Minimal size of a barchan dune.

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. 89, 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B 28, 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E 64, 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. 89, 264301 (2002)] that this flux fetch distance is itself constant. Indeed, this could not explain the protosize of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three-dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.

Nontrivial temporal scaling in a Galilean stick-slip dynamics.

We examine the stick-slip fluctuating response of a rough massive nonrotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The experiments presented here, which are reminiscent of Galileo's works with rolling objects on inclines, have brought in the last years important insights into the friction between surfaces in relative motion and are of relevance for earthquakes, differing from classical block-spring models by the mechanism of energy input in the system. Robust nontrivial temporal scaling laws appearing in the dynamics of this system are reported, and it is shown that the time-support where dissipation occurs approaches a statistical fractal set with a fixed value of dimension. The distribution of periods of inactivity in the intermittent motion of the cylinder is also studied and found to be closely related to the lacunarity of a random version of the classic triadic Cantor set on the line.