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Active motion of living organisms and artificial self-propelling particles
has been an area of intense research at the interface of biology,
chemistry and physics. Significant progress in understanding these
phenomena has been related to the observation that dynamic
self-organization in active systems has much in common with ordering in
equilibrium condensed matter such as spontaneous magnetization in
ferromagnets. The velocities of active particles may behave similar to
magnetic dipoles and develop global alignment, although interactions
between the individuals might be completely different. In this work, we
show that the dynamics of active particles in external fields can also be
described in a way that resembles equilibrium condensed matter. It follows
simple general laws, which are independent of the microscopic details of
the system. The dynamics is revealed through hysteresis of the mean
velocity of active particles subjected to a periodic orienting field. The
hysteresis is measured in computer simulations and experiments on
unicellular organisms. We find that the ability of the particles to follow
the field scales with the ratio of the field variation period to the
particles' orientational relaxation time, which, in turn, is related
to the particle self-propulsion power and the energy dissipation rate. The
collective behaviour of the particles due to aligning interactions
manifests itself at low frequencies via increased persistence of the swarm
motion when compared with motion of an individual. By contrast, at high
field frequencies, the active group fails to develop the alignment and
tends to behave like a set of independent individuals even in the presence
of interactions. We also report on asymptotic laws for the hysteretic
dynamics of active particles, which resemble those in magnetic systems.
The generality of the assumptions in the underlying model suggests that
the observed laws might apply to a variety of dynamic phenomena from the
motion of synthetic active particles to crowd or opinion dynamics.
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