Hong Et Al. Reply to Canul-chay Et Al

Canul-Chay et al. [1] have conducted the segregation experiment of binary granular mixtures in a bed and subjected the bed to vibration. They report that the reverse Brazil-Nut phenomenon (RBNP) was never observed in their experiments and thus conclude that such does not exist. However, we have clearly demonstrated in [2] by Molecular Dynamics simulations that the reverse Brazil-Nut problem not only exists, but can be determined from the solid-liquid phase boundary by a scaling theory for the crossover from RBNP. Hence, instead of disputing Canul-Chay et al.’s sound experimental results [1], in this reply we want to draw the reader’s attention to the experimental set up and the interpretation of the experimental results. First, the system considered in [1] is definitely not the same as ours, because the vibrating bed exhibits a temperature gradient along the vertical axis. In our system, the mixture is in contact with the thermal reservoir at T (this is a global temperature). Each particle is kicked by random noise such that the average kinetic energy m〈v〉/2 = T . If the reverse Brazil-Nut phenomenon cannot be found in such a vibrating system, that might teach us a lot about the sensitivity of granular matter to details of the boundary conditions (b.c.) and, on the other hand, if the RBNP is not found for this b.c. it does not exclude the possibility that it can be found for others. Second, in order to observe the reverse Brazil-Nut problem as obtained in [2], it might be essential that the bed be subjected to a constant global temperature. In any case, however, it should be essential to quench the system at a low enough temperature. There may be a way to define a global temperature for the vibrating bed with a weak deviation from the constant temperature assumption [3-7]. We now briefly describe some attempts. The density profile of a weakly excited mono-disperse granular material [4] can be either fit by a Fermi function [3] (Fig 1 of Ref. [3]), by the Enskog profile