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J R Soc Interface. 2015 Jul 6;12(108):20150015. doi: 10.1098/rsif.2015.0015.

Hysteretic dynamics of active particles in a periodic orienting field.

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Department of Mathematics, Uppsala University, PO Box 480, Uppsala 75106, Sweden School of Physics, Complex and Adaptive Systems Lab, University College Dublin, Belfield, Dublin 4, Republic of Ireland.
Conway Institute, University College Dublin, Belfield, Dublin 4, Republic of Ireland.
School of Physics, Complex and Adaptive Systems Lab, University College Dublin, Belfield, Dublin 4, Republic of Ireland


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.


active motion; collective motion; hysteresis; swarm

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