Discrete and continuum descriptions of shaken granular matter

Vertically vibrated granular matter is studied using particle simulations, experiments and continuum models. We do a in-depth analysis of the granular Leidenfrost state (a density inverted, highly agitated state) and its transition to buoyancy-driven convection. In the Leidenfrost state we report the existence and characterise collective semi-periodic oscillations of the bed of grains, which are then observed experimentally. The transition to convection is then studied in detail. Correlations of the velocity field reveal fluctuating convective flows in the Leidenfrost state, which increase their correlation as the transition is approached. The critical behaviour of the transition is then determined and a new interpretation of the transition as a coupled chain of oscillators is proposed. Furthermore, the possibility of modelling granular matter as a continuum is directly tackled by following the limit of vanishing particle size in a granular hydrodynamic model. We find that it is possible to create identical macroscopic states with different number of particles, allowing us to study inherent fluctuations in particle systems. Finally, two hydrodynamic models of the vibrated bed under different approximations are solved and compared with particle simulations.