Fig. 2: Dynamical arrest and intermittency at low and intermediate τp.
a–c Low τp = 1: a Kinetic-energy time series, E(t), at different f = 2.5, 2.0, and 1.5 (top to bottom), show regular fluctuations; both the mean and the variance reduce with decreasing f. b Density fluctuations, measured via the self-overlap function Q(t), relax more slowly as the activity f is reduced. c The slowness of the relaxation dynamics is measured by the α-relaxation time, τα, extracted from Q(t), for each f. The measured τα versus f is fitted (dashed line) using a diverging power-law form, which traces out the limit of dynamical arrest fc(τp) (dotted line) for small τp in Fig. 1. d–f Intermediate τp = 104: d Kinetic-energy time series as f is lowered, shows Gaussian fluctuations at high f > f *, intermittent bursts and quiescence and finally dynamical arrest when f ≤ fc. e Intermittency is characterised by the behaviour of the time-dependent kurtosis of the kinetic energy time series, \(\kappa (t)=\frac{\langle {(E({t}_{0}\, +\, t)\, -\, E({t}_{0}))}^{4}\rangle }{{\langle {(E({t}_{0}\, +\, t)\, -\, E({t}_{0}))}^{2}\rangle }^{2}}\). We see that in the small t end of this log plot, κ(t) increases linearly as t decreases, and should therefore diverge, when extrapolated to t → 0. The dynamical order parameter is measured from the value of κ(t) at the earliest time that we can evaluate, i.e., t = 0+. (Inset) Variation of the dynamical order parameter, the excess kurtosis, κex(0+) with f. We use the point of inflection of this curve to determine the phase boundary to the intermittent phase. f The fluctuation χ4(t) = 〈Q2(t)〉 − 〈Q(t)〉2, shows a peak at a time t for different values of f. (inset) At a fixed τp = 104, the value of the peak height hp increases sharply as f approaches f *(τp) from above, then reduces again. The value of f at which hp has a maximum, for different values of τp, also marks the boundary between the liquid and the intermittent phase (see Fig. 1).
