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 v̄ₓ≠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 eₙ. For example, the diffusion coefficient Dₓ is influenced by eₙ, but hardly depends on the roughness of the plane, while for Dy the reverse is true. The range of the inclination angle and the roughness for which a steady state exists also depends on eₙ. We discuss how these results can be understood by considering the details of the motion.