relaxation time \(\tau_\mathrm{r}\) of a polymer using the end-to-end vector autocorrelation function (ACF) time series \(C_\mathrm{ee}\).

A stretched exponential function with \(\tau\) and \(\beta\) as coefficients,

\[C_\mathrm{ee}=\exp{\left[-(t/\tau)^\beta\right]}\]

is fitted to the ACF time series, and the relaxation time is estimated using

\[\tau_\mathrm{r}=\int_0^\infty C_\mathrm{ee}\,dt=\tau\Gamma(1/\beta)\]

Parameters:

timenumpy.ndarray

Changes in time \(t-t_0\).

Shape: \((N_t,)\).

Reference unit: \(\textrm{ps}\).

acfnumpy.ndarray

End-to-end vector ACFs for the \(N_\textrm{g}\) groups over \(N_\textrm{b}\) blocks of \(N_t\) trajectory frames each.

Shape: \((N_\textrm{g},\,N_\textrm{b},\,N_t)\).

Returns:

relaxation_timefloat

Average orientational relaxation time.

Reference unit: \(\textrm{ps}\).