糖心TV Complexity Science Events
Complexity Centre and MathSys CDT events carry priority over room D1.07.
To book D1.07 please email Sheetal dot Sharma at warwick dot ac dot uk
Please note that your event booking is for D1.07 only. The adjacent common room is a private area for the MathSys Centre that cannot used as part of your booking.
Seminar Applied Maths/Complexity
Location: D1.07
James Greenberg (CMU)
Discrete LagrangianTraffic Models
We discuss some of the more popular Discrete Lagrangian Traffic
Models. We focus our attention on two of such models, namely the “Optimal Velocity
Model” and the “Intelligent Driver Model.” Both describe cars traveling on a
unidirectional, one-lane highway.
New Material will include A-Priori estimates which are independent of the number
of cars on the road. These estimates guarantee that the models are well posed;
specifically they imply no car collisions and no velocity reversals.
We also investigate Large Amplitude “Stop and Go Waves.” These are “Traveling
Wave” solutions of the underlying systems. Typically, such solutions exits and are
stable when the “Equilibrium Solutions” where cars are uniformly spaced have a
large, linearly unstable region. As with Wilson’s studies on this subject the small
wave number dispersion relation will be a critically important tool.
We also discuss how to obtain PDE models with the same basic properties as
the discrete models. These PDE systems are obtained by matching the small wave
number dispersion relationships.