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

TL;DR

This study uses molecular dynamics to show that the ratio of effective temperature to pressure governs the mobility of sheared hard spheres, revealing a crossover in relaxation behavior linked to local yield strain and shear transformation zones.

Contribution

It introduces a unified framework relating effective temperature to relaxation dynamics in sheared hard spheres across different regimes, supported by simulation data.

Findings

Shear stress and density fluctuations relate to response functions via effective temperature.

A crossover in relaxation behavior is observed when considering the ratio T_{eff}/pσ^3.

In the solid regime, relaxation time follows an exponential dependence on effective temperature.

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.