Brownian Motion of Solids (or Drops) on a Vibrated Plate, Including Dry Friction

We all know that dry friction of a solid on a solid was studied first by L. da Vinci, and that his results were rediscovered by Amontons. The basic laws have been understood — in terms of rubbing asperities — in the 20th century, mainly thanks to the British school [1]. When an object lies on a horizontal plate, it does not start to move until the horizontal force f reaches a certain threshold. For macroscopic objects, the threshold is proportional to the weight of the object. For mesoscopic objects (of micrometer size), the same sort of threshold may still exist, provided that the solid/solid contact involves a large number of asperities.