Active versus Passive Hard Disks against a Membrane: Mechanical Pressure and Instability.

We experimentally study the mechanical pressure exerted by a set of respectively passive isotropic and self-propelled polar disks onto two different flexible unidimensional membranes. In the case of the isotropic disks, the mechanical pressure, inferred from the shape of the membrane, is identical for both membranes and follows the equilibrium equation of state for hard disks. On the contrary, for the self-propelled disks, the mechanical pressure strongly depends on the membrane in use and thus is not a state variable. When self-propelled disks are present on both sides of the membrane, we observe an instability of the membrane akin to the one predicted theoretically for active Brownian particles against a soft wall. In that case, the integrated mechanical pressure difference across the membrane cannot be computed from the sole knowledge of the packing fractions on both sides, further evidence of the absence of an equation of state.

Experimental Evidence of the Gardner Phase in a Granular Glass.

Analyzing the dynamics of a vibrated bidimensional packing of bidisperse granular disks below jamming, we provide evidence of a Gardner phase deep into the glass phase. To do so, we perform several compression cycles within a given realization of the same glass and show that the particles select different average vibrational positions at each cycle, while the neighborhood structure remains unchanged. The separation between the cages obtained for different compression cycles plateaus with an increasing packing fraction, while the mean square displacement steadily decreases. This phenomenology is strikingly similar to that reported in recent numerical observations when entering the Gardner phase, for a mean-field model of glass as well as for hard spheres in finite dimension. We also characterize the distribution of the cage order parameters. Here we note several differences from the numerical results, which could be attributed to activated processes and cage heterogeneities.

Crystallization of Self-Propelled Hard Discs.

We experimentally study the crystallization of a monolayer of vibrated discs with a built-in polar asymmetry, a model system of active liquids, and contrast it with that of vibrated isotropic discs. Increasing the packing fraction ϕ, the quasicontinuous crystallization reported for isotropic discs is replaced by a transition, or a crossover, towards a "self-melting" crystal. Starting from the liquid phase and increasing the packing fraction, clusters of dense hexagonal-ordered packed discs spontaneously form, melt, split, and merge, leading to a highly intermittent and heterogeneous dynamics. For a packing fraction larger than ϕ^{*}, a few large clusters span the system size. The cluster size distribution is monotonically decreasing for ϕ<ϕ^{*}, nonmonotonic for ϕ>ϕ^{*}, and is a power law at the transition. The system is, however, never dynamically arrested. The clusters permanently melt from place to place, forming droplets of an active liquid which rapidly propagate across the system. This self-melting crystalline state subsists up to the highest possible packing fraction, questioning the stability of the crystal for active discs unless it is at ordered close packing.

Shear modulus and dilatancy softening in granular packings above jamming.

We investigate experimentally the mechanical response to shear of a monolayer of bidisperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photoelasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10(-3) and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in: both the shear modulus and the dilatancy shear soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition.

How the ideal jamming point illuminates the world of granular media.

The zero temperature properties of frictionless soft spheres near the jamming point have been extensively studied both numerically and theoretically; these studies provide a reliable base for the interpretation of experiments. However, recent work by Ikeda et al. showed that, in a parameter space of the temperature and packing fraction, experiments to date on colloids have been rather far from the theoretical scaling regime. An important question is then whether theoretical results concerning point-J are applicable to any physical/experimental system, including granular media, which we consider here. On the surface, such a-thermal, frictional systems might appear even further from the idealized case of thermal soft spheres. In this work we address this question via experiments on shaken granular materials near jamming. We have systematically investigated such systems over a number of years using hard metallic grains. The important feature of the present work is the use of much softer grains, cut from photoelastic materials, making it possible to determine forces at the grain scale, the details of the contact networks and the motion of individual grains. Using this new type of particle, we first show that the contact network exhibits remarkable dynamics. We find strong heterogeneities, which are maximum at the packing fraction ϕ*, distinct from and smaller than the packing fraction ϕ(†), where the average number of contacts per particle, z, starts to increase. In the limit of zero mechanical excitation, these two packing fractions converge at point J. We also determine dynamics on time scales ranging from a small fraction of the shaking cycle to thousands of cycles. We can then map the observed system behavior onto results from simulations of ideal thermal soft spheres. Our results indicate that the ideal jamming point indeed illuminates the world of granular media.

Bulk elastic fingering instability in Hele-Shaw cells.

We demonstrate experimentally the existence of a purely elastic, nonviscous fingering instability which arises when air penetrates into an elastomer confined in a Hele-Shaw cell. Fingers appear sequentially and propagate within the bulk of the material as soon as a critical strain, independent of the elastic modulus, is exceeded. Key elements in the driving force of the instability are the confinement of the gel and its adhesion to the plates of the cell, which result in a considerable expense of elastic energy during the growth of the air bubble.

Long-range ordering of vibrated polar disks.

Vibrated polar disks have been used experimentally to investigate collective motion of driven particles, where fully ordered asymptotic regimes could not be reached. Here we present a model reproducing quantitatively the single, binary, and collective properties of this granular system. Using system sizes not accessible in the laboratory, we show in silico that true long-range order is possible in the experimental system. Exploring the model's parameter space, we find a phase diagram qualitatively different from that of dilute or pointlike particle systems.

Rotation shields chaotic mixing regions from no-slip walls.

