Active Crowds
2021
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.
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