PIMS/AMI Seminar: Nonlinear waves in traffic flow

Continuum traffic theories whereby individual vehicles are collectively modeled have enjoyed a rich history since their popularization by M.J. Lighthill and G.B. Whitham. These models are able to elucidate the dynamics of ``phantom jams,'' transient blockages that arise without obstructions. Notwithstanding this venerated record, the possibility of self-sustained disturbances consisting of a shock matched to a transonic flow has received inadequate attention despite recent experimental evidence that such ``jamitons'' are ubiquitous. By drawing a remarkable analogy between jamitons and detonation waves, I herein identify a novel class of traveling wave solutions pertinent to heavy traffic flow. This work is done in collaboration with R.R. Rosales, J.-C. Nave, B. Seibold and A.R. Kasimov.