Traffic jams, granular flow, and soliton selection

Journal Article · Sat Jul 01 04:00:00 EDT 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.52.218· OSTI ID:165345

Kurtze, D A ^[1]; Hong, D C ^[2]

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1. Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566 (United States)
2. Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015 (United States)

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.

• OSTI ID: 165345
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 1 Vol. 52; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION
FLOW MODELS
FLUID FLOW
GRANULAR MATERIALS
KORTEWEG-DE VRIES EQUATION
NAVIER-STOKES EQUATIONS
SOLITONS
STOCHASTIC PROCESSES
TRAFFIC CONTROL
TRANSPORTATION SYSTEMS