Macroscopically equivalent granular systems with different numbers of particles

Abstract

One defining property of granular materials is their low number of constituents when compared to molecular systems. This implies that (statistical) fluctuations can have a dominant effect on the global dynamics of the system. In the following we create identical time-averaged macroscopic states with significantly different numbers of particles in order to directly study the role of fluctuations in granular systems. The dependency of the hydrodynamic conservation equations on the particles' size is derived, which directly relates to different particle-number densities. We show that, provided that the particles' dissipation is properly scaled, equivalent states can be obtained in the small particle size limit. Simulations of the granular Leidenfrost state confirm the validity of the scalings, and allow us to study the effects of fluctuations on collective oscillations. We observe that the amplitude of these oscillations decreases with the square root of the number of particles, while their frequency remains constant.