Jamming transition in granular systems

Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number Z at a critical volume fraction phi(c). Above phi(c), Z and the pressure P are predicted to increase as power laws in phi - phi(c). In experiments using photoelastic disks we corroborate a rapid increase in Z at phi(c), and power-law behavior above phi(c) for Z and P. Specifically we find a power-law increase as a function of phi - phi(c) for Z - Z(c) with an exponent beta around 0.5, and for P with an exponent psi around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.