Application of nonlinear acoustics for the study of relaxation processes in granular materials

We report observations of slow relaxation of the weak-contact network in a dry granular packing after gentle taps. Non-conventional nonlinear acoustic technique is used. Its high sensitivity makes it possible to monitor in detail the restoration of the weak-contact network. With a high precision, its relaxation rate follows a power-type law 1/t(1+n). For small n, it is close to conventionally discussed log-time relaxations in complex systems with exact 1/t rate. The actual time dependence allowed us to reconstruct the shape of the energy-barrier spectrum using a proposed model of thermally-activated relaxation. It is found that unlike uniform spectrum corresponding to the log-time behavior, the actual energy-spectrum is asymptotically exponential at high energies with a wide gap closer to zero value. Explanation of main observed features of the slow relaxation is proposed. Besides the studied non-coherent granular material, similar conclusions can be valid for other materials and systems, for which the slow evolution is related to transitions between metastable minima in two-well potentials.