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Related papers: Maxwell Model of Traffic Flows

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Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…

Physics and Society · Physics 2023-10-10 Nour Khoudari , Rabie Ramadan , Megan Ross , Benjamin Seibold

Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…

Optimization and Control · Mathematics 2010-02-11 Nadir Farhi

Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The matter (constituent…

High Energy Physics - Theory · Physics 2013-10-10 Shoichi Ichinose

We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous…

Statistical Mechanics · Physics 2009-10-31 Martin Treiber , Ansgar Hennecke , Dirk Helbing

A system of identical cars on a single-lane road is treated as a microcanonical and canonical ensemble. Behaviour of the cars is characterized by the probability of car velocity as a function of distance and velocity of the car ahead. The…

Physics and Society · Physics 2007-05-23 Anton Šurda

In heterogeneous disordered traffic, where various vehicle types operate without strict lane discipline, self-organized vehicle groups often emerge. While the formation of such groups has been recognized, their influence on macroscopic…

Physics and Society · Physics 2026-02-23 Akihito Nagahama , Nichika Asai , Claudio Feliciani , Xiaolu Jia , Katsuhiro Nishinari

We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…

Analysis of PDEs · Mathematics 2021-08-16 Wancheng Sheng , Qinglong Zhang

This paper presents scalable traffic stability analysis for both pure autonomous vehicle (AV) traffic and mixed traffic based on continuum traffic flow models. Human vehicles are modeled by a non-equilibrium traffic flow model, i.e.,…

Optimization and Control · Mathematics 2024-09-23 Kuang Huang , Xuan Di , Qiang Du , Xi Chen

A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic,…

Statistical Mechanics · Physics 2007-05-23 M. Antoni , R. Cafiero

We study transport and relaxation of spinless fermions with long-range Coulomb interactions at high temperatures through numerical simulations of out-of-equilibrium dynamics. We find that the transport and relaxation are continuously…

Strongly Correlated Electrons · Physics 2023-08-02 Zhi-hua Li

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of…

Adaptation and Self-Organizing Systems · Physics 2015-06-11 Jay Samuel L. Combinido , May T. Lim

A two-dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of…

Statistical Mechanics · Physics 2015-06-24 Jan Freund , Thorsten Poeschel

We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are…

Statistical Mechanics · Physics 2009-11-07 A. Barrat , T. Biben , Z. Racz , E. Trizac , F. van Wijland

We study the deterministic dynamics of non-interacting classical gas particles confined to a one-dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone…

Classical Physics · Physics 2011-06-28 Florian Gebhard , Kevin zu Muenster

The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…

Analysis of PDEs · Mathematics 2016-11-03 Martin Burger , Jan-Frederik Pietschmann

Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…

Systems and Control · Electrical Eng. & Systems 2021-06-09 Renátó Besenczi , Norbert Bátfai , Péter Jeszenszky , Roland Major , Fanny Monori , Márton Ispány

We develop a kinetic-theory framework to investigate the steady rheology of a dilute gas interacting via a repulsive potential under uniform shear flow. Starting from the Boltzmann equation with a restitution coefficient that depends on the…

Soft Condensed Matter · Physics 2026-04-23 Yuria Kobayashi , Makoto R. Kikuchi , Shunsuke Iizuka , Satoshi Takada

By means of Molecular Dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in 2 dimensions: a single ball confined to moving along an inclined line consisting of balls. The global…

Condensed Matter · Physics 2009-10-28 S. Dippel , G. G. Batrouni , D. E. Wolf

Finding a quantitative description of the rate of collisions between small particles suspended in mixing flows is a long-standing problem. Here we investigate the validity of a parameterisation of the collision rate for identical particles…

Fluid Dynamics · Physics 2016-06-01 K. Gustavsson , B. Mehlig

On the basis of assumptions about the behavior of driver-vehicle units concerning acceleration, deceleration, overtaking, and lane-changing maneuvers, a gas-kinetic traffic model for uni-directional multi-lane freeways is constructed.…

Statistical Mechanics · Physics 2015-06-25 Dirk Helbing