  One of the most noticeable collective motion of non-cohesive granular matter
is clustering under certain conditions. In particular, when a
quasi-two-dimensional monolayer of mono-disperse non-cohesive particles is
vertically vibrated, a solid-liquid-like transition occurs when the driving
amplitude exceeds a critical value. Here, the physical mechanism underlying
particle clustering relies on the strong interactions mediated by grain
collisions, rather than on grain-grain cohesive forces. In average, the solid
cluster resembles a drop, with a striking circular shape. We experimentally
investigate the coarse-grained solid-liquid interface fluctuations, which are
characterized through the static and dynamic correlation functions in the
Fourier space. These fluctuations turn out to be well described by the
capillary wave theory, which allows us to measure the solid-liquid interface
surface tension and mobility once the granular "thermal" kinetic energy is
determined. Despite the system is strongly out of equilibrium and that the
granular temperature is not uniform, there is energy equipartition at the
solid-liquid interface, for a relatively large range of angular wave-numbers.
Furthermore, both surface tension and mobility are consistent with a simple
order of magnitude estimation considering the characteristic energy, length and
time scales, which is very similar to what can be done for atomic systems.
  Please find the supplementary material of this article here: arXiv:1304.2646
