Pattern formation in flows of asymmetrically interacting particles: Peristaltic pedestrian dynamics as a case study

Yuri B. Gaididei, Christian Marschler, Mads Peter Sørensen*, Peter L. Christiansen, Jens Juul Rasmussen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

The influence of asymmetry in the coupling between repulsive particles is studied. A prominent example is the social force model for pedestrian dynamics in a long corridor where the asymmetry leads to anisotropy in the repulsion such that pedestrians in front, i.e., in walking direction, have a bigger influence on the pedestrian behavior than those behind. In addition to one-and two-lane free flow situations, a new traveling regime is found that is reminiscent of peristaltic motion. We study the regimes and their respective stability both analytically and numerically. First, we introduce a modified social force model and compute the boundaries between different regimes analytically by a perturbation analysis of the one-lane and two-lane flow. Afterwards, the results are verified by direct numerical simulations in the parameter plane of pedestrian density and repulsion strength from the walls.

Original languageEnglish
JournalEvolution Equations and Control Theory
Volume8
Issue number1
Pages (from-to)73-100
Number of pages28
ISSN2163-2472
DOIs
Publication statusPublished - 2019

Keywords

  • Asymmetry
  • Bifurcations and instability
  • General perturbation schemes
  • Nonlinear lattice dynamics
  • Nonlinear modes
  • Pattern formation in complex systems
  • Pedestrian flow

Cite this

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title = "Pattern formation in flows of asymmetrically interacting particles: Peristaltic pedestrian dynamics as a case study",
abstract = "The influence of asymmetry in the coupling between repulsive particles is studied. A prominent example is the social force model for pedestrian dynamics in a long corridor where the asymmetry leads to anisotropy in the repulsion such that pedestrians in front, i.e., in walking direction, have a bigger influence on the pedestrian behavior than those behind. In addition to one-and two-lane free flow situations, a new traveling regime is found that is reminiscent of peristaltic motion. We study the regimes and their respective stability both analytically and numerically. First, we introduce a modified social force model and compute the boundaries between different regimes analytically by a perturbation analysis of the one-lane and two-lane flow. Afterwards, the results are verified by direct numerical simulations in the parameter plane of pedestrian density and repulsion strength from the walls.",
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author = "Gaididei, {Yuri B.} and Christian Marschler and S{\o}rensen, {Mads Peter} and Christiansen, {Peter L.} and Rasmussen, {Jens Juul}",
year = "2019",
doi = "10.3934/eect.2019005",
language = "English",
volume = "8",
pages = "73--100",
journal = "Evolution Equations and Control Theory (Online)",
issn = "2163-2480",
publisher = "American Institute of Mathematical Sciences (A I M S Press)",
number = "1",

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Pattern formation in flows of asymmetrically interacting particles: Peristaltic pedestrian dynamics as a case study. / Gaididei, Yuri B.; Marschler, Christian; Sørensen, Mads Peter; Christiansen, Peter L.; Rasmussen, Jens Juul.

In: Evolution Equations and Control Theory, Vol. 8, No. 1, 2019, p. 73-100.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Pattern formation in flows of asymmetrically interacting particles: Peristaltic pedestrian dynamics as a case study

AU - Gaididei, Yuri B.

AU - Marschler, Christian

AU - Sørensen, Mads Peter

AU - Christiansen, Peter L.

AU - Rasmussen, Jens Juul

PY - 2019

Y1 - 2019

N2 - The influence of asymmetry in the coupling between repulsive particles is studied. A prominent example is the social force model for pedestrian dynamics in a long corridor where the asymmetry leads to anisotropy in the repulsion such that pedestrians in front, i.e., in walking direction, have a bigger influence on the pedestrian behavior than those behind. In addition to one-and two-lane free flow situations, a new traveling regime is found that is reminiscent of peristaltic motion. We study the regimes and their respective stability both analytically and numerically. First, we introduce a modified social force model and compute the boundaries between different regimes analytically by a perturbation analysis of the one-lane and two-lane flow. Afterwards, the results are verified by direct numerical simulations in the parameter plane of pedestrian density and repulsion strength from the walls.

AB - The influence of asymmetry in the coupling between repulsive particles is studied. A prominent example is the social force model for pedestrian dynamics in a long corridor where the asymmetry leads to anisotropy in the repulsion such that pedestrians in front, i.e., in walking direction, have a bigger influence on the pedestrian behavior than those behind. In addition to one-and two-lane free flow situations, a new traveling regime is found that is reminiscent of peristaltic motion. We study the regimes and their respective stability both analytically and numerically. First, we introduce a modified social force model and compute the boundaries between different regimes analytically by a perturbation analysis of the one-lane and two-lane flow. Afterwards, the results are verified by direct numerical simulations in the parameter plane of pedestrian density and repulsion strength from the walls.

KW - Asymmetry

KW - Bifurcations and instability

KW - General perturbation schemes

KW - Nonlinear lattice dynamics

KW - Nonlinear modes

KW - Pattern formation in complex systems

KW - Pedestrian flow

U2 - 10.3934/eect.2019005

DO - 10.3934/eect.2019005

M3 - Journal article

VL - 8

SP - 73

EP - 100

JO - Evolution Equations and Control Theory (Online)

JF - Evolution Equations and Control Theory (Online)

SN - 2163-2480

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