James M. Greenberg

Extensions and Amplifications of a Traffic Model of Aw and Rascle

In a recent paper [1] Aw and Rascle introduced a new model of traffic on a uni-directional highway. Here the author studies an extension of this model, one which accounts for drivers attempting to travel at their maximum allowable speed. The author looks at a Lagrangian reformulation of this problem; a formulation that leads to an effective computational algorithm for solving the resulting system. He also investigates approximation scheme introduced by Dafermos [5] for scalar conservation laws and demonstrates that this Dafermos scheme works well on this 2 x 2 system.

CONGESTION ON MULTILANE HIGHWAYS

We present a new model for traffic on a multilane freeway (with n lanes). Our basic descriptors are the car density

On the long-time behavior of ferroelectric systems

\rho

New Approaches for Chirplet Approximation

(in cars/mile), taken across all lanes in the freeway, and the average car velocity u (in miles/hour). The flux of cars across all lanes is given by

A RIGOROUS TREATMENT OF A FOLLOW-THE-LEADER TRAFFIC MODEL WITH TRAFFIC LIGHTS PRESENT ∗

\rho u = {\sum^n_{i=1}}\rho_i u_i

Elastic phase transitions: A new model

, where

Chirplet Approximation of Band-Limited, Real Signals Made Easy

\rho_i

On the existence, uniqueness, and stability of solutions of the equation PP0Xtt = E(Xx)Xxx + κXxxt

is the car density in the ith lane, and ui the velocity of cars in the ith lane. We shall track only

On the exponential stability of solutions of E(ux) uxx + λuxtx = ϱutt

\rho

Phase transitions with semi-diffuse interfaces

and u and not what is going on in each individual lane. On such multilane freeways, one often observes distinct stable equilibrium relationships between car velocity and density. Prototypical situations involve two equilibria,