Segregation as a phase transition in granular matter image

We present extensive Monte Carlo simulations on species segregation in a granular mixture of hard spheres subjected to vertical tap. By varying the diameter ratio ? and the density ratio ?, we find Brazil Nut effect (larger particles on top, BN) and Reverse Brasil Nut effect (larger particles on bottom, RBN) and we show that the BN - RBN passage can turn into a second-order phase transition. Further, from the (?, ?)-phase diagram of the system we find a generalisation of Archimedes' principle for granular matter.