A model for approximately stretched-exponential relaxation with continuously varying stretching exponents

Relaxation in glasses is often approximated by a stretched-exponential form: $f(t)=A\exp [-(t\mathrm{/}\tau {)}^{\beta }]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort'e et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $\beta$ that depends on the strain amplitude: $0.25<\beta <1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.