Phase Diagram Of The Biham-Middleton-Levine Traffic Model In Three Dimensions

Details Phase Diagram Of The Biham-Middleton-Levine Traffic Model In Three Dimensions Phase Diagram Of The Biham-Middleton-Levine Traffic Model In Three Dimensions

1999-05-03

arxiv.org/abs/cond-mat/9905014v2

Physics

Condensed Matter

Minor clarifications, 1 figure added

Scientific paper

10.1103/PhysRevE.60.5301

We study numerically the behavior of the Biham-Middleton-Levine traffic model in three dimensions. Our extensive numerical simulations show that the phase diagram for this model in three dimensions is markedly different from that in one and two dimensions. In addition to the full speed moving as well as the completely jamming phases, whose respective average asymptotic car speeds $$ equal one and zero, we observe an extensive region of car densities $\rho$ with a low but non-zero average asymptotic car speed. The transition from this extensive low average asymptotic car speed region to the completely jamming region is at least second order. We argue that this low speed region is a result of the formation of a spatially-limited-extended percolating cluster. Thus, this low speed phase is present in $n > 3$ dimensional Biham-Middleton-Levine model as well.

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