1
|
Masila DR, Mahore R. Emergence of intelligent collective motion in a group of agents with memory. CHAOS (WOODBURY, N.Y.) 2023; 33:093131. [PMID: 37729097 DOI: 10.1063/5.0148977] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 08/30/2023] [Indexed: 09/22/2023]
Abstract
Intelligent agents collect and process information from their dynamically evolving neighborhood to efficiently navigate through it. However, agent-level intelligence does not guarantee that at the level of a collective; a common example is the jamming we observe in traffic flows. In this study, we ask: how and when do the interactions between intelligent agents translate to desirable or intelligent collective outcomes? To explore this question, we choose a collective consisting of two kinds of agents with opposing desired directions of movement. Agents in this collective are minimally intelligent: they possess only a single facet of intelligence, viz., memory, where the agents remember how well they were able to travel in their desired directions and make up for their non-optimal past. We find that dynamics due to the agent's memory influences the collective, giving rise to diverse outcomes at the level of the group: from those that are undesirable to those that can be called "intelligent." When memory is short term, local rearrangement of agents leads to the formation of symmetrically jammed arrangements that take longer to unjam. However, when agents remember across longer time-scales, their dynamics become sensitive to small differences in their movement history. This gives rise to heterogeneity in the movement that causes agents to unjam more readily and form lanes.
Collapse
Affiliation(s)
- Danny Raj Masila
- Lab 10, Department of Chemical Engineering, IISc Bangalore, Bangalore 560012, Karnataka, India
| | - Rupesh Mahore
- Lab 10, Department of Chemical Engineering, IISc Bangalore, Bangalore 560012, Karnataka, India
| |
Collapse
|
2
|
Larrieu R, Moreau P, Graff C, Peyla P, Dupont A. Fish evacuate smoothly respecting a social bubble. Sci Rep 2023; 13:10414. [PMID: 37474571 PMCID: PMC10359245 DOI: 10.1038/s41598-023-36869-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 06/12/2023] [Indexed: 07/22/2023] Open
Abstract
Crowd movements are observed among different species and on different scales, from insects to mammals, as well as in non-cognitive systems, such as motile cells. When forced to escape through a narrow opening, most terrestrial animals behave like granular materials and clogging events decrease the efficiency of the evacuation. Here, we explore the evacuation behavior of macroscopic, aquatic agents, neon fish, and challenge their gregarious behavior by forcing the school through a constricted passage. Using a statistical analysis method developed for granular matter and applied to crowd evacuation, our results clearly show that, unlike crowds of people or herds of sheep, no clogging occurs at the bottleneck. The fish do not collide and wait for a minimum waiting time between two successive exits, while respecting a social distance. When the constriction becomes similar to or smaller than their social distance, the individual domains defined by this cognitive distance are deformed and fish density increases. We show that the current of escaping fish behaves like a set of deformable 2D-bubbles, their 2D domain, passing through a constriction. Schools of fish show that, by respecting social rules, a crowd of individuals can evacuate without clogging, even in an emergency situation.
Collapse
Affiliation(s)
- Renaud Larrieu
- University Grenoble Alpes, CNRS, LIPhy, F-38000, Grenoble, France
| | - Philippe Moreau
- University Grenoble Alpes, CNRS, LIPhy, F-38000, Grenoble, France
| | - Christian Graff
- University Grenoble Alpes, CNRS, LPNC, F-38000, Grenoble, France
| | - Philippe Peyla
- University Grenoble Alpes, CNRS, LIPhy, F-38000, Grenoble, France
| | - Aurélie Dupont
- University Grenoble Alpes, CNRS, LIPhy, F-38000, Grenoble, France.
| |
Collapse
|
3
|
Parisi DR, Wiebke LE, Mandl JN, Textor J. Flow rate resonance of actively deforming particles. Sci Rep 2023; 13:9455. [PMID: 37301896 DOI: 10.1038/s41598-023-36182-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Accepted: 05/29/2023] [Indexed: 06/12/2023] Open
Abstract
Lymphoid organs are unusual multicellular tissues: they are densely packed, but the lymphocytes trafficking through them are actively moving. We hypothesize that the intriguing ability of lymphocytes to avoid jamming and clogging is in part attributable to the dynamic shape changes that cells undergo when they move. In this work, we test this hypothesis by investigating an idealized system, namely, the flow of self-propelled, oscillating particles passing through a narrow constriction in two dimensions (2D), using numerical simulations. We found that deformation allows particles with these properties to flow through a narrow constriction in conditions when non-deformable particles would not be able to do so. Such a flowing state requires the amplitude and frequency of oscillations to exceed threshold values. Moreover, a resonance leading to the maximum flow rate was found when the oscillation frequency matched the natural frequency of the particle related to its elastic stiffness. To our knowledge, this phenomenon has not been described previously. Our findings could have important implications for understanding and controlling flow in a variety of systems in addition to lymphoid organs, such as granular flows subjected to vibration.
Collapse
Affiliation(s)
- Daniel R Parisi
- Instituto Tecnológico de Buenos Aires (ITBA), CONICET, C.A. de Buenos Aires, Argentina.
| | - Lucas E Wiebke
- Instituto Tecnológico de Buenos Aires (ITBA), C.A. de Buenos Aires, Argentina
| | - Judith N Mandl
- Department of Physiology and McGill Research Centre on Complex Traits, McGill University, Montreal, Canada
| | - Johannes Textor
- Data Science group, Institute for Computing and Information Sciences, Radboud University, Nijmegen, The Netherlands
| |
Collapse
|
4
|
Echeverría-Huarte I, Shi Z, Garcimartín A, Zuriguel I. Pedestrian bottleneck flow when keeping a prescribed physical distance. Phys Rev E 2022; 106:044302. [PMID: 36397559 DOI: 10.1103/physreve.106.044302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 09/26/2022] [Indexed: 06/16/2023]
Abstract
We present experimental results of pedestrian evacuations through a narrow door under a prescribed safety distancing of either 1.5 or 2 meters. In this situation, flow rate augments with pedestrian velocity due to a complete absence of flow interruptions or clogs. Accordingly, the evacuation improves when the prescribed physical distance is reduced, as this implies shortening the time lapses between the exit of consecutive pedestrians. In addition, the analysis of pedestrian trajectories reveals that the distance to the first neighbor in the evacuation process is rather similar to the one obtained when pedestrians were just roaming within the arena, hence suggesting that this magnitude depends more on the crowd state (desired speed, prescribed safety distance, etc.) than on the geometry where the pedestrian flow takes place. Also, an important difference in pedestrian behavior is observed when people are asked to walk at different speeds: whereas slow pedestrians evidence a clear preference for stop-and-go motion, fast walkers display detouring and stop-and-go behavior roughly in the same proportion.
