  Active Brownian Particles are self-propelled particles that move in a
dissipative medium subject to random forces, or noise . Additionally, they can
be confined by an external field and/or they can interact with one another. The
external field may actually be an attractive marker, for example a light field
(as in the experiment) or an energy potential or a chemical gradient (as in the
theory). The potential energy can also be the result of interparticle
attractive and/or repulsive forces summed over all particles (a mean field
potential). Four, qualitatively different motions of the particles are
possible: at small particle density their motions are approximately independent
of one another subject only to the external field and the noise, which results
in moving randomly through or performing rotational motions about a central
point in space. At increasing densities interactions play an important role and
individuals form a swarm performing several types of self-organized collective
motion. We apply this model for the description of zooplankton Daphnia swarms.
In the case of the zooplankton Daphnia (and probably many other aquatic animals
that form similar motions as well) this vortex is hydrodynamical but motivated
by the self-propelled motion of the individuals. Similar vortex-type motions
have been observed for other creatures ranging in size from bacteria to flocks
of birds and schools of fish. However, our experiment with Daphnia is unique in
that all four motions can be observed in controlled laboratory conditions with
the same animal. Moreover, the theory, presented in both continuous
differential equation and random walk forms, offers a quantitative, physically
based explanation of the four motions.
