Scaling Properties of Granular Rheology near the Jamming Transition

The theological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that shear stress, pressure, and kinetic temperature obey critical scaling near the jamming transition point, which is considered as a critical point. These scaling laws have some peculiar properties from the viewpoint of conventional critical phenomena because the exponents depend on the interparticle force model so that they are not universal. It is also found that these scaling laws imply the relation between the exponents that describe the growing correlation length.