A Macroscopic Approach to the Lane Formation Phenomenon in Pedestrian Counterflow

XIONG Tao; ZHANG Peng; WONG S. C.; SHU Chi-Wang; ZHANG Meng-Ping

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A Macroscopic Approach to the Lane Formation Phenomenon in Pedestrian Counterflow

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We simulate pedestrian counterflow by adopting an optimal path-choice strategy and a recently observed speed-density relationship. Although the whole system is symmetric, the simulation demonstrates the segregation and formation of many walking lanes for two groups of pedestrians. The symmetry breaking is most likely triggered by a small numerical viscosity or "noise", and the segregation is associated with the minimization of travel time. The underlying physics can be compared with the "optimal self-organization" mechanism in Helbing's social force model, by which driven entities in an open system tend to minimize their interaction to enable them to reach some ordering state.%We simulate pedestrian counterflow by adopting an optimal path-choice strategy and a recently observed speeddensity relationship.Although the whole system is symmetric,the simulation demonstrates the segregation and formation of many walking lanes for two groups of pedestrians.The symmetry breaking is most likely triggered by a small numerical viscosity or “noise”,and the segregation is associated with the minimization of travel time.The underlying physics can be compared with the “optimal self-organization” mechanism in Helbing's social force model,by which driven entities in an open system tend to minimize their interaction to enable them to reach some ordering state.The phenomenon of lane formation in pedestrian flows has been frequently observed through direct observation or controlled experiments.Helbing et al.[4]presented photographs to show that pedestrians could form uniform walking lanes at sufficiently high densities.Theoretically,the phenomenon was explained through an optimal self-organization mechanism,[3,6]namely,a pedestrian crowd constitutes an open system of driven entities that tends to minimize interaction and dissipation,and thus an optimal state is reached.This differs from a closed system,which is governed by the second law of thermodynamics and thus the entropy (or disorder) increases continuously.

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《中国物理快报：英文版》 |2011年第10期|277-280|共4页
作者
XIONG Tao; ZHANG Peng; WONG S. C.; SHU Chi-Wang; ZHANG Meng-Ping;
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Department of Mathematics, University of Science and Technology of China, Hefei 230026;

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072;

Department of Civil Engineering, The University of Hong Kong, Hong Kong;

Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;

Department of Mathematics, University of Science and Technology of China, Hefei 230026;

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A Macroscopic Approach to the Lane Formation Phenomenon in Pedestrian Counterflow

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