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We build a minimal, mean-field, model of plasticity of amorphous solids,based upon a phenomenology of dissipative events derived, in a preceding paper[A. Lemaitre, C. Caroli, arXiv:0705.0823] from extensive molecular simulations.It reduces to the dynamics of an ensemble of identical shear transformationzones interacting via the dynamic noise due to the long ranged elastic fieldsinduced by zone flips themselves. We find that these ingredients are sufficientto generate flip avalanches with a power-law scaling with system size,analogous to that observed in molecular simulations. We further show that thescaling properties of avalanches sensitively depend on the detailed shape ofthe noise spectrum. This points out the importance of developing a realisticcoarse-grained description of elasticity in these systems.

Plastic Response of a 2D Amorphous Solid to Quasi-Static Shear : II - Dynamical Noise and Avalanches in a Mean Field Model