  We build a mean-field model of plasticity of amorphous solids, based on the
dynamics of an ensemble shear transformation zones, interacting via intrinsic
dynamical noise generated by the zone flips themselves. We compare the
quasi-static, steady-state properties for two types of noise spectrum: (G)
Gaussian; (E) broad distribution derived from quadrupolar elastic interactions.
We find that the plastic flow proceeds via avalanches whose scaling properties
with system size are highly sensitive to noise tails. Comparison with available
data suggests that non-affine strain fields might be of paramount importance in
the small systems accessible to molecular simulations.
