Potential energy in a three-dimensional vibrated granular medium measured by NMR imaging

Fast NMR imaging was used to measure the density profile of a three-dimensional granular medium fluidized by vertical vibrations of the container. For container acceleration much larger than gravity, the rise in center of mass of the granular medium is found to scale as v(alpha)(0)/N(beta)(l) with alpha = 1.0+/-0.2 and beta = 0.5+/-0.1, where v(0) is the vibration velocity, and N(l) is the number of layers of grains in the container. This value for alpha is significantly less than found previously for experiments and simulations in one dimension ( alpha = 2) and two dimensions ( alpha = 1.3-1.5).