Isostaticity in two-dimensional pile of rigid disks

We study the static structure of piles made of polydisperse disks in the rigid limit with and without friction using molecular dynamic simulations for various disk elasticities and pile preparation procedures. The coordination numbers are calculated to examine the isostaticity of the pile structure. For the frictionless pile, it is demonstrated that the coordination number converges to 4 in the rigid limit, which implies that the structure of the rigid disk pile is isostatic. On the other hand, for the frictional case with the infinite friction constant, the coordination number depends on the preparation procedure of the pile, but we find that, in the rigid limit, the structure becomes very close to an isostatic one with the coordination number 3 when the pile is formed through the process that tends to make a pile of random configuration.