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Related papers: Linearized Theory of Traffic Flow

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A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…

Numerical Analysis · Mathematics 2017-07-28 Paola Pozzi , Björn Stinner

We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…

Dynamical Systems · Mathematics 2007-05-23 Michael Blank

In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…

Numerical Analysis · Mathematics 2025-02-21 N. Garcia-Chan , L. J. Alvarez-Vazquez , A. Martinez , M. E. Vazquez-Mendez

The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…

Fluid Dynamics · Physics 2018-07-19 Francisco Mandujano Carlos Málaga

We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…

Numerical Analysis · Mathematics 2024-11-01 Beatrice Crippa , Anna Scotti , Andrea Villa

We propose a model for the intersection of two urban streets. The traffic status of the crossroads is controlled by a set of traffic lights which periodically switch to red and green with a total period of T. Two different types of…

Statistical Mechanics · Physics 2007-05-23 M. Ebrahim Fouladvand , Masoud Nematollahi , Farzad Zolfaghari

A general, two-way coupled, point-particle formulation that accounts for the disturbance created by the dispersed particles in obtaining the undisturbed fluid flow field needed for accurate computation of the force closure models is…

Fluid Dynamics · Physics 2021-06-02 Pedram Pakseresht , Sourabh V. Apte

We study a system of interacting self-propelled particles whose walking velocity depends on the stage of the locomotion cycle. The model introduces a phase equation in the optimal velocity model for vehicular traffic. We find that the…

Physics and Society · Physics 2015-06-23 Takahiro Ezaki , Ryosuke Nishi , Daichi Yanagisawa , Katsuhiro Nishinari

Traffic-light modelling is a complex task, because many factors have to be taken into account. In particular, capturing all traffic flows in one model can significantly complicate the model. Therefore, several realistic features are…

Probability · Mathematics 2022-08-04 Rik W. Timmerman , Marko A. A. Boon

The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using…

Soft Condensed Matter · Physics 2009-11-07 Ihor Lubashevsky , Reinhard Mahnke , Peter Wagner , Sergey Kalenkov

Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…

Optimization and Control · Mathematics 2025-10-17 Maria Teresa Chiri , Christopher Denaro , Xiaoqian Gong , Benedetto Piccoli

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…

Fluid Dynamics · Physics 2014-08-04 Maxim Zaytsev , Vyacheslav Akkerman

We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…

Analysis of PDEs · Mathematics 2025-03-04 Dario Mazzoleni , Emanuela Radici , Filippo Riva

For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…

High Energy Physics - Theory · Physics 2009-10-24 A. V. Bratchikov

In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a…

Other Condensed Matter · Physics 2009-11-10 K. Thomas Waldeer

This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…

Fluid Dynamics · Physics 2023-11-06 Jean-Pierre Minier , Christophe Henry

This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across…

Systems and Control · Computer Science 2019-06-20 Matthew A. Wright , Roberto Horowitz

The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete…

Computational Physics · Physics 2020-05-26 Kenji Amagai , Yuko Hatano , Manabu Machida

In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called…

Analysis of PDEs · Mathematics 2018-04-23 Mohamed Benyahia , Carlotta Donadello , Nikodem Dymski , Massimiliano D. Rosini

We give a rigorous solution of an optimisation problem of minimizing the expected delay caused by encountering a red traffic light on a road journey. The problem incorporates simple constraints on maximum speed, acceleration and braking…

Optimization and Control · Mathematics 2025-12-03 Márton Balázs , Edward Crane , Alexander Tallis