Collapse
Affiliation(s)
- Iñaki Echeverría-Huarte
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Zhigang Shi
- State Key Laboratory of Fire Science, University of science and technology of China, 230026, Hefei, China
| | - Angel Garcimartín
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Iker Zuriguel
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| |
Collapse
|
5
|
Hou H, Wang L. Measuring Dynamics in Evacuation Behaviour with Deep Learning. ENTROPY 2022; 24:e24020198. [PMID: 35205493 PMCID: PMC8871226 DOI: 10.3390/e24020198] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Revised: 01/19/2022] [Accepted: 01/25/2022] [Indexed: 02/04/2023]
Abstract
Bounded rationality is one crucial component in human behaviours. It plays a key role in the typical collective behaviour of evacuation, in which heterogeneous information can lead to deviations from optimal choices. In this study, we propose a framework of deep learning to extract a key dynamical parameter that drives crowd evacuation behaviour in a cellular automaton (CA) model. On simulation data sets of a replica dynamic CA model, trained deep convolution neural networks (CNNs) can accurately predict dynamics from multiple frames of images. The dynamical parameter could be regarded as a factor describing the optimality of path-choosing decisions in evacuation behaviour. In addition, it should be noted that the performance of this method is robust to incomplete images, in which the information loss caused by cutting images does not hinder the feasibility of the method. Moreover, this framework provides us with a platform to quantitatively measure the optimal strategy in evacuation, and this approach can be extended to other well-designed crowd behaviour experiments.
Collapse
Affiliation(s)
- Huaidian Hou
- The Haverford School, 450 Lancaster Avenue, Haverford, PA 19010, USA;
| | - Lingxiao Wang
- Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Germany
- Institute of Physics, Goethe-University Frankfurt, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany
- Correspondence:
| |
Collapse
|
6
|
Discharge of vibrated granular silo: A grain scale approach. POWDER TECHNOL 2022. [DOI: 10.1016/j.powtec.2021.11.042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
7
|
Gao GJJ, Yang FL, Holcomb MC, Blawzdziewicz J. Enhanced flow rate by the concentration mechanism of Tetris particles when discharged from a hopper with an obstacle. Phys Rev E 2021; 103:062904. [PMID: 34271757 DOI: 10.1103/physreve.103.062904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2020] [Accepted: 05/13/2021] [Indexed: 11/07/2022]
Abstract
We apply a holistic two-dimensional (2D) Tetris-like model, where particles move based on prescribed rules, to investigate the flow rate enhancement from a hopper. This phenomenon was originally reported in the literature as a feature of placing an obstacle at an optimal location near the exit of a hopper discharging athermal granular particles under gravity. We find that this phenomenon is limited to a system of sufficiently many particles. In addition to the waiting room effect, another mechanism able to explain and create the flow rate enhancement is the concentration mechanism of particles on their way to reaching the hopper exit after passing the obstacle. We elucidate the concentration mechanism by decomposing the flow rate into its constituent variables: the local area packing fraction ϕ_{l}^{E} and the averaged particle velocity v_{y}^{E} at the hopper exit. In comparison to the case without an obstacle, our results show that an optimally placed obstacle can create a net flow rate enhancement of relatively weakly driven particles, caused by the exit-bottleneck coupling if ϕ_{l}^{E}>ϕ_{o}^{c}, where ϕ_{o}^{c} is a characteristic area packing fraction marking a transition from fast to slow flow regimes of Tetris particles. Utilizing the concentration mechanism by artificially guiding particles into the central sparse space under the obstacle or narrowing the hopper exit angle under the obstacle, we can create a manmade flow rate peak of relatively strongly driven particles that initially exhibit no flow rate peak. Additionally, the enhanced flow rate can be maximized by an optimal obstacle shape, particle acceleration rate toward the hopper exit, or exit geometry of the hopper.
Collapse
Affiliation(s)
- Guo-Jie Jason Gao
- Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan
| | - Fu-Ling Yang
- Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan
| | - Michael C Holcomb
- Department of Physics and Geosciences, Angelo State University, San Angelo, Texas 76909-0904, USA
| | - Jerzy Blawzdziewicz
- Department of Physics and Astronomy, Texas Tech University, Lubbock, Texas 79409-1051, USA.,Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409-1021, USA
| |
Collapse
|
8
|
Yu QC, Zheng N, Shi QF. Clogging of granular materials in a horizontal hopper: Effect of outlet size, hopper angle, and driving velocity. Phys Rev E 2021; 103:052902. [PMID: 34134195 DOI: 10.1103/physreve.103.052902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 04/29/2021] [Indexed: 06/12/2023]
Abstract
Due to the independence of the driving velocity and outlet size, it is possible to isolate geometrical and kinematic contributions to clogging in two-dimensional horizontal flow in a hopper driven by a conveyor belt. We experimentally investigate the geometric (outlet size and hopper angle) and kinematic effects (driving velocity) on the clogging in such a horizontal flow. Based on quantitative measurements and analysis of the avalanche size, blocking probability of a particle at the outlet, and other parameters, we show that the geometric factors can more effectively affect clogging. In addition, we find that the clogging tends to be alleviated with the increases of the driving velocity, suggesting a possible "fast is fast" behavior within a wide range of driving velocity. We borrow and modify a model from clogging in gravity-driven hoppers, which can accurately describe the shape of the clogging probability function in the conveyor belt driven flow, suggesting that these two systems could share some mechanisms for clogging.
Collapse
Affiliation(s)
- Quan-Chun Yu
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Ning Zheng
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Qing-Fan Shi
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| |
Collapse
|
9
|
Pascot A, Marouazi G, Kiesgen De Richter S. Discharge of a granular silo under mechanical vibrations. EPJ WEB OF CONFERENCES 2021. [DOI: 10.1051/epjconf/202124903037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this paper, we study the flow rate of model granular material in a silo under the influence of mechanical vibrations. Experimental measurements and discrete element simulations (DEM) are performed in a quasi-2D silo. The influence on the flow rate of the opening size and the vibration applied on the entire silo is studied. Two distinct regimes are evidenced, governed by the Froude number Fr and the relative frequency Ω. In the first regime, a decreased flow rate is observed when increasing the vibration intensity. This behavior is explained by the presence of reorganizations induced by the vibration, leading to a more homogeneous but also slower flow. In the second regime, an increased flow rate is evidenced when increasing the vibration intensity. We find this behavior comes from the intermittent nature of the flow, where the flow rate is directly controlled by the propagation of shock waves all along the silo.
Collapse
|
10
|
Pascot A, Gaudel N, Antonyuk S, Bianchin J, Kiesgen De Richter S. Influence of mechanical vibrations on quasi-2D silo discharge of spherical particles. Chem Eng Sci 2020. [DOI: 10.1016/j.ces.2020.115749] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
11
|
Echeverría-Huarte I, Zuriguel I, Hidalgo RC. Pedestrian evacuation simulation in the presence of an obstacle using self-propelled spherocylinders. Phys Rev E 2020; 102:012907. [PMID: 32795081 DOI: 10.1103/physreve.102.012907] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2020] [Accepted: 06/15/2020] [Indexed: 11/07/2022]
Abstract
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.
