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 ϕc. Above ϕc, Z and the pressure P are predicted to increase as power laws in ϕ-ϕc. In experiments using photoelastic disks we corroborate a rapid increase in Z at ϕc and power-law behavior above ϕc for Z and P. Specifically we find a power-law increase as a function of ϕ-ϕc for Z-Zc with an exponent β around 0.5, and for P with an exponent ψ 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.