Kinetic Description of Social Dynamics: From Consensus to Flocking

Derivation of coarse-grained models from microscopic CA models of traffic flows

Ilya Timofeyev

University of Houston
[SLIDES]

Cellular automata (CA) models provide a natural and detailed approach for describing various physical and biological phenomena at the microscopic level. In this talk we will consider examples of the CA formulation for the car and pedestrian traffic. In particular, we will discuss the role of the look-ahead potential for models of car traffic and generalization of the microscopic traffic rules for bi-directional pedestrian flows. Statistical assumptions leading to the derivation of mesoscopic models for averages of the stochastic CA process will be discussed and numerical simulations illustrating these assumptions will be presented. Mesoscopic models are deterministic systems of ODEs on a lattice which can be naturally written through the flux formulation, thus, leading to the derivation of PDEs for densities of the traffic flow and higher-order diffusive/dispersive corrections.

co-authors: A. Chertock, A. Kurganov, A. Polizzi, C. Hauck, Y. Sun