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 ϕ_c. Above ϕ_c, Z and the pressure P are predicted to increase as power laws in ϕ-ϕ_c. In experiments using photoelastic disks we corroborate a rapid increase in Z at ϕ_c and power-law behavior above ϕ_c for Z and P. Specifically we find a power-law increase as a function of ϕ-ϕ_c for Z-Z_c 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.