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Related papers: A Space-time Nonlocal Traffic Flow Model: Relaxati…

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Inthispaper,weintroduceanon-localPDE-ODEtrafficmodeldevotedtothedescriptionof a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general…

Analysis of PDEs · Mathematics 2024-04-04 F. A. Chiarello , J. Friedrich , S. GÖttlich

This paper develops a computational framework based on a car-following model to study traffic instability and lane changes. Building upon Newell's classical first-order car-following model, we show that, both analytically and numerically,…

Optimization and Control · Mathematics 2025-01-07 Nicholas Mankowski , Hassan Mushtaq , Hanliang Guo

We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…

Analysis of PDEs · Mathematics 2011-09-20 Christophe Berthon , Philippe G. LeFloch , Rodolphe Turpault

This paper addresses the problem of a boundary control design for traffic evolving in a large-scale urban network. The traffic state is described on a macroscopic scale and corresponds to the vehicle density, whose dynamics are governed by…

Optimization and Control · Mathematics 2021-03-17 Liudmila Tumash , Carlos Canudas-de-Wit , Maria Laura Delle Monache

We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…

Analysis of PDEs · Mathematics 2022-01-19 Helmut Abels , Yutaka Terasawa

The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid…

Chaotic Dynamics · Physics 2014-04-30 Alexander V. Milovanov , Jens Juul Rasmussen

A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model's nonlinearities are both lossless…

Fluid Dynamics · Physics 2021-10-19 Leonardo F. Toso , Ross Drummond , Stephen R. Duncan

We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…

Analysis of PDEs · Mathematics 2025-12-16 Antonin Chodron de Courcel

Nonlinear hyperbolic partial differential equations govern continuum traffic flow models. Higher-order traffic flow models consisting of continuum equations and velocity dynamics were introduced to address the limitations of the Lighthill,…

Analysis of PDEs · Mathematics 2024-07-10 Nandan Maiti , Bhargava Rama Chilukuri

We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different…

Analysis of PDEs · Mathematics 2020-12-15 Manas Bhatnagar , Hailiang Liu

In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is achieved by generalizing existing results for the local…

Analysis of PDEs · Mathematics 2026-05-26 Paulo Amorim , Alexander Keimer , Lukas Pflug , Jakob Rodestock

A kinetic model for the elasto-plastic dynamics of a flowing jammed material is proposed, which takes the form of a non-local -- Boltzmann-like -- kinetic equation for the stress distribution function. Coarse-graining this equation yields a…

Soft Condensed Matter · Physics 2015-05-13 Lyderic Bocquet , Annie Colin , Armand Ajdari

We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a…

Statistical Mechanics · Physics 2021-03-24 Johannes Feldmeier , Frank Pollmann , Michael Knap

We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely, we introduce deterministic particle schemes for the Hughes…

Numerical Analysis · Mathematics 2016-11-03 Marco Di Francesco , Simone Fagioli , Massimiliano D. Rosini , Giovanni Russo

This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…

Analysis of PDEs · Mathematics 2025-08-26 Urvashi Joshi , Aniruddha Kumar Sharma , Rajan Arora

In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a…

Analysis of PDEs · Mathematics 2021-03-12 Nastassia Pouradier Duteil

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One…

Quantum Physics · Physics 2015-10-06 Zhe-Xuan Gong , Michael Foss-Feig , Spyridon Michalakis , Alexey V. Gorshkov

We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation models the flux dependence on the solution…

Numerical Analysis · Mathematics 2026-04-30 Aekta Aggarwal , Ganesh Vaidya

This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a class of nonlocal Hamilton--Jacobi equations and establish a…

Analysis of PDEs · Mathematics 2023-10-03 Takashi Kagaya , Qing Liu , Hiroyoshi Mitake

Density fluctuations in traffic current are studied by computer simulations using the deterministic coupled map lattice model on a closed single-lane circuit. By calculating a power spectral density of temporal density fluctuations at a…

chao-dyn · Physics 2009-10-28 S. Yukawa , M. Kikuchi