Liquid-solid transition of hard spheres under gravity

We investigate the liquid-solid transition of two-dimensional hard spheres in the presence of gravity. We determine the transition temperature and the fraction of particles in the solid regime as a function of temperature via event-driven molecular-dynamics simulations and compare them with the theoretical predictions. We then examine the configurational statistics of a vibrating bed from the viewpoint of the Liquid-solid transition by explicitly determining the transition temperature and the effective temperature T of the bed, and present a relation between T and the vibration strength.