Related papers: Continuous kinematic wave models of merging traffi…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
We study the application of a recently introduced hierarchical description of traffic flow control by driver-assist vehicles to include lane changing dynamics. Lane-dependent feedback control strategies are implemented at the level of…
This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws.…
The Krauss-model is a stochastic model for traffic flow which is continuous in space. For periodic boundary conditions it is well understood and known to display a non-unique flow-density relation (fundamental diagram) for certain…
This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
The gas-kinetic foundation of fluid-dynamic traffic equations suggested in previous papers [Physica A 219, 375 and 391 (1995)] is further refined by applying the theory of dense gases and granular materials to the Boltzmann-like traffic…
The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using…
Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting…
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…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…
This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across…
This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous…
We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…
A new type of kinetic models with non-instantaneous binary collisions is considered. Collisions are described by a transport process in the joint state space of a pair of particles. The interactions are of alignment type, where the states…
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…
A recently introduced two-phase flow model by Chun Shen is studied in this work. The model is derived to describe the dynamics of immersed water bubbles in liquid water as carrier. Several assumptions are made to obtain a reduced form of…
This work focuses on the Riemann problem of Euler equations with global constant initial conditions and a single-point heating source, which comes from the physical problem of heating one-dimensional inviscid compressible constant flow. In…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…