Collapse
Affiliation(s)
- I Echeverría-Huarte
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - I Zuriguel
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - R C Hidalgo
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| |
Collapse
|
12
|
Pradeep S, Hsiao LC. Contact criterion for suspensions of smooth and rough colloids. SOFT MATTER 2020; 16:4980-4989. [PMID: 32432605 DOI: 10.1039/d0sm00072h] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We report a procedure to obtain the search distance used to determine particle contact in dense suspensions of smooth and rough colloids. This method works by summing physically relevant length scales in an uncertainty analysis and does not require detailed quantification of the surface roughness. We suspend sterically stabilized, fluorescent poly(methyl methacrylate) colloids in a refractive index-matched solvent, squalene, in order to ensure hard sphere-like behavior. High speed centrifugation is used to pack smooth and rough colloids to their respective jamming points, φJ. The jammed suspensions are subsequently diluted with known volumes of solvent to φ < φJ. Structural parameters obtained from confocal laser scanning micrographs of the diluted colloidal suspensions are extrapolated to φJ to determine the mean contact number at jamming, 〈z〉J. Contact below jamming refers to nearest neighbors at a length scale below which the effects of hydrodynamic or geometric friction come into play. Sensitivity analyses show that a deviation of the search distance by 1% of the particle diameter results in 〈z〉 changing by up to 10%, with the error in contact number distribution being magnified in dense suspensions (φ > 0.50) due to an increased number of nearest neighbors in the first coordination shell.
Collapse
Affiliation(s)
- Shravan Pradeep
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC 27695, USA.
| | | |
Collapse
|
13
|
Sun D, Lu H, Cao J, Wu Y, Guo X, Gong X. Flow mechanisms and solid flow rate prediction of powders discharged from hoppers with an insert. POWDER TECHNOL 2020. [DOI: 10.1016/j.powtec.2020.03.053] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
|
14
|
Köster G, Lehmberg D, Kneidl A. Walking on stairs: Experiment and model. Phys Rev E 2019; 100:022310. [PMID: 31574684 DOI: 10.1103/physreve.100.022310] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Indexed: 11/07/2022]
Abstract
An increasing global population forces urban planners to construct buildings and infrastructure that is extremely deep and high. Elevators and escalators serve skyscrapers and tunnels, but in an emergency people still have to walk on stairs. Computer simulations can mitigate risks of escape situations. For these situations, pedestrian locomotion models need to match reality well. Motion on stairs, however, is not nearly as well understood as motion in the plane. Publications are scarce and some are contradictory. As a result, movement on stairs is usually modeled by slowing down pedestrians by a fixed factor. But is this justified? And what happens at intermediate landings? This contribution aims to clarify inconclusive results of previous research and provide new information to directly incorporate empirical results into a parsimonious computer model. The algorithms are freely available through an open-source framework. After outlining the shortcomings of existing approaches, we present three experiments, from which we derive requirements for the computer model. Reenacting computer experiments shows the extent to which our model meets our observations. We conclude with an applied example, simulating an evacuation of Germany's famous Neuschwanstein Castle.
Collapse
Affiliation(s)
- Gerta Köster
- Munich University of Applied Sciences, Lothstrasse 34, 80335 Munich, Germany
| | - Daniel Lehmberg
- Munich University of Applied Sciences, Lothstrasse 34, 80335 Munich, Germany
| | - Angelika Kneidl
- accu:rate Institute for Crowd Simulation, Rosental 5, 80331 Munich, Germany
| |
Collapse
|
15
|
Bain N, Bartolo D. Dynamic response and hydrodynamics of polarized crowds. Science 2019; 363:46-49. [PMID: 30606837 DOI: 10.1126/science.aat9891] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Revised: 07/21/2018] [Accepted: 11/09/2018] [Indexed: 11/02/2022]
Abstract
Modeling crowd motion is central to situations as diverse as risk prevention in mass events and visual effects rendering in the motion picture industry. The difficulty of performing quantitative measurements in model experiments has limited our ability to model pedestrian flows. We use tens of thousands of road-race participants in starting corrals to elucidate the flowing behavior of polarized crowds by probing its response to boundary motion. We establish that speed information propagates over system-spanning scales through polarized crowds, whereas orientational fluctuations are locally suppressed. Building on these observations, we lay out a hydrodynamic theory of polarized crowds and demonstrate its predictive power. We expect this description of human groups as active continua to provide quantitative guidelines for crowd management.
Collapse
Affiliation(s)
- Nicolas Bain
- Laboratoire de Physique, ENS de Lyon, Université de Lyon, Université Claude Bernard, CNRS, F-69342 Lyon, France.
| | - Denis Bartolo
- Laboratoire de Physique, ENS de Lyon, Université de Lyon, Université Claude Bernard, CNRS, F-69342 Lyon, France.
| |
Collapse
|
16
|
Barois T, Boudet JF, Lanchon N, Lintuvuori JS, Kellay H. Characterization and control of a bottleneck-induced traffic-jam transition for self-propelled particles in a track. Phys Rev E 2019; 99:052605. [PMID: 31212491 DOI: 10.1103/physreve.99.052605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Indexed: 06/09/2023]
Abstract
A collection of self-propelled elongated particles is circulating in a circular track. Due to the presence of a bottleneck, the flow transits to a congested state for a sufficient number of particles, even if the whole track is not saturated. Both experiments and simulations are used to identify the transition toward congestion. An intermediate regime of coexistence is characterized by intermittency between a free flow state and a jammed state. The range of the coexistence region is found to depend explicitly on fluctuating quantities such as the distribution of the escape times from a jam and the headway time distribution between free particles. Optimization strategies, such as the "slower is faster" effect, are tested in experiments and simulations, and an increase in the traffic performances is reported.
Collapse
Affiliation(s)
- Thomas Barois
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| | | | - Nicolas Lanchon
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| | | | - Hamid Kellay
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| |
Collapse
|
17
|
Ai BQ, Meng FH, He YL, Zhang XM. Flow and clogging of particles in shaking random obstacles. SOFT MATTER 2019; 15:3443-3450. [PMID: 30942807 DOI: 10.1039/c9sm00144a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Transport of three types of particles (passive particles, active particles, and polar particles) is investigated in a random obstacle array in the presence of a dc drift force. The obstacles are static or synchronously shake along the given direction. When the obstacles are static, the average velocity is a peaked function of the dc drift force (negative differential mobility) for low particle density, while the average velocity monotonically increases with the dc drift force (positive differential mobility) for high particle density. Under the same conditions, passive particles are most likely to pass through the obstacles, while polar particles are easily trapped by the obstacles. The polar alignment can strongly reduce the overall mobility of particles. When the obstacles shake along the given direction, the optimal shaking frequency or amplitude can maximize the average velocity. It is more effective to reduce clogging for the transverse shaking than that for the longitudinal shaking.
