Master thesis – Jonas Buba

Classical Density Functional Theory for Active Particles
finished 2025-11
supervised by Michael Schmiedeberg

Abstract

Active matter systems, composed of self-driven agents, display a wide range of emergent behaviours such as collective motion, clustering, and motility-induced phase separation. Active Brownian particles constitute a minimal model for such self-propelled systems that exhibit complex nonequilibrium behaviour. Understanding the microscopic dynamics of particle collisions is important for linking individual motion to collective effects. In this work, the collision process of active Brownian hard disks is studied within the framework of dynamical density functional theory. Each particle is represented by a Gaussian density peak, introducing positional uncertainty. In this field-based description, the particle interaction is modelled via fundamental measure theory.
The analysis of the motion of density peaks throughout the course of individual collisions allows to quantify the center of mass delay of interacting particles. The results show that the time delay scales approximately as ∆t ∝ v0 with the self-propulsion velocity v0. The increase in the delay with the Gaussian width σ is faster than ∝ σ−1, and the dependence on the offset h follows a roughly Gaussian shape. The self-propulsion velocity mainly influences the diffusive relaxation after a collision, while the overall positional delay remains nearly independent of v0. Furthermore, it is demonstrated that the post-collision density profile can be approximated by a convolution of the initial profiles, suggesting a route toward a coarse-grained description of active collisions.
Future work may focus on performance improvements of the numerical implementation to enable larger-scale simulations. Furthermore, the connection to a waiting-time-based model may be possible.