0 1000 2000 3000 4000 0 2 4 6 8 10 Z* M=30m M=75m M=150m FIG. 1: Time evolution of the dimensionless scaled position Z ∗ ≡ Zg 0 /v 2 W of the movable piston located on top of the system, once the steady state has been reached. There are 420 disks in a box of width W = 70 d . In all cases the coefficient of normal restitution of the particle collisions is α = 0 . 95 and that for the particle-piston collisions is α$_{P}$ = 0 . 99. Results for three values of the mass of the piston M are shown, as indicated. Time τ is measured in accumulated number of collisions per particle. as where σ$_{Z}$ is the square root of the second central moment or standard deviation of Z , σ 2 Z ≡ < Z 2 > − L $^{2}$, and the star indicates that lengths are being measured in the dimensionless scale defined above. In Fig. 2, the obtained probability distribution of ℓ , P ( ℓ ), is plotted for a system with α = 0 . 94. Again, three values of the mass ratio have been considered, namely M = 36 m , M = 60 m , and M = 120 m . It is seen that the probability distributions are accurately fitted by a Gaussian (solid lines), at least up to values of the probability density of the order of 10 − $^{4}$. A similar behavior has been found in all the simulated systems with 7 ℓ ≡ Z − L σ$_{Z}$ = Z ∗ − L ∗ σ ∗ Z , (6)