Collapse
Affiliation(s)
- Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
| | | | | | | |
Collapse
|
18
|
Nicolas A, Kuperman M, Ibañez S, Bouzat S, Appert-Rolland C. Mechanical response of dense pedestrian crowds to the crossing of intruders. Sci Rep 2019; 9:105. [PMID: 30643181 PMCID: PMC6331639 DOI: 10.1038/s41598-018-36711-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2018] [Accepted: 11/23/2018] [Indexed: 12/04/2022] Open
Abstract
The increasing number of mass events involving large crowds calls for a better understanding of the dynamics of dense crowds. Inquiring into the possibility of a mechanical description of these dynamics, we experimentally study the crossing of dense static crowds by a cylindrical intruder, a mechanical test which is classical for granular matter. The analysis of our experiments reveals robust features in the crowds' response, comprising both similarities and discrepancies with the response of granular media. Common features include the presence of a depleted region behind the intruder and the short-range character of the perturbation. On the other hand, unlike grains, pedestrians anticipate the intruder's passage by moving much before contact and their displacements are mostly lateral, hence not aligned with the forces exerted by the intruder. Similar conclusions are reached when the intruder is not a cylinder, but a single crossing pedestrian. Thus, our work shows that pedestrian interactions even at high densities (3 to 6 ped/m2) do not reduce to mechanical ones. More generally, the avoidance strategies evidenced by our findings question the incautious use of force models for dense crowds.
Collapse
Affiliation(s)
- Alexandre Nicolas
- LPTMS UMR 8626, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France.
| | - Marcelo Kuperman
- Consejo Nacional de Investigaciones Cientficas y Técnicas, Centro Atómico Bariloche (CNEA) and Instituto, Balseiro, R8400AGP, Bariloche, Argentina
| | - Santiago Ibañez
- Consejo Nacional de Investigaciones Cientficas y Técnicas, Centro Atómico Bariloche (CNEA) and Instituto, Balseiro, R8400AGP, Bariloche, Argentina
- Universidad Nacional de Río Negro, Sede Andina, 8400, Bariloche, Argentina
| | - Sebastián Bouzat
- Consejo Nacional de Investigaciones Cientficas y Técnicas, Centro Atómico Bariloche (CNEA) and Instituto, Balseiro, R8400AGP, Bariloche, Argentina
| | - Cécile Appert-Rolland
- LPT UMR 8627, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
| |
Collapse
|
19
|
Fullard LA, Breard ECP, Davies CE, Godfrey AJR, Fukuoka M, Wade A, Dufek J, Lube G. The dynamics of granular flow from a silo with two symmetric openings. Proc Math Phys Eng Sci 2019; 475:20180462. [PMID: 30760953 DOI: 10.1098/rspa.2018.0462] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Accepted: 11/29/2018] [Indexed: 12/30/2022] Open
Abstract
The dynamics of granular flow in a rectangular silo with two symmetrically placed exit openings is investigated using particle image velocimetry (PIV), flow rate measurements and discrete element modelling (DEM). The flow of mustard seeds in a Perspex silo is recorded using a high-speed camera and the resulting image frames are analysed using PIV to obtain velocity, velocity divergence and shear rate plots. A change in flow structure is observed as the distance L between the two openings is varied. The mass flow rate is shown to be at a maximum at zero opening separation, decreasing as L is increased; it then reaches a minimum before rising to an equilibrium rate close to two times that of an isolated (non-interacting) opening. The flow rate experiment is repeated using amaranth and screened sand and similar behaviour is observed. Although this result is in contrast with some recent DEM and physical experiments in silo systems, this effect has been reported in an analogous system: the evacuation of pedestrians from a room through two doors. Our experimental results are replicated using DEM and we show that inter-particle friction controls the flow rate behaviour and explains the discrepancies in the literature results.
Collapse
Affiliation(s)
- L A Fullard
- Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - E C P Breard
- Department of Earth Sciences, University of Oregon, Eugene, OR, USA
| | - C E Davies
- School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand
| | - A J R Godfrey
- Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand
| | - M Fukuoka
- School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand
| | - A Wade
- School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand
| | - J Dufek
- Department of Earth Sciences, University of Oregon, Eugene, OR, USA
| | - G Lube
- Volcanic Risk Solutions, Massey University, Palmerston North, New Zealand
| |
Collapse
|
20
|
Reichhardt C, Reichhardt CJO. Controlled Fluidization, Mobility, and Clogging in Obstacle Arrays Using Periodic Perturbations. PHYSICAL REVIEW LETTERS 2018; 121:068001. [PMID: 30141675 DOI: 10.1103/physrevlett.121.068001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Indexed: 06/08/2023]
Abstract
We show that the clogging susceptibility and flow of particles moving through a random obstacle array can be controlled with a transverse or longitudinal ac drive. The flow rate can vary over several orders of magnitude, and we find both an optimal frequency and an optimal amplitude of driving that maximizes the flow. For dense arrays, at low ac frequencies, a heterogeneous creeping clogged phase appears in which rearrangements between different clogged configurations occur. At intermediate frequencies, a high-mobility fluidized state forms, and, at high frequencies, the system reenters a heterogeneous frozen clogged state. These results provide a technique for optimizing flow through heterogeneous media that could also serve as the basis for a particle separation method.
Collapse
Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
21
|
Vamsi Krishna Reddy A, Kumar S, Anki Reddy K, Talbot J. Granular silo flow of inelastic dumbbells: Clogging and its reduction. Phys Rev E 2018; 98:022904. [PMID: 30253544 DOI: 10.1103/physreve.98.022904] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Indexed: 06/08/2023]
Abstract
We study the discharge of inelastic, two-dimensional dumbbells through an orifice in the bottom wall of a silo using discrete element method (DEM) simulations. As with spherical particles, clogging may occur due to the formation of arches of particles around the orifice. The clogging probability decreases with increasing orifice width in both cases. For a given width, however, the clogging probability is much higher for the nonspherical particles due to their arbitrary orientations and the possibility of geometrical interlocking. We also examine the effect of placing a fixed, circular obstacle above the orifice. The clogging probability depends strongly on the vertical and lateral position of the obstacle, as well as its size. By suitably placing the obstacle the clogging probability can be significantly reduced compared to a system with no obstacle. We attempt to elucidate the clogging reduction mechanism by examining the packing fraction, granular temperature, and velocity distributions of the particles in the vicinity of the orifice.
