Related papers: Particle hopping models and traffic flow theory
Some implications of the simplest accounting of defects of compatibility in the velocity field on the structure of the classical Navier-Stokes equations are explored, leading to connections between classical elasticity, the elastic theory…
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…
As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation…
Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
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 modelling of traffic flow using methods and models from physics has a long history. In recent years especially cellular automata models have allowed for large-scale simulations of large traffic networks faster than real time. On the…
The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
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…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
We consider a Hamiltonian system of particles, interacting through of a smooth pair potential. We look at the system on a space scale of order {\epsilon}^1, times of order {\epsilon}^2, and mean velocities of order {\epsilon}, with…
This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at…
ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by…
The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean-Vlasov…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Fluid flows are typically studied by solving the Navier--Stokes equation. One of the fundamental assumptions of this equation is Stokes' hypothesis. This hypothesis assumes bulk viscosity, to be identically zero. The Stokes' hypothesis is a…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…