Related papers: A traffic flow model with non-smooth metric intera…
This is a technical note where we solve the additive eigenvalue problem associated to a dynamics of a 2D-traffic system. The traffic modeling is not explained here. It is available in \cite{Far08}. It consists of a microscopic road traffic…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter model ``dust'' fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue that…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…
In this paper we present a non-local numerical scheme based on the Local Discontinuous Galerkin method for a non-local diffusive partial differential equation with application to traffic flow. In this model, the velocity is determined by…
We extend the analysis by Esedo\={g}lu and Otto (2015) of thresholding energies for the celebrated multiphase Bence-Merriman-Osher algorithm for computing mean curvature flow of interfacial networks, to the case of differing space-dependent…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of probability measures, where paths are solutions of the continuity equation and the action is…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at theoretical level and by molecular dynamic simulations. To understand some of these features…
The emerging connected and automated vehicle technologies allow vehicles to perceive and process traffic information in a wide spatial range. Modeling nonlocal interactions between connected vehicles and analyzing their impact on traffic…
Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases,…
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…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and…
Describing superfluid turbulence at intermediate scales between the inter-vortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $\cal{L}$. The closure of such an equation for…
We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time…