Collapse
Affiliation(s)
- A Vamsi Krishna Reddy
- Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - Sonu Kumar
- Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - K Anki Reddy
- Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India
| | - Julian Talbot
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| |
Collapse
|
22
|
Parisi DR, Cruz Hidalgo R, Zuriguel I. Active particles with desired orientation flowing through a bottleneck. Sci Rep 2018; 8:9133. [PMID: 29904139 PMCID: PMC6002477 DOI: 10.1038/s41598-018-27478-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Accepted: 06/01/2018] [Indexed: 11/22/2022] Open
Abstract
We report extensive numerical simulations of the flow of anisotropic self-propelled particles through a constriction. In particular, we explore the role of the particles’ desired orientation with respect to the moving direction on the system flowability. We observe that when particles propel along the direction of their long axis (longitudinal orientation) the flow-rate notably reduces compared with the case of propulsion along the short axis (transversal orientation). And this is so even when the effective section (measured as the number of particles that are necessary to span the whole outlet) is larger for the case of longitudinal propulsion. This counterintuitive result is explained in terms of the formation of clogging structures at the outlet, which are revealed to have higher stability when the particles align along the long axis. This generic result might be applied to many different systems flowing through bottlenecks such as microbial populations or different kind of cells. Indeed, it has already a straightforward connection with recent results of pedestrian (which self-propel transversally oriented) and mice or sheep (which self-propel longitudinally oriented).
Collapse
Affiliation(s)
- Daniel R Parisi
- Instituto Tecnológico de Buenos Aires, CONICET, Lavardén 315, 1437 C, A. de Buenos Aires, Argentina.
| | - Raúl Cruz Hidalgo
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080, Pamplona, Spain
| | - Iker Zuriguel
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080, Pamplona, Spain
| |
Collapse
|
23
|
Nicolas A, Garcimartín Á, Zuriguel I. Trap Model for Clogging and Unclogging in Granular Hopper Flows. PHYSICAL REVIEW LETTERS 2018; 120:198002. [PMID: 29799232 DOI: 10.1103/physrevlett.120.198002] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Indexed: 06/08/2023]
Abstract
Granular flows through narrow outlets may be interrupted by the formation of arches or vaults that clog the exit. These clogs may be destroyed by vibrations. A feature which remains elusive is the broad distribution p(τ) of clog lifetimes τ measured under constant vibrations. Here, we propose a simple model for arch breaking, in which the vibrations are formally equivalent to thermal fluctuations in a Langevin equation; the rupture of an arch corresponds to the escape from an energy trap. We infer the distribution of trap depths from experiments made in two-dimensional hoppers. Using this distribution, we show that the model captures the empirically observed heavy tails in p(τ). These heavy tails flatten at large τ, consistently with experimental observations under weak vibrations. But, here, we find that this flattening is systematic, which casts doubt on the ability of gentle vibrations to restore a finite outflow forever. The trap model also replicates recent results on the effect of increasing gravity on the statistics of clog formation in a static silo. Therefore, the proposed framework points to a common physical underpinning to the processes of clogging and unclogging, despite their different statistics.
Collapse
Affiliation(s)
- Alexandre Nicolas
- LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Ángel Garcimartín
- Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, 31080 Pamplona, Spain
| | - Iker Zuriguel
- Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, 31080 Pamplona, Spain
| |
Collapse
|
24
|
Hidalgo RC, Goñi-Arana A, Hernández-Puerta A, Pagonabarraga I. Flow of colloidal suspensions through small orifices. Phys Rev E 2018; 97:012611. [PMID: 29448456 DOI: 10.1103/physreve.97.012611] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Indexed: 06/08/2023]
Abstract
In this work, we numerically study a dense colloidal suspension flowing through a small outlet driven by a pressure drop using lattice-Boltzmann methods. This system shows intermittent flow regimes that precede clogging events. Several pieces of evidence suggest that the temperature controls the dynamic state of the system when the driving force and the aperture size are fixed. When the temperature is low, the suspension's flow can be interrupted during long time periods, which can be even two orders of magnitude larger than the system's characteristic time (Stokes). We also find that strong thermal noise does not allow the formation of stable aggregate structures avoiding extreme clogging events, but, at the same time, it randomizes the particle trajectories and disturbs the advective particle flow through the aperture. Moreover, examining the particle velocity statistics, we obtain that in the plane normal to the pressure drop the colloids always move as free particles regardless of the temperature value. In the pressure drop direction, at high temperature the colloids experience a simple balance between advective and diffusive transport, but at low temperature the nature of the flow is much more complex, correlating with the occurrence of very long clogging events.
Collapse
Affiliation(s)
- R C Hidalgo
- Departamento de Física y Matemática Aplicada, Facultad de Ciencias, and Universidad de Navarra, 31080 Pamplona, Spain
| | - A Goñi-Arana
- Departamento de Ingeniería Biomédica (TECNUN), Universidad de Navarra, 20009 San Sebastian, Spain
| | - A Hernández-Puerta
- Departamento de Ingeniería Biomédica (TECNUN), Universidad de Navarra, 20009 San Sebastian, Spain
| | - I Pagonabarraga
- Departament de Física Fonamental, Carrer Martí i Franqués 1, Universitat de Barcelona, 08028 Barcelona, Spain
| |
Collapse
|
25
|
Patterson GA, Fierens PI, Sangiuliano Jimka F, König PG, Garcimartín A, Zuriguel I, Pugnaloni LA, Parisi DR. Clogging Transition of Vibration-Driven Vehicles Passing through Constrictions. PHYSICAL REVIEW LETTERS 2017; 119:248301. [PMID: 29286724 DOI: 10.1103/physrevlett.119.248301] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2017] [Indexed: 06/07/2023]
Abstract
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.
