Diagonal patterns and chevron effect in intersecting traffic flows

We study a lattice model of two perpendicular intersecting flows of pedestrians represented by hard core particles of two types, eastbound (`') and northbound (`'). Each flow takes place on a strip of width M so that the intersection is an M× M square lattice. In experiment and simulation there occurs on this square spontaneous formation of a diagonal pattern of alternating and 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.