Julien Cividini, Cecile Appert-Rolland, Hendrik-Jan Hilhorst
We study a lattice model of two perpendicular intersecting flows of pedestrians represented by hard core particles of two types, eastbound (`${\cal E}$') and northbound (`${\cal N}$'). 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 ${\cal E}$ and ${\cal N}$ particles. By a linear stability analysis of the corresponding mean-field equations we point out the origin of this pattern formation phenomenon. A refined investigation reveals that for large enough $M$ the pattern actually consists of chevrons rather than straight diagonals. We provide an explanation for this chevron effect.
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http://arxiv.org/abs/1209.1529
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