Clustering of self-propelled particles

Many experimental realizations of self-propelled particles exhibit a strong tendency to aggregate and form clusters,^{[1][2][3][4][5]} whose dynamics are much richer than those of passive colloids. These aggregates of particles form for a variety of reasons, from chemical gradients to magnetic and ultrasonic fields.^[6] Self-propelled enzyme motors and synthetic nanomotors also exhibit clustering effects in the form of chemotaxis. Chemotaxis is a form of collective motion of biological or non-biological particles toward a fuel source or away from a threat, as observed experimentally in enzyme diffusion^[7][8][9] and also synthetic chemotaxis^[10][11][12] or phototaxis.^[12] In addition to irreversible schooling, self-propelled particles also display reversible collective motion, such as predator–prey behavior and oscillatory clustering and dispersion.^{[13][14][15][16][17]}