Characterization of the Clogging Transition in Vibrated Granular Media.

The existence of a transition from a clogged to an unclogged state has been recently proposed for the flow of macroscopic particles through bottlenecks in systems as diverse as colloidal suspensions, granular matter, or live beings. Here, we experimentally demonstrate that, for vibrated granular media, such a transition genuinely exists, and we characterize it as a function of the outlet size and vibration intensity. We confirm the suitability of the "flowing parameter" as the order parameter, and we find out that the rescaled maximum acceleration of the system should be replaced as the control parameter by a dimensionless velocity that can be seen as the square root of the ratio between kinetic and potential energy. In all the investigated scenarios, we observe that, for a critical value of this control parameter S_{c}, there seems to be a continuous transition to an unclogged state. The data can be rescaled with this critical value, which, as expected, decreases with the orifice size D. This leads to a phase diagram in the S-D plane in which clogging appears as a concave surface.

Estimating density limits for walking pedestrians keeping a safe interpersonal distancing.

With people trying to keep a safe distance from others due to the COVID-19 outbreak, the way in which pedestrians walk has completely changed since the pandemic broke out1,2. In this work, laboratory experiments demonstrate the effect of several variables-such as the pedestrian density, the walking speed and the prescribed safety distance-on the interpersonal distance established when people move within relatively dense crowds. Notably, we observe that the density should not be higher than 0.16 pedestrians per square meter (around 6 m2 per pedestrian) in order to guarantee an interpersonal distance of 1 m. Although the extrapolation of our findings to other more realistic scenarios is not straightforward, they can be used as a first approach to establish density restrictions in urban and architectonic spaces based on scientific evidence.

Pedestrian evacuation simulation in the presence of an obstacle using self-propelled spherocylinders.

We explore the role that the obstacle position plays in the evacuation time of agents when leaving a room. To this end, we simulate a system of nonsymmetric spherocylinders that have a prescribed desired velocity and angular orientation. In this way, we reproduce the nonmonotonous dependence of the pedestrian flow rate on the obstacle distance to the door. For short distances, the obstacle delays the evacuation because the exit size is effectively reduced; i.e., the distance between the obstacle and the wall is smaller than the door width. By increasing the obstacle distance to the door, clogging is reduced leading to an optimal obstacle position (maximum flow rate) in agreement with results reported in numerical simulations of pedestrian evacuations and granular flows. For further locations, however, a counterintuitive behavior occurs as the flow rate values fall again below the one corresponding to the case without obstacle. Analyzing the head-times distribution, we evidence that this new feature is not linked to the formation of clogs, but is caused by a reduction of the efficiency of the agent's instantaneous flow rate when the exit is not blocked.

Multifractal Intermittency in Granular Flow through Bottlenecks.

We experimentally analyze the intermittent nature of granular silo flow when the discharge is controlled by an extracting belt at the bottom. We discover the existence of four different scenarios. For low extraction rates, the system is characterized by an on-off intermittency. When the extraction rate is increased the structure functions of the grains velocity increments, calculated for different lag times, reveal the emergence of multifractal intermittency. Finally, for very high extraction rates that approach the purely gravitational discharge, we observe that the dynamics become dependent on the outlet size. For large orifices the behavior is monofractal, whereas for small ones, the fluctuations of the velocity increments deviate from Gaussianity even for very large time lags.

Nonergodicity in silo unclogging: Broken and unbroken arches.

We report an experiment on the unclogging dynamics in a two-dimensional silo submitted to a sustained gentle vibration. We find that arches present a jerking motion where rearrangements in the positions of their beads are interspersed with quiescent periods. This behavior occurs for both arches that break down and those that withstand the external perturbation: Arches evolve until they either collapse or get trapped in a stable configuration. This evolution is described in terms of a scalar variable characterizing the arch shape that can be modeled as a continuous-time random walk. By studying the diffusivity of this variable, we show that the unclogging is a weakly nonergodic process. Remarkably, arches that do not collapse explore different configurations before settling in one of them and break ergodicity much in the same way than arches that break down.

Decoupling Geometrical and Kinematic Contributions to the Silo Clogging Process.

Based on the implementation of a novel silo discharge procedure, we are able to control the grains velocities regardless of the outlet size. This allows isolating the geometrical and kinematic contributions to the clogging process. We find that, for a given outlet size, reducing the grains velocities to extremely low values leads to a clogging probability increment of almost two orders of magnitude, hence revealing the importance of particle kinematics in the silo clogging process. Then, we explore the contribution of both variables, outlet size and grains velocity, and we find that our results agree with an already known exponential expression that relates clogging probability with outlet size. We propose a modification of such expression revealing that only two parameters are necessary to fit all the data: one is related with the geometry of the problem, and the other with the grains kinematics.

Slow relaxation dynamics of clogs in a vibrated granular silo.

