Related papers: Analysis and Control of a Non-Local PDE Traffic Fl…
This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…
In this paper we propose a novel traffic flow model based on understanding the city as a porous media, this is, streets and building-blocks characterizing the urban landscape are seen now as the fluid-phase and the solid-phase of a porous…
In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
We study closed, embedded hypersurfaces in Euclidean space evolving by fully nonlinear curvature flows, whose speed is given by a symmetric, monotone increasing, $1$-homogeneous, positive underlying speed function $F$ composed with a…
We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some…
Methods of dynamical system's theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent…
We study dynamic traffic assignment with side-constraints. We first give a counter-example to a key result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical edge-delay…
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several…
We have studied the distribution of traffic flow $q$ for the Nagel-Schreckenberg model by computer simulations. We applied a large-deviation approach, which allowed us to obtain the distribution $P(q)$ over more than one hundred decades in…
We consider non-degenerate SDEs with a $\beta$-Holder continuous and bounded drift term and driven by a Levy noise $L$ which is of $\alpha$-stable type. If $\alpha \in [1,2)$ and $\beta \in (1 - \frac{\alpha}{2},1) $ we show pathwise…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the traffic flow over the on-ramp and off-ramps. We approximate the problem using an upwind-type…
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…
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…
Consider a balance law where the flux depends explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below,…
The macroscopic traffic flow model is widely used for traffic control and management. To incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity inherent in the classic Lighthill-Whitham-Richards (LWR)…
As an example for the optimization of unstable flows, we present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. It exploits the naturally occuring fluctuations of traffic flow and…
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…