How transversal fluctuations affect the friction of a particle on a rough incline

We present molecular-dynamics simulations of a sphere moving down an inclined plane consisting of similar spheres of smaller size. For a certain range of inclinations, the sphere moves down the plane with a mean velocity ${\overline{v}}_{x}\ensuremath{\ne}0.$ We investigate the properties of the motion in this steady state and the limits for its existence for a certain set of parameters. It is found that the steady-state velocity of the particle is independent of material properties and depends only on the geometry of the system. This means that the particle experiences an effective velocity-dependent friction force, with an effective ``viscosity'' determined only by the geometry. The fluctuations of the motion, however, can depend on the coefficient of restitution ${e}_{n}.$ For example, the diffusion coefficient ${D}_{x}$ is influenced by ${e}_{n},$ but hardly depends on the roughness of the plane, while for ${D}_{y}$ the reverse is true. The range of the inclination angle and the roughness for which a steady state exists also depends on ${e}_{n}.$ We discuss how these results can be understood by considering the details of the motion.