Diagonal patterns and chevron effect in intersecting traffic flows

Laboratoire de Physique Théorique, Université Paris-Sud and CNRS UMR 8627 - bâtiment 210, 91405 Orsay Cedex, France, EU

^(a) julien.cividini@th.u-psud.fr
^(b) cecile.appert-rolland@th.u-psud.fr
^(c) henk.hilhorst@th.u-psud.fr

Received: 8 February 2013
Accepted: 2 April 2013

Abstract

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.