Fig. 5: Conventional and generalized Einstein relations for different shaker settings.
From: Emergent memory from tapping collisions in active granular matter
Einstein relation is shown as a function of the energy injected by the shaker E = (2πf)2A2/2, where f [Hz] and A [mm] are frequency and amplitude of the oscillation of the shaker, respectively. As indicated by the horizontal axis, we consider three different packing fractions of the active bath: ϕ = 0 (pentagons) i.e., only the passive tracer, ϕ = 0.15 (triangles), and ϕ = 0.3 (diamonds). In each panel, colors represent the shaker frequency: f = 80 Hz (red), 100 Hz (blue), 120 Hz (yellow). a–c Einstein relation for the rotational degree of freedom, \(\langle {\Omega }^{2}\rangle {\tau }_{\Omega }/{D}_{{{{{{{{\rm{r}}}}}}}}}^{{{{{{{{\rm{eff}}}}}}}}}\). d–f Conventional Einstein relation for the translational degree of freedom, \(\langle {{{{{{{{\bf{V}}}}}}}}}^{2}\rangle M/({\Gamma }_{{{{{{{{\rm{r}}}}}}}}}{D}_{{{{{{{{\rm{t}}}}}}}}}^{{{{{{{{\rm{eff}}}}}}}}})\). g, h Generalized active Einstein relation for \({D}_{{{{{{{{\rm{t}}}}}}}}}^{{{{{{{{\rm{eff}}}}}}}}}\), given by Eq. (7). In all the panels, points reflect experimental data and black dashed lines are eye guides marking one, i.e., the validity of the Einstein relations. In all the panels, error bars represent one standard deviation.
