Distributions of velocity

We have also studied the distribution of horizontal velocities in stripes at different heights (here the mean values are height dependent, as shown in the plots of the velocity profile). These distributions are displayed in Fig. fig:c_v showing the emergence of non-Gaussianity mainly in the case with $r_w<r$ and only in the stripes near the bottom wall. The authors of the experiment [6] claim that the distributions of velocity are very close to the Gaussian and try to fit their data with the rheological model proposed by Jenkins and Richman. This model postulates a quasi-Gaussian equilibrium to calculate the transport coefficients. Near the bottom wall the Gaussian approximation seems a very poor approximation of the real distribution, as shown by the results of our simulations: this is an effect of the inelasticity of the collisions but also of the proximity of the boundary, where high spatial gradients can put the gas out of Gaussian equilibrium.

Figure: Distribution of horizontal velocities for the Inclined Channel Model, measured on stripes at different heights and rescaled in order to have the same mean and variance. The inset shows the normalized number density profile with the position of the chosen stripes. $N=500$, $N_w \approx 56$, $r=0.95$, $r_w=0.95$ in the above frame and $r_w=0.4$ in the bottom frame, $g_x=1$, $g_y=-2$ (i.e.: the inclination angle $\phi =\pi /6$)