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Unravelling the puzzling intermediate states in the Biham-Middleton-Levine traffic mode | | L.E. Olmos
; J.D. Muñoz
; | | Date: |
16 Feb 2015 | | Abstract: | The Biham-Middleton-Levine (BML) traffic model, a cellular automaton with
east-bound and north-bound cars moving by turns on a square lattice, has been
an underpinning model in the study of collective behaviour by cars, pedestrians
and even internet packages. Contrary to initial beliefs that the model exhibits
a sharp phase transition from freely flowing to fully jammed, it has been
reported that it shows intermediate stable phases, where jams and freely
flowing traffic coexist, but there is no clear understanding of their origin.
Here, we analyze the model as an anisotropic system with a preferred fluid
direction (north-east) and find that it exhibits two differentiated phase
transitions: either if the system is longer in the flow direction
(longitudinal) or perpendicular to it (transversal). The critical densities
where these transitions occur enclose the density interval of intermediate
states and can be approximated by mean-field analysis, all derived from the
anisotropic exponent relating the longitudinal and transversal correlation
lengths. Thus, we arrive to the interesting result that the puzzling
intermediate states in the original model are just a superposition of these two
different behaviours of the phase transition, solving by the way most mysteries
behind the BML model, which turns to be a paradigmatic example of such
anisotropic critical systems. | | Source: | arXiv, 1502.4587 | | Services: | Forum | Review | PDF | Favorites | |
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