$i$th particle and find the particle which has the largest $N_i$.

In addition, we measured the histograms of the velocity distribution and radial distribution functions, $W(u)$ and $C(x)$, respectively. The latter was defined as the number of particles in the spherical layer of the radius $x$ around each particle, normalized by the volume of such layer, disregarding the nonuniformity of the system and the boundary effect.

The measurements of the ”scalar” quantities such as energy, kinetic energy, pressure, and velocity distribution moments were taken in time intervals $\t_{meas}$, which were selected sufficiently long to avoid measuring the unchanged configuration repeatedly and sufficiently short not to miss the important details of the system evolution. We usually pick $\t_{meas}$ of the order of the uniform density sphere crossing time $\t_{cross}^u=\pi$, which is a half period of the oscillation of a particle released with zero velocity at the container wall. The histogram data, such as the velocity distribution and the radial distribution functions, was incremented at each $\t_{meas}$ and accumulated over a longer time period $\t_{hist}$, $\t_{hist}\sim 10$ – $10^3 \times
\t_{meas}$.

Our attempts to resolve the high-density part of the radial density profile of the system turned out to be fruitless due 