Title: A phase diagram for jammed granular matter

Author (Poster): Chaoming Song, City College of New York

Abstract:

We employ a statistical mechanics theoretical framework to demonstrate the phase diagram of jammed matter and provide a statistical characterization of the RLP and RCP. The state variables of jammed matter are the stress, volume and ompactivity $(\sigma,V,X)$. Statistical mechanics then predicts the phase space of the available random jammed configurations, and the concomitant equations of state relating observables such as average coordination number, $Z$, entropy, $S$ and volume fraction $\phi$. In the isostatic limit ($\sigma\to0$), theory predicts a line of zero compactivity providing a statistical definition of the highest density of RCP characterized by a constant $\phi_{RCP}=0.634$ for any interparticle friction coefficient $\mu$ and $Z$. The lowest density of RLP appears as a line of infinite compactivity parameterized by $\mu$ and $Z$, ending at the minimum possible density theoretically predicted to be $\phi_{RLP}=0.543$. The nature of the disorder of the packings is statistically characterized by the entropy which is calculated to be larger in the random loose case than in the random close case.