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 ${ensuremath{phi}}_{c}$. Above ${ensuremath{phi}}_{c}$, $Z$ and the pressure $P$ are predicted to increase as power laws in $ensuremath{phi}ensuremath{-}{ensuremath{phi}}_{c}$. In experiments using photoelastic disks we corroborate a rapid increase in $Z$ at ${ensuremath{phi}}_{c}$ and power-law behavior above ${ensuremath{phi}}_{c}$ for $Z$ and $P$. Specifically we find a power-law increase as a function of $ensuremath{phi}ensuremath{-}{ensuremath{phi}}_{c}$ for $Zensuremath{-}{Z}_{c}$ with an exponent $ensuremath{beta}$ around 0.5, and for $P$ with an exponent $ensuremath{psi}$ 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.