Jamming of Frictional Spheres

Packings of monodisperse, frictional spheres are studied for a wide range in particle friction coefficient on approach to the jamming transition - the point where the packing loses mechanical stability. In particular, we focus on dynamical properties through the study of the vibrational normal modes. The dynamical matrix includes terms that take into account the rotational degrees of freedom due to non-central forces in the presence of friction. The influence of friction on the normal mode frequencies and particle polarization vectors are examined. Distinct from frictionless systems, for finite friction, the normal modes now allow for particle rotations.