described above. We complement this analysis with preliminary results from dissipative molecular-dynamics sim- ulations that access strain-rates above the qua- sistatic regime. This allows us to assess the im- portance of dynamic effects in limiting access to certain regions of the landscape. Indeed, the re- sults at larger strain rate are system size indepen- dent, and reveal a surprising growth of the strength of the heterogeneities with increasing packing frac- tion away from φ$_{c}$ . The molecular dynamics simulations were per- formed by integrating Newton’s equations of mo- tion with elastic forces as deduced from Eq. (1) and dissipative forces Our system consists of N soft spherical particles with harmonic contact interactions Two particles, having radii r$_{i}$ and r$_{j}$ , only interact, when they are “in contact”, i.e. when their distance r is less than the interaction diameter r$_{c}$ = r$_{i}$ + r$_{j}$ . This system has been studied in several contexts, for example in. 16,26,32 The mixture consists of two types of particles (50 : 50) with radii r$_{1}$ = 0 . 5 d and r$_{2}$ = 0 . 7 d in two-dimensions. Three different system-sizes have been simulated with N = 900, 1600 and 2500 particles, respectively. The unit of length is the diameter, d , of the smaller par- ticle, the unit of energy is kd $^{2}$, where k is the spring constant of the interaction potential. We use quasistatic shear simulation, and compare some of the results with those obtained from dissipative molecular-dynamics simulations at zero tempera- ture. Quasistatic simulations consists of successively applying small steps of shear followed by a mini- mization of the total potential energy. The shear is implemented with Lee-Edwards boundary con- ditions with an elementary strain step of Δ γ = 5 · 10 $^{$_{−}$5}$. After each change in boundary condi- tions the particles are moved affinely to define the starting configuration for the minimization, which is performed using conjugate gradient techniques. 33 The minimization is stopped when the nearest en- ergy minimum is found. Thus, as the energy land- scape evolves under shear the system always re- mains at a local energy minimum, characterized by a potential energy, a pressure p and a shear stress σ . As is readily apparent from Fig. 1, a typical feature of quasistatic stress-strain relations is the interplay of “elastic branches” and “plastic events”. During elastic branches stress grows linearly with strain and the response is reversible. In plastic events the stress drops rapidly and energy is dissipated. In setting the elementary strain step, Δ γ , care must be taken to properly resolve these events. Too large strain steps would make the simulations miss certain relaxation events. We chose a strain step small enough, such that most minimization steps do not involve any plastic relaxations. In conse- quence, the elastic branches are well resolved, each consisting of many individual strain steps. The succession of elastic and plastic events de- fines the flow of the material just above its yield- stress σ$_{y}$ ( φ ). The value of the yield-stress depends on volume-fraction and nominally vanishes at φ$_{c}$ (see Fig. 2). For finite systems, however, finite-size effects dominate close to φ$_{c}$ such that one cannot observe a clear vanishing of σ$_{y}$ . Rather, as Fig. 1 shows, one enters an intermittent regime, i.e. a fi- nite interval in volume-fraction in which the stress- proportional to the velocity differences along the direction ˆ r$_{ij}$ that connects the particle pair. The damping coefficient is chosen to be b = 1. Rough boundaries are used during the shear, the bound- aries being built by freezing some particles at the extreme ends in the y -direction, from a quenched liquid configuration at a given φ . The system is sheared by driving one of the walls at a fixed ve- locity in the x direction, using periodic boundary conditions in this direction. For all system sizes, the distance between the top and bottom boundaries is 52 . 8 d and each of the boundaries has a thickness of 4 . 2 d . The system size is changed by modifying the length of the box in the x -direction. 3 Results 3.1 Quasistatic simulations 2 Simulations ⃗ F$_{ij}$ = − b [( ⃗ v$_{i}$ − ⃗ v$_{j}$ ) · ˆ r$_{ij}$ ] ˆ r$_{ij}$, (2) E ( r ) = k ( r − r$_{c}$ ) 2 . (1) 3