| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
|
|
|
|
A Macroscopic Approach to the Lane Formation Phenomenon in Pedestrian Counterflow |
| XIONG Tao1, ZHANG Peng2**, WONG S. C.3, SHU Chi-Wang4, ZHANG Meng-Ping1
|
1Department of Mathematics, University of Science and Technology of China, Hefei 230026
2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072
3Department of Civil Engineering, The University of Hong Kong, Hong Kong
4Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
|
|
| Cite this article: |
|
XIONG Tao, ZHANG Peng, WONG S. C. et al 2011 Chin. Phys. Lett. 28 108901 |
|
|
|
|
Abstract 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.
|
| Keywords:
89.40.-a
89.40.Bb
02.60.Cb
|
|
|
Received: 29 January 2011
Published: 28 September 2011
|
|
|
|
|
|
|
|
[1] Burstedde C, Klauck K, Schadschneider A and Zittartz J 2001 Physica A 295 507
[2] Drake J S, Schofer J L and May A D 1967 Proc. 3rd Int. Symp. on Theory of Traffic Flow (New York:Elsevier)
[3] Helbing D 2001 Rev. Mod. Phys. 73 1067
[4] Helbing D, Farkás I J, Molnár P and Vicsek T 2002 Pedestrian and Evacuation Dynamics ed Schreckenberg M and Sharma S D (Berlin:Springer) pp 21–58
[5] Helbing D and Molnár P 1995 Phys. Rev. E 51 4282
[6] Helbing D and Vicsek T 1999 New J. Phys. 1 13
[7] Huang L, Wong S C, Zhang M, Shu C W and Lam W H K 2009 Transp. Res. B 43 127
[8] Jiang R and Wu Q S 2007 Physica A 373 683
[9] Jiang Y Q, Xiong T, Zhang M, Wong S C, Shu C W and Zhang P 2009 Acta Math. Sci. 29 1541
[10] Kuang H, Li X, Song T and Dai S 2008 Phys. Rev. E 78 066117
[11] Kuang H, Song T, Li X L and Dai S Q 2008 Chin. Phys. Lett. 25 1498
[12] Löhner R 2008 Applied CFD Techniques: An Introduction Based on Finite Element Methods (England: John Wiley & Sons)
[13] Shu C W 1998 Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws In Advanced Numerical Approximation of Nonlinear Hyperbolic Equations ed Cockburn B, Johnson C, Shu C W and Tadmor E Lecture Notes in Mathematics 1697 (Berlin: Springer) pp 325–432
[14] Wong S C, Leung W L, Chan S H, Lam W H K, Yung N H C, Liu C Y and Zhang P 2010 J. Transp. Engin. 136 234
[15] Xiong T, Zhang M, Shu C W, Wong S C and Zhang P 2011 Comput.-Aided Civil and Infrastructure Engin. 26 298
[16] Zhao H K 2005 Math. Comput. 74 603
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
