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rameter for a continuous jamming transition. The quantity Δ z $^{2}$N would then be analogous to a sus- ceptibility, χ ∼ p − $^{γ}$, diverging with an exponent γ = 0 . 7. 

Our results are different than those of Henkes and Chakraborty, 37 where fluctuations of z are found to be independent of pressure, Δ z ∼ p $^{0}$. Note, how- ever, the subtle difference in ensemble. These au- thors study a pressure-ensemble, in which states are generated by quenching random particle configura- tions to the local minimum of the potential energy landscape (similar to the procedure in Ref. $^{16}$). One may view these states as the inherent structures of a high temperature liquid. Our ensemble then corre- sponds to the inherent structures of a driven glassy material. We fix volume-fraction and sample only states that are connected by the trajectory of the system in phase-space. The ensemble therefore re- flects the dynamics of the system and the region of phase-space where it is guided to. 

## 3.1.2 Yield properties 

We now go beyond the properties of the elastic states and discuss aspects related to their failure during the plastic events. As indicated in the in- troduction, plastic events can be viewed as bifurca- tions in energy-landscape. A local energy minimum vanishes and the system has to search for a new minimum at lower energy and stress. In quasistatic dynamics this process is instantaneous. The asso- ciated stress-drop is therefore visible as a vertical line in the stress-strain relation (Fig. 1). 

In the following we characterize the amount of dissipation during a plastic event by the associated stress-drop, Δ σ . The frequency of plastic events is discussed in terms of the length of elastic branches, Δ γ$_{avg}$ . 

Just like the probability distributions within the elastic states, the functions P (Δ σ ) and P (Δ γ$_{avg}$ ) (Figs. 5 and 6) are universal and can be rescaled on a single master-curve. Here, it is sufficient to use the first moment of the distribution, i.e. the ensemble-averaged stress drops and elastic-branch lengths, respectively. As the logarithmic scale in the inset in Fig. 5 shows, the collapse for the stress- drop distribution is quite good for large as well as for small stress drops. The black line repre- sents a fit of the form Δ σ $_{−}$1 exp( − Δ σ/σ$_{L}$ ) with the stress-scale σ$_{L}$ ≈ 5Δ σ$_{avg}$ . The intermediate 

<img src='content_image/417992.jpg'>

power-law behaviour P ∼ Δ σ $_{−}$1 reflects the lack of scale related to a typical event size. The only rele- vant scale is the exponential cut-off at σ$_{L}$ . Tewari et al. 38 have reported an exponent of − 0 . 7 in the energy-drop distribution at finite-strain rates. The simulated systems are somewhat smaller, however. Kabla et al. 39 have found an exponent of − 1 . 5 in a vertex model for foams, in agreement with renor- malization group arguments. 40 

The exponential tail has been observed in sev- eral different studies 8,11,11,41,42 in two and in three spatial dimensions. Tsamados et al. 11 have further- more related this feature of the stress-drop distri- bution to the diversity of local flow-defects causing the plastic event. 

A similar universality has been observed by Mal- oney and Lemaˆıtre. 8 Their simulations are con- ducted with three different interaction potentials but without changing the density, which is set to high values far away from the rigidity transition. 

