Fractal aggregation of active particles

Abstract

We study active run-and-tumble particles in two dimensions with an additional two-state internal variable characterizing their motile or nonmotile state. Motile particles change irreversibly into nonmotile ones upon collision with a nonmotile particle. The system evolves towards an absorbing state where all particles are nonmotile. We initialize the system with one nonmotile particle in a bath of motile ones and study numerically the kinetics of relaxation to the absorbing state and its structure as a function of the density of the initial bath of motile particles and of their tumbling rate. We find a crossover from fractal aggregates at low density to homogeneous ones at high density. The persistence of single-particle dynamics as quantified by the tumbling rate pushes this crossover to a higher density and can be used to tune the porosity of the aggregate. At the lowest density the fractal dimension of the aggregate approaches that obtained in single-particle diffusion-limited aggregation. Our results could be exploited for the design of structures of desired porosity. The model is a first step towards the study of the collective dynamics of active particles that can exchange biological information.