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 stabilityboth analytically and numerically. First, we introduce a modified social forcemodel and compute the boundaries between different regimes analytically bya perturbation analysis of the one-lane and two-lane flow. Afterwards, theresults are verified by direct numerical simulations in the parameter plane ofpedestrian density and repulsion strength from the walls.
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Figure 2.
Transverse stationary distance
Figure 4.
Bifurcation diagrams obtained from the linear stability analysis for
Figure 5.
The same as in Fig. 4 for
Figure 6.
The order parameter
Figure 7.
Staggered transversal coordinates
Figure 8.
Longitudinal distances between nearest neighbors
Figure 10.
The stationary value of the inverse width $\kappa$ vs the mean distance $a$ obtained from Eq. (81). The solid (dashed) curve presents a stable (unstable) solution. The curves are plotted in the mean distance interval
Figure 11.
Spatio-temporal evolution of the local distance between lanes
Figure 12.
Velocity of the peristaltic pulse as a function of the inverse density. Comparison of the analytical results obtained from Eq. (90) (solid curve) and full scale numerical results (dots). The social interaction is weakly asymmetric
Figure 13.
Panel (a): The modulus of elliptic function
Figure 14.
Two stationary localized solutions
Figure 15.
Staggered transversal coordinate
Figure 16.
Pulse velocity in the vicinity of the bifurcation point
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