Avalanches and di?usion in model bubble rafts near jamming

Energy dissipation distributions and particle displacement statistics are studied in the mean field version of Durian's bubble model. A two dimensional (2D) bi-disperse mixture is simulated at various strain rates, $\dot{\gamma}$, and packing ratios, $\phi$, above the close packing limit, $\phi_c$. Well above $\phi_c$, and at sufficiently low $\dot{\gamma}$, the system responds in a highly intermittent way, reminiscent of other dynamically critical systems with a power law distribution of energy dissipation. As one increases $\dot{\gamma}$ at fixed $\phi$ or tunes $\phi\rightarrow \phi_c$ at fixed $\dot{\gamma}$, the intermittent behavior vanishes. Displacement distributions are non-Fickian at short times but cross to a Fickian regime at a universal strain, $\Delta\gamma_*$, independent of $\dot{\gamma}$ and $\phi$. Despite the profound differences in short-time dynamics, at intermediate $\Delta\gamma$ the systems surprisingly exhibit qualitatively similar spatial patterns of deformation, with lines of slip extending across large fractions of the simulation cell. The results raise new questions about the nature of quasistatic shear near $\phi_c$ and should have important consequences for various kinds of jammed systems.