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The authors have argued for a universal value of the “flow-strain” σ$_{y}$/g of a few percent. Appar- ently, this can only be true far away from φ$_{c}$ . As the yield-stress vanishes faster than the shear mod- ulus, one finds a ratio σ$_{y}$/g ∼ δφ 1 / 2 that vanishes at point J. Thus, particle configurations at the on- set of jamming are highly fragile and susceptible to even minute changes in the boundary conditions. 

The average stress-drop as well as the average length of elastic branches change with pressure and system-size as displayed in Figs. 5 and 6 $^{2}$. As a function of pressure one observes an increase but with a slope that depends on system-size. The av- 

erage stress-drops increase somewhat slower with pressure than the yield-stress $^{3}$. The relative stress fluctuations Δ σ$_{avg}$/σ$_{y}$ are thus slightly enhanced at small pressures close to φ$_{c}$ . The same trend is also visible in the total stress fluctuations as calculated by 〈 ( σ − 〈 σ 〉 ) 2 〉 . The overall scale of both, Δ σ$_{avg}$ and Δ γ$_{avg}$ , de- creases with system-size to give a smooth stress- 

strain relation in the thermodynamic limit. Pre- vious studies 8,10,11 have observed a scaling of the stress-drops with N $_{−}$1 / $^{2}$. This includes 8 a sys- tem of harmonically interacting particles, as stud- ied here, but at a rather high pressure. In gen- eral, we observe a weaker dependence on system- size, with an effective exponent that increases with pressure. Our data is consistent, however, with the value of 1 / 2 being the relevant high-pressure limit. 

## 3.2 Dynamical correlations 

Let us now turn to the dynamics of the system. In particular we want to characterize dynamic corre- lations in the motion of particles. While at volume- fractions above φ$_{c}$ the isostaticity length-scale l ⋆ is clearly finite $^{4}$, there is nevertheless a large dynam- ical length-scale related to the flow arrest. This has, for example, been evidenced in a system of Lennard-Jones particles with dissipative dynam- ics. 15 We will show below that a similar length- scale occurs in our system of purely repulsively in- teracting particles, independent of the distance to φ$_{c}$ . 

Let us start by presenting the results from the quasistatic simulations. To define a dynamical cor- relation length we study heterogeneities in the par- ticle mobilities. To this end we use the overlap- function 43,44 

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of particles undergoing nonaffine displacements u$_{i}$$_{na}$ during a strain interval of γ $^{5}$. Particles mov- ing farther than the distance a (“mobile”), have 

