Crossing pedestrian traffic flows, the diagonal stripe pattern, and the chevron effect
Résumé
We study two perpendicular intersecting flows of pedestrians. The latter are represented either by moving hard core particles of two types, eastbound ($\mathcal {E}$) and northbound ($\mathcal {N}$), or by two density fields, $\rho ^{\mathcal {E}}_t({\mathbf r})$ and $\rho ^{\mathcal {N}}_t({\mathbf r})$. Each flow takes place on a lattice strip of width M so that the intersection is an M × 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 Δθ0 and determine its dependency on the parameters governing the boundary conditions.