plitude with volume-fraction, signalling enhanced correlations away from φ$_{c}$ . their yield-stress with the breakdown of the rigidity of the solid state at point J. This is not due to the special choice of the pa- rameter a = 0 . 01. We have found the same trend when fixing γ and viewing χ$_{4}$ as function of a as for the quasistatic simulations in Fig. 7. Finally, we have also calculated the absolute maximum of χ$_{4}$ , viewed as function of both a and γ . In all cases, the amplitude increases with volume-fraction. Both, the increase of the length-scale with lowering the strain-rate and the increase with volume-fraction are consistent with the recently proposed elasto- plastic model of Bocquet et al. 13 Given the trend in Fig. 10, one may specu- late about a vanishing dynamical correlation length (taken at constant strain-rate ˙ γ = 10 $_{−}$4 outside the quasistatic regime), as φ$_{c}$ is approached. Such a behavior is indeed compatible with our data and has recently been observed in the rheology of a concentrated emulsion confined in gaps of differ- ent thickness. 49 Here we interpret this surprising feature in the following way: at a given packing fraction, dynamical correlations increase with de- creasing ˙ γ , and saturate at a N -dependent value in the quasistatic regime. This cross-over to the qua- sistatic regime does not only depend on system-size but also on packing fraction: ˙ γ$_{qs}$ ( N, φ ). For φ closer to φ$_{c}$ the energy landscape becomes increasingly flat. Particle relaxations take longer 50 and smaller strain-rates are needed to allow for full relaxation into the local energy minimum. Thus, smaller strain-rates are needed to reach the qua- sistatic behavior and ˙ γ$_{qs}$ decreases towards φ$_{c}$ . Hence, reducing φ towards φ$_{c}$ at a fixed strain rate is ”equivalent” to increasing the strain rate relative to ˙ γ$_{qs}$ , and results in a decrease of dynamical corre- lations. In contrast, corrrelations taken at a strain rate ˙ γ = ˙ γ$_{qs}$ ( φ ), are independent of φ and given by their quasi-static values, as displayed in Fig. 8. We found that this breakdown is visible in the en- semble of states visited during a flow simulation in a similar way as in the linear elasticity of the solid. For example (Fig. 4), we showed that the average number of particle contacts scale with the square- root of pressure, just as in linear elasticity. In con- trast, the fluctuations around this average value show a distinct behavior that has not been observed previously. We showed that the contact-number fluctuations actually diverge upon approaching the critical volume-fraction from above, making the contact number an ideal candidate for an order parameter of a continuous jamming transition as observed under steady shear. The relative fluctua- tions of the shear modulus and those of the shear stress also diverge in the same limit. Going beyond the characterization of the average elastic proper- ties we have studied the statistics of plastic events (Figs. 5 and 6). It seems that all distributions have universal scaling forms reminiscent of standard crit- ical phenomena. From all these results, it would be tempting to say that it is the energy landscape as a whole that becomes critical at point J. Isostatic elastic- ity would then be just one aspect of this criticality, another one could be the intermediate power-law tail in the stress-drop distribution. This critical as- pect is also illustrated by the intermittency in the stress response of finite-size systems (see Fig.1) and by the growth of an isostatic correlation length in the quasistatic response when point J is approached from below. 28 At strain-rates above the quasistatic regime, the dynamics limits access to certain regions of the en- ergy landscape. While the dynamics is still highly correlated, the dynamical correlation length, as measured by the amplitude of the four-point sus- ceptibility χ$_{4}$ , remains finite and actually decreases with lowering the volume-fraction towards φ$_{c}$ . In the quasistatic regime we have shown that χ$_{4}$ reflects, in two ways, the interplay of elastic load- ing and plastic energy release (Fig. 8). First, the typical strain-scale of heterogeneity is set by the fre- quency of plastic events. Second, the amplitude of χ$_{4}$ scales with system-size, which highlights the fact that the quasistatic, plastic flow regime is, in fact, a finite-size dominated regime with a correlation length that is limited by system size. This behavior We have discussed the small strain-rate elasto- plastic flow of an athermal model system of soft harmonic spheres. In particular, we were inter- ested in the flow properties at and above a critical volume-fraction (point J), at which the yield-stress of the material vanishes. This regime combines the more traditional elasto-plastic flow of solids above 4 Discussion and Conclusion 10