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Traffic jams, granular flow, and soliton selection

Traffic jams, granular flow, and soliton selection The flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow. In a certain range of traffic density, steady flow becomes unstable against the growth of a cluster, or ‘‘phantom’’ traffic jam, which moves at a slower speed than the otherwise homogeneous flow. We show that near the onset of this instability, traffic flow is described by a perturbed Korteweg–de Vries (KdV) equation. The traffic jam can be identified with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Traffic jams, granular flow, and soliton selection

Kurtze, Douglas A
Physical Review E , Volume 52 (1) – Jul 1, 1995
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1995 The American Physical Society
ISSN
1095-3787
DOI
10.1103/PhysRevE.52.218
Publisher site
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Abstract

The flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow. In a certain range of traffic density, steady flow becomes unstable against the growth of a cluster, or ‘‘phantom’’ traffic jam, which moves at a slower speed than the otherwise homogeneous flow. We show that near the onset of this instability, traffic flow is described by a perturbed Korteweg–de Vries (KdV) equation. The traffic jam can be identified with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation.

Journal

Physical Review E – American Physical Society (APS)

Published: Jul 1, 1995

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