The nature of the transition between static and flowing regimes in granular media 1,2 provides a key to understanding their dynamics. When a pile of sand starts flowing, avalanches occur on its inclined free surface. Previously, studies 3 of avalanches in granular media have considered the time series of avalanches in rotating drums 4 , or in piles continuously fed with material. Here we investigate single avalanches created by perturbing a static layer of glass beads on a rough inclined plane. We observe two distinct types of avalanche, with evidence for different underlying physical mechanisms. Perturbing a thin layer results in an avalanche propagating downhill and also laterally owing to collisions between neighbouring grains, causing triangular tracks; perturbing a thick layer results in an avalanche front that also propagates upwards, grains located uphill progressively tumbling down because of loss of support. The perturbation threshold for triggering an avalanche is found to decrease to zero at a critical slope. Our results may improve understanding of naturally occurring avalanches on snow slopes 5 where triangular tracks are also observed.The experiments are done on an inclined plane covered with velvet cloth. This surface is chosen so that the glass beads (180-300 m in diameter), our granular material, have a larger friction with it than between themselves. A thin layer of grains can thus remain static on the plane up to a larger angle than if it were on a grain pile. We set the plane to an angle J (larger than the pile angle J 0 ) and pour glass beads abundantly at the top. The moving beads leave behind a static layer of uniform thickness h(J) (arrow leading to point a in Fig. 1; the geometry of the system is shown in Fig. 1 inset). This effect is explained by the variation of the friction of the successive grain layers with their distance to the surface of the inclined slope 6 : it is maximum for the bottom layer, and decreases continuously to the value for a thick pile. The top static layer is that which has a large enough friction coefficient on the underlying layers m(h) to come to a stop. At inclination angle J, the friction coefficient of this top static layer is then mðhÞ ¼ tanJ. The measurements h(J) of Fig. 1 thus give the variation of the coefficient of friction with depth 7 . We obtain a simple exponential decay as in ref. 7:

We report experiments on the shape and motion of millimetre-sized drops sliding down a plane in a situation of partial wetting. When the Bond number based on the component of gravity parallel to the plane Bo α exceeds a threshold, the drops start moving at a steady velocity which increases linearly with Bo α. When this velocity is increased by tilting the plate, the drops change their aspect ratio: they become longer and thinner, but maintain a constant, millimetre-scale height. As their aspect ratio changes, a threshold is reached at which the drops are no longer rounded but develop a 'corner' at their rear: the contact line breaks into two straight segments meeting at a singular point or at least in a region of high contact line curvature. This structure then evolves such that the velocity normal to the contact line remains equal to the critical value at which the corner appears, i.e. to a maximal speed of dewetting. At even higher velocities new shape changes occur in which the corner changes into a 'cusp', and later a tail breaks into smaller drops (pearling transition). Accurate visualizations show four main results. (i) The corner appears when a critical non-zero value of the receding contact angle is reached. (ii) The interface then has a conical structure in the corner regime, the in-plane and out-of-plane angles obeying a simple relationship dictated by a lubrication analysis. (iii) The corner tip has a finite non-zero radius of curvature at the transition to a corner, and its curvature diverges at a finite capillary number, just before the cusp appears. (iv) The cusp transition occurs when the corner opening in-plane half-angle reaches a critical value of about 45 • .