Collapse
Affiliation(s)
- G A Patterson
- Instituto Tecnológico de Buenos Aires, CONICET, Lavardén 315, 1437 C. A. de Buenos Aires, Argentina
| | - P I Fierens
- Instituto Tecnológico de Buenos Aires, CONICET, Lavardén 315, 1437 C. A. de Buenos Aires, Argentina
| | - F Sangiuliano Jimka
- Instituto Tecnológico de Buenos Aires, Lavardén 315, 1437 C. A. de Buenos Aires, Argentina
| | - P G König
- Instituto Tecnológico de Buenos Aires, Lavardén 315, 1437 C. A. de Buenos Aires, Argentina
| | - A Garcimartín
- Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, Pamplona 31080, Spain
| | - I Zuriguel
- Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, Pamplona 31080, Spain
| | - L A Pugnaloni
- Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, CONICET, Avenida 60 Esq. 124, 1900 La Plata, Argentina
| | - D R Parisi
- Instituto Tecnológico de Buenos Aires, CONICET, Lavardén 315, 1437 C. A. de Buenos Aires, Argentina
| |
Collapse
|
26
|
Hong X, Kohne M, Morrell M, Wang H, Weeks ER. Clogging of soft particles in two-dimensional hoppers. Phys Rev E 2017; 96:062605. [PMID: 29347308 DOI: 10.1103/physreve.96.062605] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Indexed: 06/07/2023]
Abstract
Using experiments and simulations, we study the flow of soft particles through quasi-two-dimensional hoppers. The first experiment uses oil-in-water emulsion droplets in a thin sample chamber. Due to surfactants coating the droplets, they easily slide past each other, approximating soft frictionless disks. For these droplets, clogging at the hopper exit requires a narrow hopper opening only slightly larger than the droplet diameter. The second experiment uses soft hydrogel particles in a thin sample chamber, where we vary gravity by changing the tilt angle of the chamber. For reduced gravity, clogging becomes easier and can occur for larger hopper openings. Our simulations mimic the emulsion experiments and demonstrate that softness is a key factor controlling clogging: with stiffer particles or a weaker gravitational force, clogging is easier. The fractional amount a single particle is deformed under its own weight is a useful parameter measuring particle softness. Data from the simulation and hydrogel experiments collapse when compared using this parameter. Our results suggest that prior studies using hard particles were in a limit where the role of softness is negligible, which causes clogging to occur with significantly larger openings.
Collapse
Affiliation(s)
- Xia Hong
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Meghan Kohne
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Mia Morrell
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Haoran Wang
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| |
Collapse
|
27
|
Sticco IM, Cornes FE, Frank GA, Dorso CO. Beyond the faster-is-slower effect. Phys Rev E 2017; 96:052303. [PMID: 29347791 DOI: 10.1103/physreve.96.052303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Indexed: 06/07/2023]
Abstract
The "faster-is-slower" effect arises when crowded people push each other to escape through an exit during an emergency situation. As individuals push harder, a statistical slowing down in the evacuation time can be achieved. The slowing down is caused by the presence of small groups of pedestrians (say, a small human cluster) that temporarily block the way out when trying to leave the room. The pressure on the pedestrians belonging to this blocking cluster increases for increasing anxiety levels and/or a larger number of individuals trying to leave the room through the same door. Our investigation shows, however, that very high pressures alter the dynamics in the blocking cluster and, thus, change the statistics of the time delays along the escaping process. A reduction in the long lasting delays can be acknowledged, while the overall evacuation performance improves. We present results on this phenomenon taking place beyond the faster-is-slower regime.
Collapse
Affiliation(s)
- I M Sticco
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - F E Cornes
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - G A Frank
- Unidad de Investigación y Desarrollo de las Ingenierías, Universidad Tecnológica Nacional, Facultad Regional Buenos Aires, Av. Medrano 951, 1179 Buenos Aires, Argentina
| | - C O Dorso
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Física de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| |
Collapse
|
28
|
Main factor causing "faster-is-slower" phenomenon during evacuation: rodent experiment and simulation. Sci Rep 2017; 7:13724. [PMID: 29057948 PMCID: PMC5651978 DOI: 10.1038/s41598-017-14007-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Accepted: 10/04/2017] [Indexed: 11/25/2022] Open
Abstract
Understanding crowd flow at bottlenecks is important for preventing accidents in emergencies. In this research, a crowd evacuation passing through a narrow exit connected with guide-walls is analysed using the discrete element method based on physical and psychological modelling in parallel with empirical rodent research. Results of rodent experiment and simulation demonstrate the faster-is-slower (FIS) effect, which is a well-known phenomenon in pedestrian dynamics. As the angle of the guide-walls increases, agents rapidly evacuate the room even though they have low velocity. The increase in this angle causes agents to form lanes. It is validated that ordered agents evacuate expeditiously with relatively low velocity despite expectations to the contrary. The extracted experimental and simulation data strongly suggest that the agents’ standard deviation of velocity can be a key factor causing the FIS effect. It is found that the FIS effect can be eliminated by controlling the standard deviation.
Collapse
|
29
|
Seitz MJ, Bode NWF, Köster G. How cognitive heuristics can explain social interactions in spatial movement. J R Soc Interface 2017; 13:rsif.2016.0439. [PMID: 27581483 DOI: 10.1098/rsif.2016.0439] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2016] [Accepted: 08/03/2016] [Indexed: 11/12/2022] Open
Abstract
The movement of pedestrian crowds is a paradigmatic example of collective motion. The precise nature of individual-level behaviours underlying crowd movements has been subject to a lively debate. Here, we propose that pedestrians follow simple heuristics rooted in cognitive psychology, such as 'stop if another step would lead to a collision' or 'follow the person in front'. In other words, our paradigm explicitly models individual-level behaviour as a series of discrete decisions. We show that our cognitive heuristics produce realistic emergent crowd phenomena, such as lane formation and queuing behaviour. Based on our results, we suggest that pedestrians follow different cognitive heuristics that are selected depending on the context. This differs from the widely used approach of capturing changes in behaviour via model parameters and leads to testable hypotheses on changes in crowd behaviour for different motivation levels. For example, we expect that rushed individuals more often evade to the side and thus display distinct emergent queue formations in front of a bottleneck. Our heuristics can be ranked according to the cognitive effort that is required to follow them. Therefore, our model establishes a direct link between behavioural responses and cognitive effort and thus facilitates a novel perspective on collective behaviour.
Collapse
Affiliation(s)
- Michael J Seitz
- Department of Computer Science and Mathematics, Munich University of Applied Sciences, 80335 Munich, Germany Department of Informatics, Technische Universität München, 85748 Garching, Germany
| | - Nikolai W F Bode
- Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UB, UK
| | - Gerta Köster
- Department of Computer Science and Mathematics, Munich University of Applied Sciences, 80335 Munich, Germany
| |
Collapse
|
30
|
Pedestrian collective motion in competitive room evacuation. Sci Rep 2017; 7:10792. [PMID: 28883459 PMCID: PMC5589747 DOI: 10.1038/s41598-017-11197-x] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2016] [Accepted: 08/17/2017] [Indexed: 11/30/2022] Open
Abstract
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.
