Figure 1

(a) Linear and (b) logarithmic plots of the velocity distribution $P(v_x∕{\sigma }_x)$ measured in the steady state region for a system with $N=130$, $f=50\mathrm{Hz}$, and $\Gamma =20$. Distributions are shown for clean particles (●) and particles with a small amount of added graphite (★). Also shown is the non-Gaussian result [Eq. (1), dashed line] from the experiment in [15], with $\alpha =1.51$ and $B=0.8$. (c) Comparison between the experiment (●) and simulation (엯) with ${\mu }_w=0.075$. (d) Comparison of simulations with ball-ball friction ${\mu }_b=0.5$ and with ball-wall friction ${\mu }_w=0.075$ (엯) and ${\mu }_w=0$ (☆). The experimental distributions are not precisely symmetric about $v_x=0$ due to the container tilting slightly when shaking. To match the asymmetry in the experiment, gravity in the simulation was tilted 1.9° with respect to the normal to the top of the container. This does not affect the functional form of the distributions when compared to simulations without the tilt.Reuse & Permissions

Figure 2

Double-logarithmic plot of the velocity distribution functions. $P_{\alpha }\left(v\right)$ has slope $-\alpha$; to guide the eye, slope $\alpha =3∕2$ is shown by a dashed line and $\alpha =2$ (a Gaussian) by a solid line. Experimental results are shown for clean stainless steel (SS) particles (•) and SS particles with graphite added (⋆). Simulation results are shown for three different values of ball-wall friction ${\mu }_w$ with the ball-ball friction held fixed, ${\mu }_b=0.5$. The data sets have been offset for clarity.Reuse & Permissions

Figure 3

Horizontal velocity of a single ball on a vertically oscillating plate in (a) simulation (${\mu }_w=0.4$ and ${\mu }_b=0.5$) and (b) experiment. The larger, less frequent jumps are the result of collisions with the bottom plate; these collisions are indicated by the dotted vertical lines. The more frequent smaller changes are the result of collisions with the sidewalls; these changes are clearer in the enlarged scale of the insets. The regions depicted in the insets are indicated by arrows.Reuse & Permissions

Figure 4

Velocity distribution $P(v∕\sigma )$ for a model of a damped driven particle. The distributions are shown for increasing damping $\gamma$: 0, 0.005, and 0.010. The inset compares the tails of the distributions for the model with a Gaussian distribution (solid line, $\alpha =2$) and a distribution with $\alpha =1.5$ (dashed line). The data sets are offset for clarity.Reuse & Permissions