This paper treats the problem of optimizing a coordinated ramp metering strategy based on a distributed macroscopic traffic model. The Lighthill, Whitham and Richards (LWR) model is extended to include on/off-ramps with on-ramp flow saturations and an optimal control formulation is proposed. Using optimization techniques in Banach spaces, a solution is shown to exist and the necessary optimalit...

Based on the low of the eighth power of speed of M.J. Lighthill this article has derived the calculating formula for the air dynamic noise power in the compressor, and analysed the factors to affect the noise, also indicated that the dynamic noise in the compressor mainly comes from the valve jet noise; the principle to reduce the dynamic noise is to get a small Reynolds number Re; the emphasis...

The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the models, we consider follow-the-leader type with different types drivers and vehicles which are distributed randomly on road. After a rescaling, show that cumulative distribution function converges solution model. We also establish connection between model so-called Lig...

This article is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway traffic is constructed, which results in a dynamical system in which observation the operator is linear. This article presents a new scalar hyperbolic partial ...

Cell-phones equipped with a global positioning system (GPS) provide new opportunities for location-based services and traffic estimation. When traveling on-board vehicles, these phones can be used to accurately provide position and velocity of the vehicle as probe traffic sensors. This article presents a new technique to incorporate mobile probe measurements into highway traffic flow models, an...

Generalizing prior work of P. W. Anderson and E. R. Huggins, we show that a "detailed Josephson-Anderson relation" holds for drag on finite body held at rest in classical incompressible fluid flowing with velocity ${\bf V}.$ The relation asserts an exact equality between the instantaneous power consumption by drag, $-{\bf F}\cdot{\bf V},$ vorticity flux across potential mass current, $-(1/2)\in...

The two components of combustion noise, namely the direct noise induced by heat release fluctuations in the flow and the indirect noise caused by acceleration of entropy perturbations through mean flow gradients resulting in acoustic radiation, are examined by considering different types of inhomogeneous wave equations deduced from the balance equations of fluid dynamics. This is accomplished b...

The head-on collision between two dust-acoustic solitary waves in an unmagnetized dusty plasma is investigated, including consideration of the dust charge variation. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collision are derived. The effects of the ratio of ion temperature to electron temperature, the ratio of the number...