Abstract
We study statistical properties of vibrated granular monolayers using molecular dynamics simulations. We show that at high excitation strengths, the system is in a gas state, particle motion is isotropic, and the velocity distributions are Gaussian. As the vibration strength is lowered, the system's dimensionality is effectively reduced from three to two. Below a critical excitation strength, a cluster phase occurs, and the velocity distribution becomes bimodal. In this phase, the system consists of clusters of immobile particles arranged in close-packed hexagonal arrays, and gas particles whose energy equals the first excited state of an isolated particle on a vibrated plate.