Related papers: Boundary-induced phase transitions in a space-cont…
Boundary-induced phase transitions are one of the surprising phenomena appearing in nonequilibrium systems. These transitions have been found in driven systems, especially the asymmetric simple exclusion process. However, so far no direct…
We discuss the effects of open boundary conditions and boundary induced drift on condensation phenomena in the pair-factorized steady states transport process, a versatile model for stochastic transport with tunable nearest-neighbour…
In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
In this work, we propose an alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters. Our approach is based on a mesoscopic viewpoint of the traffic system in terms of the dynamics of…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
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…
We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…
We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS)…
We study boundary induced phase transitions in a driven lattice gas exhibiting metastability. The phase diagram for open systems, parameterized by the input and output rates, consists of two regions corresponding to the free flow and jammed…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…
In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front…
We present a model of traffic flow, with rules that describe the behaviour of automated vehicles in an open system. We show first of all that the fundamental diagram of this system collapses to a point, where states of free and jammed…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…
A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…