Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions

José M. Pastor, Angel Garcimartín, Paula A. Gago, Juan P. Peralta, César Martín-Gómez, Luis M. Ferrer, Diego Maza, Daniel R. Parisi, Luis A. Pugnaloni, and Iker Zuriguel

Phys. Rev. E 92, 062817 – Published 15 December 2015

Abstract

The “faster-is-slower” (FIS) effect was first predicted by computer simulations of the egress of pedestrians through a narrow exit [D. Helbing, I. J. Farkas, and T. Vicsek, Nature (London) 407, 487 (2000)]. FIS refers to the finding that, under certain conditions, an excess of the individuals' vigor in the attempt to exit causes a decrease in the flow rate. In general, this effect is identified by the appearance of a minimum when plotting the total evacuation time of a crowd as a function of the pedestrian desired velocity. Here, we experimentally show that the FIS effect indeed occurs in three different systems of discrete particles flowing through a constriction: (a) humans evacuating a room, (b) a herd of sheep entering a barn, and (c) grains flowing out a 2D hopper over a vibrated incline. This finding suggests that FIS is a universal phenomenon for active matter passing through a narrowing.

Received 29 June 2015

DOI:https://doi.org/10.1103/PhysRevE.92.062817

Authors & Affiliations

José M. Pastor¹, Angel Garcimartín¹, Paula A. Gago^2,3, Juan P. Peralta², César Martín-Gómez⁴, Luis M. Ferrer⁵, Diego Maza¹, Daniel R. Parisi^3,6,*, Luis A. Pugnaloni^2,3, and Iker Zuriguel¹

¹Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
²Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, Av. 60 Esq. 124 S/N, 1900 La Plata, Argentina
³Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Rivadavia 1917 (1033), C. A. de Buenos Aires, Argentina
⁴Departamento de Construcción, Instalaciones y Estructuras, Escuela Técnica Superior de Arquitectura, Universidad de Navarra, E-31080 Pamplona, Spain
⁵Departamento de Patología Animal, Facultad de Veterinaria, Universidad de Zaragoza, Miguel Servet 177, 50013 Zaragoza, Spain
⁶Instituto Tecnológico de Buenos Aires, 25 de Mayo 444, (1002) C. A. de Buenos Aires, Argentina

^*dparisi@itba.edu.ar

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Vol. 92, Iss. 6 — December 2015

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Images

Figure 1
Experimental results of the egress of $95 \pm$ 3 pedestrians through a 69-cm-wide door. Upper left and middle: The top panels show snapshots of the room during the evacuation drill for a low (left) and high (middle) level of competitiveness (i.e., low and high driving force). The lower panels display the corresponding spatiotemporal diagrams. Lower left: Survival function of the time lapses $τ$ between two consecutive pedestrians for low (blue circles), medium (green triangles), and high (red crosses) competitiveness. The solid lines represent the fittings obtained with the Clauset-Shalizi-Newman method [22], and the corresponding power-law exponents are $α^{low} = 6.8 \pm 1$ ; $α^{medium} = 5.5 \pm 0.8$ , and $α^{high} = 4.2 \pm 0.4$ . Lower middle: mean $τ$ as a function of the driving force (i.e., competitiveness level). Error bars indicate 95% confidence intervals calculated by bootstrapping. Right upper and lower: Quantification of competitiveness. In the right upper panel is the maximum group speed when approaching the door at the beginning of the evacuation for each experimental run. The mean speed (dashed lines) and one standard deviation are $v_{d}^{low} = 0.410 \pm 0.071 m / s$ ; $v_{d}^{medium} = 0.497 \pm 0.077 m / s$ ; $v_{d}^{high} = 0.717 \pm 0.075 m / s$ . The right lower panel shows the sum of the number of times that any of the 128 pressure sensors at the doorposts registered a value above $30 {N / cm}^{2}$ [23]. The dashed horizontal lines correspond to the averages obtained for each competitiveness level.
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Figure 2
Experimental results of $75 \pm 10$ sheep passing through a 94-cm door. Left: snapshot of the herd for low competitiveness (corresponding to experiments at $T = 25 \pm 2^{\circ}$ ) and (middle), high competitiveness (corresponding to experiments at $T = 10 \pm 5^{\circ}$ ) and their associated spatiotemporal diagrams. Upper right: Average $τ$ as a function of the initial group speed (which quantifies the competitiveness level). Vertical error bars indicate 95% confidence intervals calculated by bootstrapping. Horizontal error bars are standard error. Lower right: Survival function of the time lapses $τ$ between the passage of two consecutive sheep for low (blue circles) and high (red crosses) competitiveness. The solid lines represent the fits obtained with the Clauset-Shalizi-Newman method [22], and the corresponding power-law exponents are $α^{low} = 4.5 \pm 0.3$ and $α^{high} = 3.3 \pm 0.2$ .
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Figure 3
Experimental quasi-2D hopper on a vibrated incline. Upper left: Sketch of the apparatus (side view on the left, and front view on the right). Upper right: Survival functions of the time lapses $τ$ between the passage of two consecutive glass beads for six different angles of inclination $θ$ . Arrows indicate the curve trends when increasing the component of the gravity $g sin (θ)$ parallel to the incline. Lower left: Mean $τ$ as a function of the component of the gravity parallel to the incline. Lower right: Same results as in lower-left panel after splitting the signal in two regimes: for the flowing part we consider only $τ < 0.05$ s (red triangles, left axis) and for the clogging episodes only $τ > 0.05$ s (black circles, right axis). Note the difference in the scale of both axes. In the lower panels, error bars or symbol size indicate 95% confidence intervals calculated by bootstrapping.
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