Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Abstract

Using molecular dynamics simulation, we calculate fluctuations and response for steadily sheared hard spheres over a wide range of packing fractions $\phi$ and shear strain rates $\gamma$, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature $T_{eff}$ that is equal to or larger than the kinetic temperature $T_{kin}$. We find a crossover in the relationship between the relaxation time $\tau$ and the the nondimensionalized effective temperature $T_{eff}/p\sigma^3$, where $p$ is the pressure and $\sigma$ is the sphere diameter. In the solid response regime, the behavior at fixed packing fraction satisfies $\tau\gamma\propto \exp(-cp\sigma^3/T_{eff})$, where $c$ depends weakly on $\phi$, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on $T_{eff}/p\sigma^3$ as it depends on $T_{kin}/p\sigma^3$ in equilibrium. This regime includes both near-equilibrium conditions where $T_{eff} ~ T_{kin}$ and far-from-equilibrium conditions where $T_{eff} \ne T_{kin}$. We discuss the implications of our results for systems with soft repulsive interactions.