Related papers: Hydrodynamic traffic flow models including random …
We illustrate the potential of PDE-based traffic flow control in cardiovascular flow analysis, monitoring, and control, presenting a PDE-based control-oriented formulation, for 1-D blood flow dynamics in the presence of stenosis. This is…
Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation.…
We extend the classical LWR traffic model allowing different maximal speeds to different vehicles. Then, we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macro- scopic model displaying 2 phases,…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…
In this paper, we consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ with multiplicative noise. We first show that the solutions to the stochastic equations of second…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
With the emergence of autonomous vehicles, it is important to understand their impact on the transportation system. However, conventional traffic simulations are time-consuming. In this paper, we introduce an analytical traffic model for…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of…
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…
In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -- microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity…
Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding is practically important for designing variable speed limit and ramp metering strategies. In this study, we attempt to develop a…
A most important aspect in the field of traffic modeling is the simulation of bottleneck situations. For their realistic description a macroscopic multi-lane model for uni-directional freeways including acceleration, deceleration, velocity…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…
This contribution summarizes and explains various principles from physics which are used for the simulation of traffic flows in large street networks, the modeling of destination, transport mode, and route choice, or the simulation of urban…
We propose a fluidic continuum model of vacuum and a sink flow model of microscopic particles. The movements of a microscopic particle driven by a stochastic force was studied based on stochastic mechanics. We show that there exists a…