Active crowds

  • This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in the 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.

Export metadata


Number of document requests

Additional Services

Share in Twitter Search Google Scholar
Author:Maria Bruna, Martin Burger, Jan-Frederik PietschmannORCiDGND, Marie-Therese Wolfram
Frontdoor URL
Parent Title (English):Active particles, volume 3: advances in theory, models, and applications
Place of publication:Cham
Editor:Nicola Bellomo, José Antonio Carrillo, Eitan Tadmor
Type:Part of a Book
Year of first Publication:2022
Release Date:2023/02/20
First Page:35
Last Page:73
Series:Modeling and Simulation in Science, Engineering and Technology
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Inverse Probleme