Institute for Mathematical Innovation

IMI Landscape Lecture

Organised jointly with the Department of Mathematical Sciences

 

  

Professor Rodolfo Ruben Rosales, MIT, USA

Phantom traffic jams, jamitons, detonation waves, and subcharacteristics

 

Time: Friday 22 April 2016, 15.15 pm - 16.15 pm
Venue: Wolfson Lecture Theatre (Building 4W, Room 1.7)

Abstract: Phantom traffic jams are both annoying to the drivers, and very interesting mathematically. These are traffic jams that occur spontaneously, without apparent cause. I will begin with a review of traffic flow theory, and introduce examples of continuum models. The simplest is a kinematic equation, the Lighthill-Whitham-Richards [LWR] model, which expresses the conservation of vehicles - under the assumption that the vehicle flow is a function of the density.

"Second order" models of traffic flow include a second equation: an evolution equation for the flow velocity characterized by a relaxation time τ. An important question is whether the LWR model is recovered in the limit τ=0. The answer lies in whether a "sub-characteristic condition" is satisfied. When it is not, phantom jams and jamitons (spontaneously generated nonlinear traveling waves with an "event" horizon) occur. I will discuss these issues, the ensuing dynamics, and the mathematical analogy between jamitons and detonations.

 

Members of all departments at the University of Bath are welcome to attend.