We experimentally explore the vibration-induced unclogging of arches halting the flow in a two-dimensional silo. The endurance of arches is determined by carrying out a survival analysis of their breaking times. By analyzing the dynamics of two morphological variables, we demonstrate that arches evolve toward less regular structures and it seems that there may exist a certain degree of irregularity that the arch reaches before collapsing. Moreover, we put forward that σ (the standard deviation of all angles between consecutive beads) describes faithfully the morphological evolution of the arch. Focusing on long-lasting arches, we study σ calculating its two-time autocorrelation function and its mean-squared displacement. In particular, the apparent logarithmic increase of the correlation and the decrease of the mean-squared displacement of σ when the waiting time is increased reveal a slowing down of the dynamics. This behavior is a clear hallmark of aging phenomena and confirms the lack of ergodicity in the unclogging dynamics. Our findings provide new insights on how an arch tends to destabilize and how the probability that it breaks with a long sustained vibration decreases with time.

Clogging Transition of Vibration-Driven Vehicles Passing through Constrictions.

We report experimental results on the competitive passage of elongated self-propelled vehicles rushing through a constriction. For the chosen experimental conditions, we observe the emergence of intermittencies similar to those reported previously for active matter passing through narrow doors. Noteworthy, we find that, when the number of individuals crowding in front of the bottleneck increases, there is a transition from an unclogged to a clogged state characterized by a lack of convergence of the mean clog duration as the measuring time increases. It is demonstrated that this transition-which was reported previously only for externally vibrated systems such as colloids or granulars-appears also for self-propelled agents. This suggests that the transition should also occur for the flow through constrictions of living agents (e.g., humans and sheep), an issue that has been elusive so far in experiments due to safety risks.

Experimental Study of Ordering of Hard Cubes by Shearing.

We experimentally analyze the compaction dynamics of an ensemble of cubic particles submitted to a novel type of excitation. Instead of the standard tapping procedure used in granular materials we apply alternative twists to the cylindrical container. Under this agitation, the development of shear forces among the different layers of cubes leads to particle alignment. As a result, the packing fraction grows monotonically with the number of twists. If the intensity of the excitations is sufficiently large, an ordered final state is reached where the volume fraction is the densest possible compatible with the boundary condition. This ordered final state resembles the tetratic or cubatic phases observed in colloids.

Pedestrian collective motion in competitive room evacuation.

When a sizable number of people evacuate a room, if the door is not large enough, an accumulation of pedestrians in front of the exit may take place. This is the cause of emerging collective phenomena where the density is believed to be the key variable determining the pedestrian dynamics. Here, we show that when sustained contact among the individuals exists, density is not enough to describe the evacuation, and propose that at least another variable -such as the kinetic stress- is required. We recorded evacuation drills with different degrees of competitiveness where the individuals are allowed to moderately push each other in their way out. We obtain the density, velocity and kinetic stress fields over time, showing that competitiveness strongly affects them and evidencing patterns which have been never observed in previous (low pressure) evacuation experiments. For the highest competitiveness scenario, we detect the development of sudden collective motions. These movements are related to a notable increase of the kinetic stress and a reduction of the velocity towards the door, but do not depend on the density.

Simulating competitive egress of noncircular pedestrians.

We present a numerical framework to simulate pedestrian dynamics in highly competitive conditions by means of a force-based model implemented with spherocylindrical particles instead of the traditional, symmetric disks. This modification of the individuals' shape allows one to naturally reproduce recent experimental findings of room evacuations through narrow doors in situations where the contact pressure among the pedestrians was rather large. In particular, we obtain a power-law tail distribution of the time lapses between the passage of consecutive individuals. In addition, we show that this improvement leads to new features where the particles' rotation acquires great significance.

Stability of clogging arches in a silo submitted to vertical vibrations.

We present experimental results on the endurance of arches that block the outlet of a two-dimensional silo when subjected to vertical vibration. In a recent paper [C. Lozano et al., Phys. Rev. Lett. 109, 068001 (2012)], it was shown that the arch resistance against vibrations is determined by the maximum angle among those formed between each particle in the bridge and its two neighbors: the larger the maximum angle is, the weaker the bridge. It has also been reported that the breaking time distribution shows a power-law tail with an exponent that depends on the outlet size, the vibration intensity, and the load [I. Zuriguel et al., Sci. Rep. 4, 7324 (2014)]. Here we connect these previous works, demonstrating the importance of the maximum angle in the arch on the exponent of the breaking time distribution. Besides, we find that the acceleration needed to break an arch does not depend on the ramp rate of the applied acceleration, but it does depend on the outlet size above which the arch is formed. We also show that high frequencies of vibration reveal a change in the behavior of the arches that endure very long times. These arches have been identified as a subset with special geometrical features. Therefore, arches that cannot be broken by means of a given external excitation might exist.

Disentangling the Free-Fall Arch Paradox in Silo Discharge.

