Data from: Hysteretic dynamics of active particles in a periodic orienting field

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.

活生物体与人工自驱动粒子的主动运动（Active motion），一直是生物学、化学与物理学交叉领域的研究热点。学界对这类现象的理解所取得的重大进展，源于一项关键观测：主动系统中的动态自组织，与平衡态凝聚态物质的有序化过程存在诸多共通之处，例如铁磁体中的自发磁化现象。主动粒子的运动速度可类比磁偶极子，并能形成全局对齐，尽管个体间的相互作用可能截然不同。
本研究表明，外场中的主动粒子动力学，同样可采用类似平衡态凝聚态物质的方式进行描述。其遵循与系统微观细节无关的简洁普适定律。该动力学特性通过受周期性定向场作用的主动粒子平均速度的磁滞现象得以揭示。
我们通过计算机模拟与单细胞生物实验，对该磁滞现象进行了测量。研究发现，粒子跟随外场的能力，与场变化周期同粒子取向弛豫时间的比值成正比；而该弛豫时间又与粒子自推进功率及能量耗散率密切相关。
由于对齐相互作用的存在，粒子的集体行为在低频下得以体现：相较于单个粒子的运动，群体运动的持续性显著提升。与之相反，在高场频率下，主动粒子群无法形成有效对齐，即便存在相互作用，也倾向于表现为一组独立个体。
我们还报道了主动粒子磁滞动力学的渐近定律，其与磁系统中的同类定律高度相似。本研究底层模型的假设具有普适性，这意味着所观测到的定律，可应用于从合成主动粒子运动，到人群或舆论动态的各类动态现象。