On the modeling of granular traffic flow by the kinetic theory for active particles trend to equilibrium and macroscopic behavior

On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives

“…This aspect is considered in a recent paper by Gramani [85], which has shown that even in space uniform flow the above phenomena play an interesting role in the description of fluid patterns in agreement with the experimental observations of Kerner [127]. For instance, Figure 8.1 shows the velocity diagram and the speed variance versus density for a constant distribution of a variable called activity that models the ability of drivers, as depicted by model [68].…”

“…The analysis of [85] is limited to the case of constant (with respect to time) probability distribution of the activity variable. On the other hand, such a distribution is modified by interactions among vehicles and depends on local density conditions.…”

A Dynamic Probabilistic Model for Heterogeneous Data Fusion: A Pilot Case Study from Computer-Aided Detection of Depression

“…This goal has been achieved by the use of a recently introduced «limiting form» of the kinetic-theoretic language [14], a scheme of models based on the use of a generalization of Boltzmann equation governing gas dynamics [15,16], which in the last fifty years has been proposed to describe the evolution of many-particle systems in which the interactions between elements go far beyond purely mechanical ones, and can produce unexpected and not deterministically predictable behaviors, both mechanical and non-mechanical. The elements of the system are themselves no longer just particles in the mechanical sense, but individuals of the most varied nature: cells [17][18][19][20][21], cars [22,23], insects (dynamics of swarms) [24], and finally, human beings and possibly care structures [21,[25][26][27][28][29].…”