Rheology and dynamical heterogeneity in frictionless beads at jamming density

We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dot{\gamma }$ is realized. The system behaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to ${\dot{\gamma }}^{1\mathrm{/}{\delta }_S}$, where $1\mathrm{/}{\delta }_S=0.64(2)$. It is also found that the relaxation time $\tau$ and the correlation length $\xi$ of the velocity increase obeying power laws: $\tau \sim {\dot{\gamma }}^{-\beta }$ and $\xi \sim {\dot{\gamma }}^{-\alpha }$, where $\beta =0.27(3)$ and $\alpha =0.23(3)$.