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Related papers: Side-Constrained Dynamic Traffic Equilibria

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This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…

Systems and Control · Electrical Eng. & Systems 2019-12-03 Hossein Rastgoftar , Ella Atkins

Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a…

Statistical Mechanics · Physics 2009-11-07 Dirk Helbing , Davide Batic , Martin Schoenhof , Martin Treiber

The dynamical formulation of optimal transport, also known as Benamou-Brenier formulation or Computational Fluid Dynamics formulation, amounts to write the optimal transport problem as the optimization of a convex functional under a PDE…

Numerical Analysis · Mathematics 2020-05-25 Hugo Lavenant

This paper concerns a new class of discontinuous dynamical systems for constrained optimization. These dynamics are particularly suited to solve nonlinear, non-convex problems in closed-loop with a physical system. Such approaches using…

Optimization and Control · Mathematics 2020-05-11 Adrian Hauswirth , Florian Dörfler , Andrew Teel

We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a…

Computer Science and Game Theory · Computer Science 2020-05-05 Marcus Kaiser

We study dynamical transportation networks in a framework that includes extensions of the classical Cell Transmission Model to arbitrary network topologies. The dynamics are modeled as systems of ordinary differential equations describing…

Optimization and Control · Mathematics 2014-10-28 Enrico Lovisari , Giacomo Como , Anders Rantzer , Ketan Savla

A novel continuum model has been developed to address the vehicle size heterogeneity in mixed traffic. By incorporating the principle of vehicle area conservation, a new set of traffic flow variables centered on the concept of vehicle area…

Analysis of PDEs · Mathematics 2026-04-27 Nandan Maiti , Bhargava Rama Chilukuri

Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…

Optimization and Control · Mathematics 2025-11-04 Anqi Dong , Karl Henrik Johansson , Johan Karlsson

This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…

Mathematical Physics · Physics 2015-06-15 Chun-Xiu Wu , Peng Zhang , S. C. Wong , Keechoo Choi

By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…

Chaotic Dynamics · Physics 2007-05-23 Michael Blank

In this article, we demonstrate that in a transport model of particles with kinetic constraints, long-lived spatial structures are responsible for the blocking dynamics and the decrease of the current at strong driving field. Coexistence…

Disordered Systems and Neural Networks · Physics 2015-03-20 Francesco Turci , Estelle Pitard

The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…

Fluid Dynamics · Physics 2023-06-21 Maxim A. Olshanskii

A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…

Optimization and Control · Mathematics 2018-01-23 Jonathan Korman , Robert J. McCann

In a recent paper [M. Colangeli \textit{et al.}, J.\ Stat.\ Mech.\ P04021, (2011)] it was argued that the Fluctuation Relation for the phase space contraction rate $\Lambda$ could suitably be extended to non-reversible dissipative systems.…

Dynamical Systems · Mathematics 2015-06-03 Matteo Colangeli , Lamberto Rondoni

Traditional DTA models of large cities suffer from prohibitive computation times and calibration/validation can become major challenges faced by practitioners. The empirical evidence in 2008 in support of the existence of a Macroscopic…

Analysis of PDEs · Mathematics 2018-12-04 Rafegh Aghamohammadi , Jorge A. Laval

This paper firstly show that a recent model (Tian et al., Transpn. Res. B 71, 138-157, 2015) is not able to well replicate the evolution concavity in traffic flow, i.e. the standard deviation of vehicles increases in a concave/linear way…

Cellular Automata and Lattice Gases · Physics 2015-07-16 Junfang Tian , Rui Jiang , Guangyu Li , Martin Treiber , Ning Jia , Shoufeng Ma

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

The article is dedicated to discussion of irreversibility and foundation of statistical mechanics "from the first principles". Taking into account infinitesimal and, as it seems, neglectful for classical mechanics fluctuations of the…

Quantum Physics · Physics 2007-05-23 V. E. Shemi-zadeh

Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the $2D$ conformal algebra. In the case…

Mathematical Physics · Physics 2015-09-08 Stoimen Stoimenov , Malte Henkel

We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase…

Analysis of PDEs · Mathematics 2026-03-05 Dieter Bothe , Matthias Köhne