We report on the decay of a passive scalar in chaotic mixing protocols where the wall of the vessel is rotated, or a net drift of fluid elements near the wall is induced at each period. As a result the fluid domain is divided into a central isolated chaotic region and a peripheral regular region. Scalar patterns obtained in experiments and simulations converge to a strange eigenmode and follow an exponential decay. This contrasts with previous experiments [Gouillart, Phys. Rev. Lett. 99, 114501 (2007)] with a chaotic region spanning the whole domain, where fixed walls constrained mixing to follow a slower algebraic decay. Using a linear analysis of the flow close to the wall, as well as numerical simulations of Lagrangian trajectories, we study the influence of the rotation velocity of the wall on the size of the chaotic region, the approach to its bounding separatrix, and the decay rate of the scalar.

Spatiotemporal hierarchy of relaxation events, dynamical heterogeneities, and structural reorganization in a supercooled liquid.

We identify the pattern of microscopic dynamical relaxation for a two-dimensional glass-forming liquid. On short time scales, 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 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.

Creep motion of an intruder within a granular glass close to jamming.

We experimentally study the dynamics of an intruder dragged at a constant force in a horizontally vibrated monolayer of grains. At moderate packing fractions, the intruder moves rapidly as soon as the force is applied. Above some threshold value it has an intermittent creep motion with strong fluctuations reminiscent of "crackling noise". These fluctuations are critical at the jamming transition varphi_{J} unveiled in a previous study. The transition separates a regime with local free volume rearrangements from a regime where the displacement field is strongly heterogeneous and resembles force chain patterns.

Building blocks of dynamical heterogeneities in dense granular media.

We investigate experimentally the connection between short time dynamics and long time dynamical heterogeneities within a dense granular media under cyclic shear. We show that dynamical heterogeneities result from a two time scales process. Short time but already collective events consisting in clustered cage jumps concentrate most of the nonaffine displacements. On larger time scales, such clusters appear aggregated both temporally and spatially in avalanches which eventually build the large scales dynamical heterogeneities. Our results indicate that facilitation plays an important role in the relaxation process although it does not appear to be conserved as proposed in many models studied in the literature.

Slow decay of concentration variance due to no-slip walls in chaotic mixing.

Chaotic mixing in a closed vessel is studied experimentally and numerically in different two-dimensional (2D) flow configurations. For a purely hyperbolic phase space, it is well known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincaré section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.

Walls inhibit chaotic mixing.

We report on experiments of chaotic mixing in a closed vessel, in which a highly viscous fluid is stirred by a moving rod. We analyze quantitatively how the concentration field of a low-diffusivity dye relaxes towards homogeneity, and we observe a slow algebraic decay of the inhomogeneity, at odds with the exponential decay predicted by most previous studies. Visual observations reveal the dominant role of the vessel wall, which strongly influences the concentration field in the entire domain and causes the anomalous scaling. A simplified 1D model supports our experimental results. Quantitative analysis of the concentration pattern leads to scalings for the distributions and the variance of the concentration field consistent with experimental and numerical results.

Flow rule, self-channelization, and levees in unconfined granular flows.

Unconfined granular flows along an inclined plane are investigated experimentally. During a long transient, the flow gets confined by quasistatic banks but still spreads laterally towards a well-defined asymptotic state following a nontrivial process. Far enough from the banks a scaling for the depth averaged velocity is obtained, which extends the one obtained for homogeneous steady flows. Close to jamming it exhibits a crossover towards a nonlocal rheology. We show that the levees, commonly observed along the sides of the deposit upon interruption of the flow, disappear for long flow durations. We demonstrate that the morphology of the deposit builds up during the flow, in the form of an underlying static layer, which can be deduced from surface velocity profiles, by imposing the same flow rule everywhere in the flow.

Memory of the unjamming transition during cyclic tiltings of a granular pile.

Discrete numerical simulations are performed to study the evolution of the microstructure and the response of a granular packing during successive loading-unloading cycles, consisting of quasistatic rotations in the gravity field between opposite inclination angles. We show that internal variables--e.g., stress and fabric of the pile--exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behavior of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak-contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phase description--strong- and weak-contact networks--for a granular system, as soon as it has approached the unjamming transition.

Subdiffusion and cage effect in a sheared granular material.

We investigate experimentally the diffusion properties of a bidimensional bidisperse dry granular material under quasistatic cyclic shear. The comparison of these properties with results obtained both in computer simulations of hard spheres systems and Lennard-Jones liquids and experiments on colloidal systems near the glass transition demonstrates a strong analogy between the statistical behavior of granular matter and these systems, despite their intrinsic microscopic differences (thermal vs athermal). More specifically, we study in detail the cage dynamics responsible for the subdiffusion in the slow relaxation regime, and obtain the values of relevant time and length scales.

Dynamical heterogeneity close to the jamming transition in a sheared granular material.

The dynamics of a bidimensional dense granular packing under cyclic shear is experimentally investigated close to the jamming transition. Measurement of multipoint correlation functions are produced. The self-intermediate scattering function, displaying slower than exponential relaxation, suggests dynamic heterogeneity. Further analysis of four point correlation functions reveal that the grain relaxations are strongly correlated and spatially heterogeneous, especially at the time scale of the collective rearrangements. Finally, a dynamical correlation length is extracted from a spatiotemporal pattern of mobility. Our experimental results open the way to a systematic study of dynamic correlation functions in granular materials.