Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow

We confront a recent visco-plastic description of dense granular flows [P. Jop et al, Nature, {\bf 441} (2006) 727] with multi-directional inhomogeneous steady flows observed in non-smooth contact dynamics simulations of 2D half-filled rotating drums. Special attention is paid to check separately the two underlying fundamental statements into which the considered theory can be recast, namely (i) a single relation between the invariants of stress and strain rate tensors and (ii) the alignment between these tensors. Interestingly, the first prediction is fairly well verified over more than four decades of small strain rate, from the surface rapid flow to the quasi-static creep phase, where it is usually believed to fail because of jamming. On the other hand, the alignment between stress and strain rate tensors is shown to fail over the whole flow, what yields an apparent violation of the visco-plastic rheology when applied without care. In the quasi-static phase, the particularly large misalignment is conjectured to be related to transient dilatancy effects

Super-diffusion around the rigidity transition: Levy and the Lilliputians

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.Comment: 7 pages, 6 figure

The Jamming point street-lamp in the world of granular media

The Jamming of soft spheres at zero temperature, the J-point, has been extensively studied both numerically and theoretically and can now be considered as a safe location in the space of models, where a street lamp has been lit up. However, a recent work by Ikeda et al, 2013 reveals that, in the Temperature/Packing fraction parameter space, experiments on colloids are actually rather far away from the scaling regime illuminated by this lamp. Is it that the J-point has little to say about real system? What about granular media? Such a-thermal, frictional, systems are a-priori even further away from the idealized case of thermal soft spheres. In the past ten years, we have systematically investigated horizontally shaken grains in the vicinity of the Jamming transition. We discuss the above issue in the light of very recent experimental results. First, we demonstrate that the contact network exhibits a remarkable dynamics, with strong heterogeneities, which are maximum at a packing fraction phi star, distinct and smaller than the packing fraction phi dagger, where the average number of contact per particle starts to increase. The two cross-overs converge at point J in the zero mechanical excitation limit. Second, a careful analysis of the dynamics on time scales ranging from a minute fraction of the vibration cycle to several thousands of cycles allows us to map the behaviors of this shaken granular system onto those observed for thermal soft spheres and demonstrate that some light of the J-point street-lamp indeed reaches the granular universe.Comment: 20 pages, 23 figures, submitted to Soft Matte

Avalanches and Dynamical Correlations in supercooled liquids

We identify the pattern of microscopic dynamical relaxation for a two dimensional glass forming liquid. On short timescales, bursts of irreversible particle motion, called cage jumps, aggregate into clusters. On larger time scales, clusters aggregate both spatially and temporally into avalanches. This propagation of mobility, or dynamic facilitation, takes place along the soft regions of the systems, which have been identified by computing isoconfigurational Debye-Waller maps. Our results characterize the way in which dynamical heterogeneity evolves in moderately supercooled liquids and reveal that it is astonishingly similar to the one found for dense glassy granular media.Comment: 4 pages, 3 figure

Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass

The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom associated with contact dynamics control the appearance of macroscopic rigidity. We provide decisive experimental evidence that this transition is a critical phenomenon, with increasingly collective and heterogeneous rearrangements occurring at length scales much smaller than the grains' diameter, presumably reflecting the contact force network fluctuations. Dynamical correlation time and length scales soar on both sides of the transition, as the volume fraction varies over a remarkably tiny range ($\delta \phi/\phi \sim 10^{-3}$). We characterize the motion of individual grains, which becomes super-diffusive at the jamming transition $\phi_J$, signaling long-ranged temporal correlations. Correspondingly, the system exhibits long-ranged four-point dynamical correlations in space that obey critical scaling at the transition density.Comment: 4 pages, 8 figure

Temperature in nonequilibrium systems with conserved energy

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature T_{th}^{-1}. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.Comment: 4 pages, 1 figure, final versio

Turbulence lifetimes: what we can learn from the physics of glasses

In this note, we critically discuss the issue of the possible finiteness of the turbulence lifetime in subcritical transition to turbulence in shear flows, which attracted a lot of interest recently. We briefly review recent experimental and numerical results, as well as theoretical proposals, and compare the difficulties arising in assessing this issue in subcritical shear flow with that encountered in the study of the glass transition. In order to go beyond the purely methodological similarities, we further elaborate on this analogy and propose a qualitative mapping between these two apparently unrelated situations, which could possibly foster new directions of research in subcritical shear flows.Comment: 10 pages, 4 figure

An hydrodynamic shear instability in stratified disks

We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity $\Omega$ decreases outwards with radius $r$. At not too small stratification, its growth rate is a fraction of $\Omega$. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when $d \ln \Omega / d \ln r =-3/2$ (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.Comment: 19 pages, 13 figures, to appear in A&