Jamming Transition in Granular Systems

Abstract

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 ${\varphi }_c$. Above ${\varphi }_c$, $Z$ and the pressure $P$ are predicted to increase as power laws in $\varphi -{\varphi }_c$. In experiments using photoelastic disks we corroborate a rapid increase in $Z$ at ${\varphi }_c$ and power-law behavior above ${\varphi }_c$ for $Z$ and $P$. Specifically we find a power-law increase as a function of $\varphi -{\varphi }_c$ 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.