A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small $1-r$ and large $L$, where $r$ is the restitution coefficient and $L$ the size of the container. We show that if the particle density $n_0$ and $(1-r^2)(n_0 Ld)$ where $d$ is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, $<E >/N$, tends to a constant whereas the mean dissipated power per particle, $<D >/N$, decreases like $1/\sqrt{N}$ when $N$ increases, provided that $(1-r^2)(n_0 Ld)^2 < 1$. The relative fluctuations of $E$, $D$ and the power injected by the moving boundary, $I$, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power $I(t)$ injected by the moving boundary.}