Journal
PHYSICAL REVIEW E
Volume 79, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.79.056113
Keywords
detonation waves; entropy; nonlinear dynamical systems; road traffic; shock waves
Categories
Funding
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0813648] Funding Source: National Science Foundation
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In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic (inviscid) continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway [Y. Sugiyama , N. J. Phys. 10, 033001 (2008)], our numerical calculations show that nonlinear traveling waves are attracting solutions, with the time evolution of the system converging toward a wave-dominated configuration. Theoretical principles are elucidated by considering examples of traffic flow on open and closed roadways.
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