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

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

2011-03-18

arxiv.org/abs/1103.3704v2

Physics

Condensed Matter

Soft Condensed Matter

9 pages, 6 figures. Major revision: added results and analysis for sheared inelastic hard spheres to complement the previous r

Scientific paper

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.

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