Diagonal patterns and chevron effect in intersecting traffic flows

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.

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• Wake-mediated interaction between driven particles crossing a perpendicular flow
• Stripe formation instability in crossing traffic flows
• Two dimensional outflows for cellular automata with shuffle updates
• Reversal of tracer advection and Hall drift in an interacting chiral fluid
• Modeling of pedestrians
• Structure and dynamics in the low-density phase of a two-dimensional cellular automaton model of traffic flow