Crossing pedestrian traffic flows,diagonal stripe pattern, and chevron effect

TL;DR

This paper investigates the spontaneous formation of diagonal striped patterns, including chevron effects, in intersecting pedestrian flows through simulations and stability analysis, revealing how these patterns depend on boundary conditions.

Contribution

It introduces a combined particle and field model to analyze chevron pattern formation in pedestrian traffic intersections, supported by stability analysis and simulations.

Findings

Chevron patterns occur in both particle and field simulations.

The chevron angle depends on boundary conditions.

Pattern formation is explained by linear stability analysis.

Abstract

We study two perpendicular intersecting flows of pedestrians. The latter are represented either by moving hard core particles of two types, eastbound ($\symbp$) and northbound ($\symbm$), or by two density fields, $\rhop_t(\brr)$ and $\rhom_t(\brr)$. Each flow takes place on a lattice strip of width $M$ so that the intersection is an $M\times M$ square. We investigate the spontaneous formation, observed experimentally and in simulations, of a diagonal pattern of stripes in which alternatingly one of the two particle types dominates. By a linear stability analysis of the field equations we show how this pattern formation comes about. We focus on the observation, reported recently, that the striped pattern actually consists of chevrons rather than straight lines. We demonstrate that this `chevron effect' occurs both in particle simulations with various different update schemes and in field simulations. We quantify the effect in terms of the chevron angle $\Delta\theta_0$ and determine its dependency on the parameters governing the boundary conditions.