Collapse
|
31
|
Shahhoseini Z, Sarvi M. Collective movements of pedestrians: How we can learn from simple experiments with non-human (ant) crowds. PLoS One 2017; 12:e0182913. [PMID: 28854221 PMCID: PMC5576663 DOI: 10.1371/journal.pone.0182913] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Accepted: 07/26/2017] [Indexed: 11/27/2022] Open
Abstract
Introduction Understanding collective behavior of moving organisms and how interactions between individuals govern their collective motion has triggered a growing number of studies. Similarities have been observed between the scale-free behavioral aspects of various systems (i.e. groups of fish, ants, and mammals). Investigation of such connections between the collective motion of non-human organisms and that of humans however, has been relatively scarce. The problem demands for particular attention in the context of emergency escape motion for which innovative experimentation with panicking ants has been recently employed as a relatively inexpensive and non-invasive approach. However, little empirical evidence has been provided as to the relevance and reliability of this approach as a model of human behaviour. Methods This study explores pioneer experiments of emergency escape to tackle this question and to connect two forms of experimental observations that investigate the collective movement at macroscopic level. A large number of experiments with human and panicking ants are conducted representing the escape behavior of these systems in crowded spaces. The experiments share similar architectural structures in which two streams of crowd flow merge with one another. Measures such as discharge flow rates and the probability distribution of passage headways are extracted and compared between the two systems. Findings Our findings displayed an unexpected degree of similarity between the collective patterns emerged from both observation types, particularly based on aggregate measures. Experiments with ants and humans commonly indicated how significantly the efficiency of motion and the rate of discharge depend on the architectural design of the movement environment. Practical applications Our findings contribute to the accumulation of evidence needed to identify the boarders of applicability of experimentation with crowds of non-human entities as models of human collective motion as well as the level of measurements (i.e. macroscopic or microscopic) and the type of contexts at which reliable inferences can be drawn. This particularly has implications in the context of experimenting evacuation behaviour for which recruiting human subjects may face ethical restrictions. The findings, at minimum, offer promise as to the potential benefit of piloting such experiments with non-human crowds, thereby forming better-informed hypotheses.
Collapse
Affiliation(s)
- Zahra Shahhoseini
- Centre for Disaster Management and Public Safety, School of Engineering, The University of Melbourne, Australia
- * E-mail:
| | - Majid Sarvi
- Centre for Disaster Management and Public Safety, School of Engineering, The University of Melbourne, Australia
| |
Collapse
|
32
|
Dwi Wibowo RM, Perdanakusuma DS, Tanggo EH. MECHANISM OF APOPTOSIS INHIBITION TO SQUAMOUS CELL CARCINOMA OF ORAL CANCER IN CISPLATIN TREATMENT. FOLIA MEDICA INDONESIANA 2017. [DOI: 10.20473/fmi.v53i1.5482] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
This study was to approve the increased secretion of Hsp 70, DNA damage, and inhibitor apoptosis protein in cisplatin therapy which influence apoptosis of oral cancer cell and to know mechanism of molecular pathology. This study was an in vitro experimental laboratory using Randomized Block Design. Cell culture of oral cancer divided from cisplatin resistance cancer cell and cancer cell never induce cisplatin. Two group of cancer cell would be given cisplatin therapy. Secretion of Hsp 70, DNA damage, Inhibitor of apoptosis protein, and apoptosis index would be examined. Cisplatin resistance cancer cell group showed lower apoptosis than never induce cisplatin cancer cell. Elevated secretion of Hsp 70 in cisplatin therapy group (p= 0.000, b=0.881). Lower secretion of DNA damage protein in cisplatin resistance cancer cell and it was not going apoptosis. In path regression analysis, cisplatin was significans through IAP pathway (p=0.000, b=0.726) to apoptosis. All type of cell cultures were also significans through IAP pathway (p=0.000, b=0.496) to apoptosis. Elevated IAP secretion influenced apoptosis (b= 1.000). In conclusion, cisplatin used IAP pathway to apoptosis. All type of cell cultures also used IAP pathway to apoptosis. Cisplatin resistance cell culture had stronger effect to IAP and IAP increased inhibition to apoptosis.
Collapse
|
33
|
Zuriguel I, Janda Á, Arévalo R, Maza D, Garcimartín Á. Clogging and unclogging of many-particle systems passing through a bottleneck. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714001002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
34
|
Guerrero B, Lozano C, Zuriguel I, Garcimartín A. Dynamics of breaking arches under a constant vibration. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714003016] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
35
|
Hidalgo R, Rubio-Largo S, Alonso-Marroquin F, Weinhart T. Non-spherical granular flows down inclined chutes. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714003007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
36
|
Sieben A, Schumann J, Seyfried A. Collective phenomena in crowds-Where pedestrian dynamics need social psychology. PLoS One 2017; 12:e0177328. [PMID: 28591142 PMCID: PMC5462364 DOI: 10.1371/journal.pone.0177328] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Accepted: 04/09/2017] [Indexed: 11/18/2022] Open
Abstract
This article is on collective phenomena in pedestrian dynamics during the assembling and dispersal of gatherings. To date pedestrian dynamics have been primarily studied in the natural and engineering sciences. Pedestrians are analyzed and modeled as driven particles revealing self-organizing phenomena and complex transport characteristics. However, pedestrians in crowds also behave as living beings according to stimulus-response mechanisms or act as human subjects on the basis of social norms, social identities or strategies. To show where pedestrian dynamics need social psychology in addition to the natural sciences we propose the application of three categories-phenomena, behavior and action. They permit a clear discrimination between situations in which minimal models from the natural sciences are appropriate and those in which sociological and psychological concepts are needed. To demonstrate the necessity of this framework, an experiment in which a large group of people (n = 270) enters a concert hall through two different spatial barrier structures is analyzed. These two structures correspond to everyday situations such as boarding trains and access to immigration desks. Methods from the natural and social sciences are applied. Firstly, physical measurements show the influence of the spatial structure on the dynamics of the entrance procedure. Density, waiting time and speed of progress show large variations. Secondly, a questionnaire study (n = 60) reveals how people perceive and evaluate these entrance situations. Markedly different expectations, social norms and strategies are associated with the two spatial structures. The results from the questionnaire study do not always conform to objective physical measures, indicating the limitations of models which are based on objective physical measures alone and which neglect subjective perspectives.
Collapse
Affiliation(s)
- Anna Sieben
- Chair of Social Theory and Social Psychology, Ruhr-Universität Bochum, Bochum, Germany
| | - Jette Schumann
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - Armin Seyfried
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
- School of Architecture and Civil Engineering, University of Wuppertal, Wuppertal, Germany
- * E-mail:
| |
Collapse
|
37
|
Abstract
Grains exiting an underwater silo exhibit an unexpected surge in discharge rate as they empty. This contrasts with the constant flow rate of dry granular hoppers and the decreasing flow rate of pure liquids. Here we find that this surge depends on hopper diameter and happens also in air. The surge can be turned off by fixing the rate of fluid flow through the granular packing. With no flow control, dye injected on top of the packing gets drawn into the grains. We conclude that the surge is caused by a self-generated pumping of fluid through the packing. The effect is modelled via a driving pressure set by the exit speed of the grains. This highlights a surprising and unrecognized role that interstitial fluid plays in setting the discharge rate, and perhaps in controlling clog formation, for granular hoppers whether in air or under water. Hourglasses measure time because the discharge rate of dry sand is constant. Here Koivisto et al. show that when such a system contains water there is a surge in discharge because the fluid drains faster than the grains, which might help us understand the transport of grains in silos.
