相关论文: Boltzmann-type description with cutoff of Follow-t…

Starting from microscopic interaction rules we derive kinetic models of Fokker--Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the corresponding Boltzmann model. As particular cases,…

The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…

In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…

In classical kinetic or kinetic-like models a particle free path distribution is exponensial, but this is more likely to be an exception than a rule. In this paper we derive a linear Boltzmann-like equation for a general free path…

This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the…

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…

In this paper we present a Boltzmann-type kinetic approach to the modelling of road traffic, which includes control strategies at the level of microscopic binary interactions aimed at the mitigation of speed-dependent road risk factors.…

We introduce and discuss spatially homogeneous Maxwell-type models of the nonlinear Boltzmann equation undergoing binary collisions with a random component. The random contribution to collisions is such that the usual collisional invariants…

We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of…

A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…

We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle…

In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster…

In this paper we study a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. These minimal microscopic interaction rules lead to complex…

We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…

The article discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle systems with collisional dynamics.

This paper examines the optimal velocity follow-the-leader dynamics, a microscopic traffic model, and explores different aspects of the dynamical model, with particular emphasis on collision analysis. More precisely, we present a rigorous…

We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and internal energy as mean free path goes to zero. To overcome the stiffness induced by the…

In dilute gas kinetic theory, model collision dynamics such as Bhatnagar-Gross-Krook (BGK) model is often used to get a better insight and numerical modelling. BGK model and its variants assume that highly nonlinear collision term can be…