Velocity correlations and spatial dependencies between neighbors in a unidirectional flow of pedestrians

The aim of the paper is an analysis of self-organization patterns observed in the unidirectional flow of pedestrians. On the basis of experimental data from Zhang et al. [J. Zhang et al., J. Stat. Mech. (2011) P0600410.1088/1742-5468/2011/06/P06004], we analyze the mutual positions and velocity correlations between pedestrians when walking along a corridor. The angular and spatial dependencies of the mutual positions reveal a spatial structure that remains stable during the crowd motion. This structure differs depending on the value of n, for the consecutive nth-nearest-neighbor position set. The preferred position for the first-nearest neighbor is on the side of the pedestrian, while for further neighbors, this preference shifts to the axis of movement. The velocity correlations vary with the angle formed by the pair of neighboring pedestrians and the direction of motion and with the time delay between pedestrians' movements. The delay dependence of the correlations shows characteristic oscillations, produced by the velocity oscillations when striding; however, a filtering of the main frequency of individual striding out reduces the oscillations only partially. We conclude that pedestrians select their path directions so as to evade the necessity of continuously adjusting their speed to their neighbors'. They try to keep a given distance, but follow the person in front of them, as well as accepting and observing pedestrians on their sides. Additionally, we show an empirical example that illustrates the shape of a pedestrian's personal space during movement.