Active Brownian particles in external force fields: Field-theoretical models, generalized barometric law, and programmable density patterns

J Bickmann and S Bröker and M te Vrugt and R Wittkowski, PHYSICAL REVIEW E, 108, 044601 (2023).

DOI: 10.1103/PhysRevE.108.044601

We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.

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