Search results for "Flow model"

Probabilistic description of traffic flow

2005

Abstract A stochastic description of traffic flow, called probabilistic traffic flow theory, is developed. The general master equation is applied to relatively simple models to describe the formation and dissolution of traffic congestions. Our approach is mainly based on spatially homogeneous systems like periodically closed circular rings without on- and off-ramps. We consider a stochastic one-step process of growth or shrinkage of a car cluster (jam). As generalization we discuss the coexistence of several car clusters of different sizes. The basic problem is to find a physically motivated ansatz for the transition rates of the attachment and detachment of individual cars to a car cluster…

Application of thermodynamics to driven systems

2007

Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic varia…

The parameter identification in the Stokes system with threshold slip boundary conditions

2020

The paper is devoted to an identification of the slip bound function g in the Stokes system with threshold slip boundary conditions assuming that g depends on the tangential velocity 𝑢𝜏 . To this end the optimal control approach is used. To remove its nonsmoothness we use a regularized form of the slip conditions in the state problem. The mutual relation between solutions to the original optimization problem and the problems with regularized states is analyzed. The paper is completed by numerical experiments. peerReviewed

Nonlocal Second Order Vehicular Traffic Flow Models And Lagrange-Remap Finite Volumes

2011

In this paper a second order vehicular macroscopic model is derived from a microscopic car–following type model and it is analyzed. The source term includes nonlocal anticipation terms. A Finite Volume Lagrange–remap scheme is proposed.

Particle flow modelling in slurry-fed stirred vessels

2004

In this paper experimental information on the retention time distribution (RTD) of solid particles in a high-aspect-ratio vessel, stirred by three equally spaced Rushton turbines, is presented. The relevant data were obtained by a special technique named twin system approach (TSA) that greatly simpli+es the handling of particle-laden streams and is therefore particularly suited for investigating particle RTD in 9ow systems. The technique fundamentals are +rst summarized, together with the data analysis procedure. This lastly requires a numerical deconvolution operation that is easily performed with the help of Z-transforms. Two di;erent approaches for excluding the spurious contributions of…

Modelling wet-air oxidation of phenol in a trickle-bed reactor using active carbon as a catalyst

2016