Temperature measurement in the convective and segregated vibrated bed of   powder : A numerical study
  In numerically simulated vibrated beds of powder, we measure temperature under convection by the generalized Einstein's relation. The spatial temperature distribution turns out to be quite uniform except for the boundary layers. In addition to this, temperature remains uniform even if segregation occurs. This suggests the possibility that there exists some "thermal equilibrium state" even in a vibrated bed of powder. This finding may lead to a unified view of the dynamic steady state of granular matter. 
Satoru Kiyono and Y-h. Taguchi