Collapse
|
38
|
Hidalgo RC, Parisi DR, Zuriguel I. Simulating competitive egress of noncircular pedestrians. Phys Rev E 2017; 95:042319. [PMID: 28505803 DOI: 10.1103/physreve.95.042319] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Indexed: 06/07/2023]
Abstract
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.
Collapse
Affiliation(s)
- R C Hidalgo
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - D R Parisi
- Instituto Tecnológico de Buenos Aires, Lavarden 389, (C1437FBG) C. A. de Buenos Aires, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas, Godoy Cruz 2290 (C1425FQB), C. A. de Buenos Aires, Argentina
| | - I Zuriguel
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| |
Collapse
|
39
|
Zuriguel I, Olivares J, Pastor JM, Martín-Gómez C, Ferrer LM, Ramos JJ, Garcimartín A. Effect of obstacle position in the flow of sheep through a narrow door. Phys Rev E 2016; 94:032302. [PMID: 27739797 DOI: 10.1103/physreve.94.032302] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2016] [Indexed: 06/06/2023]
Abstract
In a recent work [Phys. Rev. E 91, 022808 (2015)PLEEE81539-375510.1103/PhysRevE.91.022808] it was reported that placing an obstacle in front of a gate has a beneficial effect in the flow of sheep through it. Here, we extend such results by implementing three different obstacle positions. We have observed that the flow is improved in two cases, while it worsens in the other one; the last instance happens when the obstacle is too close to the door. In this situation, the outcomes suggest that clogging develops between the doorjamb and the obstacle, contrary to the cases when the obstacle is farther, in which case clogging always occurs at the very door. The effectiveness of the obstacle (a strategy put forward to alleviate clogging in emergency exits) is therefore quite sensitive to its location. In addition, the study of the temporal evolution of the flow rate as the test develops makes evident a steady behavior during the entire duration of the entrance. This result is at odds with recent findings in human evacuation tests where the flow rate varies over time, therefore challenging the fairness of straightforward comparisons between pedestrian behavior and animal experimental observations.
Collapse
Affiliation(s)
- Iker Zuriguel
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Jorge Olivares
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - José M Pastor
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - César Martín-Gómez
- Departamento de Construcción, Instalaciones y Estructuras, Escuela Técnica Superior de Arquitectura, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Luis M Ferrer
- Departamento de Patología Animal, Facultad de Veterinaria, Universidad de Zaragoza, Miguel Servet 177, 50013 Zaragoza, Spain
| | - Juan J Ramos
- Departamento de Patología Animal, Facultad de Veterinaria, Universidad de Zaragoza, Miguel Servet 177, 50013 Zaragoza, Spain
| | - Angel Garcimartín
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| |
Collapse
|
40
|
Nicolas A, Bouzat S, Kuperman MN. Statistical fluctuations in pedestrian evacuation times and the effect of social contagion. Phys Rev E 2016; 94:022313. [PMID: 27627323 DOI: 10.1103/physreve.94.022313] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Indexed: 06/06/2023]
Abstract
Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models is now available, their calibration and test against empirical data are generally restricted to global averaged quantities; the statistics compiled from the time series of individual escapes ("microscopic" statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the microscopic statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with features that afford a semiquantitative reproduction of the experimental microscopic statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on microscopic statistics.
Collapse
Affiliation(s)
- Alexandre Nicolas
- Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche, and Instituto Balseiro, R8400AGP Bariloche, Argentina
| | - Sebastián Bouzat
- Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche, and Instituto Balseiro, R8400AGP Bariloche, Argentina
| | - Marcelo N Kuperman
- Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche, and Instituto Balseiro, R8400AGP Bariloche, Argentina
| |
Collapse
|
41
|
Laar TVD, Klooster ST, Schroën K, Sprakel J. Transition-state theory predicts clogging at the microscale. Sci Rep 2016; 6:28450. [PMID: 27328715 PMCID: PMC4916426 DOI: 10.1038/srep28450] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2016] [Accepted: 06/03/2016] [Indexed: 12/01/2022] Open
Abstract
Clogging is one of the main failure mechanisms encountered in industrial processes such as membrane filtration. Our understanding of the factors that govern the build-up of fouling layers and the emergence of clogs is largely incomplete, so that prevention of clogging remains an immense and costly challenge. In this paper we use a microfluidic model combined with quantitative real-time imaging to explore the influence of pore geometry and particle interactions on suspension clogging in constrictions, two crucial factors which remain relatively unexplored. We find a distinct dependence of the clogging rate on the entrance angle to a membrane pore which we explain quantitatively by deriving a model, based on transition-state theory, which describes the effect of viscous forces on the rate with which particles accumulate at the channel walls. With the same model we can also predict the effect of the particle interaction potential on the clogging rate. In both cases we find excellent agreement between our experimental data and theory. A better understanding of these clogging mechanisms and the influence of design parameters could form a stepping stone to delay or prevent clogging by rational membrane design.
Collapse
Affiliation(s)
- T. van de Laar
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
- Laboratory of Food Process Engineering, Wageningen University, Wageningen, The Netherlands
| | - S. ten Klooster
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
| | - K. Schroën
- Laboratory of Food Process Engineering, Wageningen University, Wageningen, The Netherlands
| | - J. Sprakel
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
| |
Collapse
|
42
|
Pastor JM, Garcimartín A, Gago PA, Peralta JP, Martín-Gómez C, Ferrer LM, Maza D, Parisi DR, Pugnaloni LA, Zuriguel I. Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015. [PMID: 26764754 DOI: 10.1088/1367-2630/aaf4ca] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
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.
Collapse
Affiliation(s)
- José M Pastor
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Angel Garcimartín
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Paula A Gago
- Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, Av. 60 Esq. 124 S/N, 1900 La Plata, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Rivadavia 1917 (1033), C. A. de Buenos Aires, Argentina
| | - Juan P Peralta
- Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, Av. 60 Esq. 124 S/N, 1900 La Plata, Argentina
| | - César Martín-Gómez
- Departamento de Construcción, Instalaciones y Estructuras, Escuela Técnica Superior de Arquitectura, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Luis M Ferrer
- Departamento de Patología Animal, Facultad de Veterinaria, Universidad de Zaragoza, Miguel Servet 177, 50013 Zaragoza, Spain
| | - Diego Maza
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| | - Daniel R Parisi
- Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Rivadavia 1917 (1033), C. A. de Buenos Aires, Argentina
- Instituto Tecnológico de Buenos Aires, 25 de Mayo 444, (1002) C. A. de Buenos Aires, Argentina
| | - Luis A Pugnaloni
- Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, Av. 60 Esq. 124 S/N, 1900 La Plata, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Rivadavia 1917 (1033), C. A. de Buenos Aires, Argentina
| | - Iker Zuriguel
- Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain
| |
Collapse
|