Diagonal patterns and chevron effect in intersecting traffic flows

TL;DR

This paper models intersecting pedestrian flows on a lattice, revealing spontaneous diagonal pattern formation and chevron effects due to linear instability and nonlinear interactions.

Contribution

It introduces a lattice model for intersecting pedestrian flows and explains the emergence of diagonal and chevron patterns through linear and nonlinear stability analysis.

Findings

Spontaneous diagonal pattern formation observed in simulations.

Chevron patterns explained by nonlinear mode interactions.

Pattern formation linked to linear instability of mean field equations.

Abstract

We study a lattice model of two perpendicular intersecting flows of pedestrians represented by hard core particles of two types, eastbound (`$\pE$') and northbound (`$\pN$'). Each flow takes place on a strip of width $M$ so that the intersection is an $M\times M$ square lattice. In experiment and simulation there occurs on this square spontaneous formation of a diagonal pattern of alternating $\pE$ and $\pN$ particles. We show that this pattern formation may be understood in terms of a linear instability of the corresponding mean field equations. A refined investigation reveals that the pattern actually consists of chevrons rather than straight diagonals. We explain this effect as the consequence of the existence of a nonlinear mode sustained by the interaction between the two types of particles.