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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.
Majmudar et al. (Mon,) studied this question.