Effective temperature and jamming transition in dense, gently sheared granular assemblies

We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the shear rate for slow enough shear suggesting that it is the effective temperature of the jammed packing. However, we also show that the agreement of the effective temperature for different observables is only approximate, for very long times, suggesting that this defintion may not capture the full thermodynamics of the system. On the other hand, we find good agreement between the dynamical effective temperature and a compactivity calculated assuming that all jammed states are equiprobable. Therefore, this definition of temperature may capture an instance of the ergodic hypothesis for granular materials as proposed by theoretical formalisms for jamming. Finally, our simulations indicate that the average shear stress and apparent shear viscosity follow the usual relation with the shear rate for complex fluids. Our results show that the application of shear induces jamming in packings whose particles interact by tangential forces.     

Driven lattice gas with nearest-neighbor exclusion: shear-like drive

We study the lattice gas with nearest-neighbor exclusion on the square lattice and Kawasaki (hopping) dynamics, under the influence of a nonuniform drive, via Monte Carlo simulation. The drive, which favors motion along the +x direction and inhibits motion in the opposite direction, varies linearly with y. (The boundaries along the drive direction are periodic, so that the system is not described by an equilibrium Gibbs distribution.) As in the uniformly driven case [R. Dickman, Phys. Rev. E 64, 16124 (2001)], the onset of sublattice ordering occurs at a lower density than in equilibrium, but here an unexpected feature appears: particles migrate out of the high-drive region. For intermediate system sizes (L ≃100), the accumulation of particles is sufficient for the low-drive region to become ordered at a global density of about 0.3. Above this density we observe a surprising reversal in the density profile, with particles accumulating to the high-drive region, due to jamming. For larger systems (L≥200) particles quickly jam in the high-drive region, as occurs under uniform drive, and the accumulation of particles in the low-field region is severely reduced.     

From crystal to amorphous: A novel route to unjamming in soft disk packings

Numerical studies on the unjamming packing fraction of bi- and polydisperse disk packings, which are generated through compression of a monodisperse crystal, are presented. In bidisperse systems, a fraction f ₊ = 0.400 up to 0.800 of the total number of particles has their radii increased by D \Delta R , while the rest has their radii decreased by the same amount. Polydisperse packings are prepared by changing all particle radii according to a uniform distribution in the range [- D \Delta R,D \Delta R] . The results indicate that the critical packing fraction is never larger than the value for the initial monodisperse crystal, f₀ \phi_{0}^{} = p \pi/?{12} \sqrt{{12}} , and that the lowest value achieved is approximately the one for random close packing. These results are seen as a consequence of the interplay between the increase in small-small particle contacts and the local crystalline order provided by the large-large particle contacts.