Figure 1

Schematic plot of the investigated system. A monodisperse 3D grains pack of spheres immersed in a fluid is subject to dynamics made of flow pulses of velocity $V$ and duration ${\tau }_0$. Before applying a pulse we wait for the pack to settle. The flow-pulse dynamics is repeated up to reach stationary conditions (see Fig. 2).Reuse & Permissions

Figure 2

Compaction of systems subject to tapping dynamics with ${\tau }_0=0.03\mathrm{s}$ and different values of the fluid velocity as indicated, averaged over 32 runs. Solid black circles refer to simulations with 4 times more particles, outlining the absence of finite size effects. Dashed lines are fits to a stretched exponential law [Eq. (1)].Reuse & Permissions

Figure 3

The main panel shows the volume fraction $\varphi$ attained at stationarity (see Fig. 2) measured when the pack is settled, as a function of $V$, for the shown values of ${\tau }_0$: the stronger the pulses, the fluffier the pack. The inset shows the dependence of the volume fraction fluctuations on $V$ and ${\tau }_0$.Reuse & Permissions

Figure 4

(Upper panel) The $\Delta \varphi$ data of Fig. 3 (same symbols are used) are here plotted as a function of $\varphi$: they collapse on a single master curve, showing that $\Delta \varphi$ is in a one-to-one correspondence with $\varphi$, irrespectively of the dynamical protocol used to arrive at $\varphi$. The dotted line is a linear best fit. A similarly good collapse is also found (lower panel) when we plot the radial distribution function $g(r)$ for packs having the same volume fraction (the same packs of Fig. 3 are shown with the same symbols). In particular, we show $g(r)$ for $\varphi =0.615$ and $\varphi =0.575$ (shifted for clarity). The open circles in both panels are the corresponding ensemble averages independently calculated from Eq. (2): within numerical errors, they scale on the same curves, pointing out that this statistical mechanics measure is an excellent approximation of the time averages over the pulse dynamics.Reuse & Permissions

Figure 5

The equation of state of granular materials at rest, showing the volume fraction $\varphi$ as a function of the configurational temperature, $T_{\mathrm{conf}}$. Ensemble averages are obtained via the Monte Carlo procedure, while time averages are obtained from the data of Fig. 3 via the use of the static fluctuation-dissipation relation [22].Reuse & Permissions