Related papers: Entropy solutions for a traffic model with phase t…

Hypotheses and some results of the three-phase traffic theory by the author are compared with results of the fundamental diagram approach to traffic flow theory. A critical discussion of model results about congested pattern features which…

We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular…

Experimental results for congested pedestrian traffic are presented. For data analysis we apply a method providing measurements on an individual scale. The resulting velocity-density relation shows a coexistence of moving and stopping…

In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…

We propose an efficient method for reconstructing traffic density with low penetration rate of probe vehicles. Specifically, we rely on measuring only the initial and final positions of a small number of cars which are generated using…

A macroscopic model is proposed to depict the traffic dynamics involved in urban traffic systems. The link dynamics are described based on the cell-transmission model and bounded by the link capacities, while the flow dynamics are proposed…

Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…

Recent applications of a new methodology to measure fundamental traffic relations on freeways shows that many of the critical parameters of the flow-density and speed-spacing diagrams depend on vehicle length. In response to this fact, we…

We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic…

The dynamics of multicomponent gas mixtures with vanishing barycentric velocity is described by Maxwell-Stefan equations with mass diffusion and heat conduction. The equations consist of the mass and energy balances, coupled to an algebraic…

Aerodynamic drag can be partially approximated by the entropy flux across fluid domain boundaries with a formula due to Oswatitsch. In this paper, we build the adjoint solution that corresponds to this representation of the drag and…

We provide a model to understand how adverse weather conditions modify traffic flow dynamic. We first prove that the microscopic Free Flow Speed of the vehicles is changed and then provide a rule to model this change. For this, we consider…

We study the spatiotemporal patterns resulting from different boundary conditions for a microscopic traffic model and contrast it with empirical results. By evaluating the time series of local measurements, the local traffic states are…

We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…

Starting from the multi-species Boltzmann equation for a gas mixture, we propose the formal derivation of the isentropic two-phase flow model introduced in [Romenski, E., and Toro, E. F., Comput. Fluid Dyn. J., 13 (2004)]. We examine the…

Motivated by the traffic flow model with Arrhenius look-ahead relaxation dynamics introduced in [A. Sopasakis and M.A. Katsoulakis, SIAM J. Appl. Math., 66 (2006), p. 921--944], this paper proposes a traffic flow model with look ahead…

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…

Enstrophy, half the integral of the square of vorticity, plays a role in 2D turbulence theory analogous to that played by kinetic energy in the Kolmogorov theory of 3D turbulence. It is therefore interesting to obtain a description of the…

We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…

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…