Fig. 5: Phenomenological model of a diffusing uniform sphere of non-interacting tumbling athermal ABPs in an exponentially growing domain.

a Time series of the mixing efficiency η_M for different motility values (transparent gray lines) with the respective fits of the mixing efficiency derived from a model of the diffusion of a uniform sphere on an exponentially growing domain. b Fit parameter D as a function of the motility. The black line indicates critical diffusivity D_∞ at which the expansion suppresses diffusion such that no mixing to η_M = 1/2 is possible. This is reached around a motility of M_∞ ≈ 1000. c Persistence time of rotational dynamics. Dark blue line is based on fits of exponential decays on the orientation autocorrelation, obtained from the time series of velocity directions between division events (Supplementary Fig. 12). Light blue line combines this with additional tumbles according to Eq. (12). d Tangential velocities from motility forces only, in the absence of steric interactions (yellow line, active velocity \({\bar{v}}_{{{{\rm{a}}}}}\)) increase with the motility parameter, while tangential velocities from the simulation (purple line) begin to increase only above a certain motility threshold. The inferred self-propulsion velocity in the phenomenological model (light blue line) largely captures this.