Motion of grains down a bumpy surface

We summarize in this article an extensive experimental and theoretical effo rt carried out to understand the behavior of a single ball when rolling dow n a bumpy surface. This may appear to be a simple problem but in fact is on e that displays a rich variety of different behaviors which allow us to und erstand better dissipative systems such as granular media. Studies performe d previously have shown that the motion of the single ball on the rough sur face can be characterized by three different dynamic regimes according to t he different values of the two control parameters, the inclination angle th eta and the ratio Phi=R/r, where R is the radius of the rolling ball and r the radius of the glass beads which make up the rough surface. The three re gimes are a decelerated regime A, a stationary regime B, characterized by a constant average velocity and a jumping regime C. This result was found to be independent of the composition of the rolling ball and the rough surfac e. It has been demonstrated that regime B is characterized by a viscous-lik e friction force that appears for specific parameter values. This friction force can be explained by a model whose central ingredient is the geometry of the surface. The trajectory of the ball in regime B can be pictured as a driven random walk motion where the fluctuations of the local velocities a re due to collisions of the moving sphere and the surface grains. A detaile d analysis of diffusive properties of the motion is discussed. (C) 1999 Ame rican Institute of Physics. [S1054-1500(99)02103-5].