Active Crowds
Statistical Mechanics
2022-11-11 v2 Analysis of PDEs
Adaptation and Self-Organizing Systems
Abstract
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential equations for the particle density. The macroscopic models share common features, such as cross diffusion or degenerate mobilities. We then take the diversity of macroscopic models to a uniform structure and work out potential similarities and differences. Moreover, we discuss boundary effects and possible applications in life and social sciences. This is complemented by numerical simulations that highlight the effects of different boundary conditions.
Cite
@article{arxiv.2107.06392,
title = {Active Crowds},
author = {Maria Bruna and Martin Burger and Jan-Frederik Pietschmann and Marie-Therese Wolfram},
journal= {arXiv preprint arXiv:2107.06392},
year = {2022}
}