Dense human flow has been a concern for the safety of public events for a long time. Macroscopic pedestrian models, which are mainly based on fluid dynamics, are often used to simulate huge crowds due to their low computational costs (COLOMBO and ROSINI, 2005). Similar approaches are used in the field of traffic simulations (LIGHTHILL and WHITHAM, 1955). A combined macroscopic simulation of veh...

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...

Steady supersonic two-dimensional flows governed by the Navier-Stokes equations are considered. For flows past a thin body, the Oseen theory is shown to fail at large distances. An investigation of the equations bridging the linear and non-linear zones is made. From this, it follows that the resulting equations are a system of Burgers and diffusion equations. The Whitham theory is shown to resu...

Abstract. We study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlevé I hierarchy. It is shown that this solution gives a valid asympto...

We investigate the Dijkgraaf-Vafa proposal when supersymmetry is broken. We consider U(N) SYM with chiral adjoint matter where the coupling constants in the tree-level superpotential are promoted to chiral spurions. The holomorphic part of the low-energy glueball superpotential can still be analyzed. We compute the holomorphic supersymmetry breaking contributions using methods of the geometry u...

Fundamental diagrams of vehicular traffic flow are generally multivalued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, c...

A mathematical macroscopic traffic flow model known as Lighthill, Whitham and Richards (LWR) model appended with a closure nonlinear velocity-density relationship yielding a quasilinear first order (hyperbolic) partial differential equation as an initial boundary value problem (IBVP) was considered. The traffic model IBVP by finite difference method which leads to a first order explicit upwind ...

In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results r...

This paper deals with the classic second order Payne-Whitham macroscopic model, commonly known as PW-Model, used to represent and forecast traffic conditions in a freeway. The results of the model may show a misbehavior similar to the instability of numerical solutions of partial differential equations. Since this model comes from a partial differential equation system, we use some stability ru...