A collection of squirmers have been know to form a polar order, the alignment of swimming direction, of its own accord, when the absolute value of the “swimming parameter” (see the articles below for the precise definition) is low enough.

Although this consequence itself was well-accepted, its origin remained unsolved.

We have clarified the mechanism of the polar order formation in terms of a mean-field like description.

Note that while this proposed description works very well for most values of swimming parameter, it fails for the parameter range at which we observe strong swarming behavior.

(Do hydrodynamically assisted binary collisions lead to orientational ordering of microswimmers?, The European Physical Journal E 40 (11), 95 (2017))

Explanation will appear

(Purely hydrodynamic origin for swarming of swimming particles, Physical Review E 93 (4), 043114 (2016))