Applied and Computational Mathematics Seminar
Monday, March 31, 2014 - 14:00
1 hour (actually 50 minutes)
Initially homogeneous vehicular traffic flow can become inhomogeneous even in the absence of obstacles. Such ``phantom traffic jams'' can be explained as instabilities of a wide class of ``second-order'' macroscopic traffic models. In this unstable regime, small perturbations amplify and grow into nonlinear traveling waves. These traffic waves, called ``jamitons'', are observed in reality and have been reproduced experimentally. We show that jamitons are analogs of detonation waves in reacting gas dynamics, thus creating an interesting link between traffic flow, combustion, water roll waves, and black holes. This analogy enables us to employ the Zel'dovich-von Neumann-Doering theory to predict the shape and travel velocity of the jamitons. We furthermore demonstrate that the existence of jamiton solutions can serve as an explanation for multi-valued parts that fundamental diagrams of traffic flow are observed to exhibit.