Several theoretical predictions of the mass flow rate of granular media discharged from a silo are based on the spontaneous development of a free-fall arch region, the existence of which is still controversial. In this Letter, we study experimentally and numerically the particle flow through an orifice placed at the bottom of 2D and 3D silos. The implementation of a coarse-grained technique allows a thorough description of all the kinetic and micromechanical properties of the particle flow in the outlet proximities. Though the free-fall arch does not exist as traditionally understood--a region above which particles have negligible velocity and below which particles fall solely under gravity action--we discover that the kinetic pressure displays a well-defined transition in a position that scales with the outlet size. This universal scaling explains why the free-fall arch picture has served as an approximation to describe the flow rate in the discharge of silos.

Granular segregation driven by particle interactions.

We report the results of an experimental study of particle-particle interactions in a horizontally shaken granular layer that undergoes a second order phase transition from a binary gas to a segregation liquid as the packing fraction C is increased. By focusing on the behavior of individual particles, the effect of C is studied on (1) the process of cluster formation, (2) cluster dynamics, and (3) cluster destruction. The outcomes indicate that the segregation is driven by two mechanisms: attraction between particles with the same properties and random motion with a characteristic length that is inversely proportional to C. All clusters investigated are found to be transient and the probability distribution functions of the separation times display a power law tail, indicating that the splitting probability decreases with time.

Flow and clogging of a sheep herd passing through a bottleneck.

We present an experimental study of a flock passing through a narrow door. Video monitoring of daily routines in a farm has enabled us to collect a sizable amount of data. By measuring the time lapse between the passage of consecutive animals, some features of the flow regime can be assessed. A quantitative definition of clogging is demonstrated based on the passage time statistics. These display broad tails, which can be fitted by power laws with a relatively large exponent. On the other hand, the distribution of burst sizes robustly evidences exponential behavior. Finally, borrowing concepts from granular physics and statistical mechanics, we evaluate the effect of increasing the door size and the performance of an obstacle placed in front of it. The success of these techniques opens new possibilities regarding their eventual extension to the management of human crowds.

Influence of the feeding mechanism on deposits of square particles.

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

Stress distribution of faceted particles in a silo after its partial discharge.

We present experimental and numerical results of the effect that a partial discharge has on the morphological and micro-mechanical properties of non-spherical, convex particles in a silo. The comparison of the particle orientation after filling the silo and its subsequent partial discharge reveals important shear-induced orientation, which affects stress propagation. For elongated particles, the flow induces an increase in the packing disorder which leads to a reduction of the vertical stress propagation developed during the deposit generated prior to the partial discharge. For square particles, the flow favors particle alignment with the lateral walls promoting a behavior opposite to the one of the elongated particles: vertical force transmission, parallel to gravity, is induced. Hence, for elongated particles the flow developed during the partial discharge of the silo leads to force saturation with depth whereas for squares the flow induces hindering of the force saturation observed during the silo filling.

Segregation pattern competition in a thin rotating drum.

Results are presented of an experimental investigation into patterned size segregation of binary granular mixtures in a thin rotating drum that is half full. It is observed that streaks of small particles are formed within regions of large ones where the integer number of streaks is fixed over a range of rotation rate of the drum. Different patterns form in adjacent parameter ranges and the dynamics associated with the exchange between neighboring states is analyzed using angular spatiotemporal diagrams. These help to reveal properties of the merging mechanism for streaks of small particles. We report experimental evidence that the merging of streaks is mediated by the movement of a surplus material in a direction opposite to that of the rotation of the drum. The excess material is distributed throughout the pattern and the extra streak eventually disappears.

Flow-rate fluctuations in the outpouring of grains from a two-dimensional silo.

We present experimental results obtained with a two-dimensional silo discharging under gravity through an orifice at the flat bottom. High-speed measurements provide enough time resolution to detect every single bead that goes out and this allows the measurement of the flow rate in short-time windows. Two different regimes are clearly distinguished: one for large orifices, which can be described by Gaussian fluctuations, and another for small orifices, in which extreme events appear. The frontier between those two regimes coincides with the outlet size below which jamming events are frequent. Moreover, it is shown that the power spectrum of the flow-rate oscillations is not dominated by any particular frequency.

Stress dip under a two-dimensional semipile of grains.

The origin of stress dip under the apex of a standard sandpile has stimulated significant debate within the scientific community. On the other hand, it could be argued that a semipile built against a vertical wall is of more practical interest since it serves as a model of dams, dykes, and embankments. There is surprisingly little information available for the stress distribution in this case. Here we show clear experimental evidence that the presence of the wall enhances the dip under a granular pile significantly. Our investigation provides insight into the influence of walls on the orientation of force chains and this appears to be key in enhancing the dip. Moreover, numerical simulations and experiments with different kinds of particles show that the vertical wall induces an alignment of isotropic particles.