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.活体生物与人工自驱动粒子的主动运动（Active motion），已然成为生物、化学与物理交叉学科领域的前沿研究热点。学界对这类现象的认知突破，与一项关键观测结果紧密关联：主动系统中的动态自组织，与铁磁体（ferromagnets）的自发磁化等平衡态凝聚态物质（equilibrium condensed matter）的有序化过程存在高度共性。尽管个体间的相互作用机制可能完全迥异，但主动粒子的运动速度可表现出类似磁偶极子（magnetic dipoles）的行为，并形成全局取向一致的集体状态。 本研究证实，处于外场（external fields）中的主动粒子动力学，同样可通过类比平衡态凝聚态物质的框架进行描述。其遵循一套与系统微观细节无关的简洁普适规律。该动力学特性可通过受周期性取向场作用的主动粒子平均速度（mean velocity）的磁滞现象得以表征。我们通过计算机模拟（computer simulations）与单细胞生物（unicellular organisms）实验对该磁滞效应进行了定量测量。 研究发现，粒子追随外场的能力，与外场变化周期同粒子取向弛豫时间（orientational relaxation time）的比值正相关；而取向弛豫时间本身又与粒子的自驱动功率（self-propulsion power）及能量耗散率（energy dissipation rate）密切相关。相较于单个粒子的运动，在低频场条件下，由于取向相互作用（aligning interactions），粒子群体将表现出运动持续性（persistence of the swarm motion）提升的集体行为。与之相反，当外场频率较高时，主动粒子群无法形成全局取向一致的状态，即便存在相互作用，群体仍会表现为类似独立个体的集合行为。 本研究还报道了主动粒子磁滞动力学的渐近律（asymptotic laws），其形式与磁系统（magnetic systems）中的渐近规律高度相似。底层模型所采用假设的普适性表明，我们观测到的规律可推广至多种动态现象场景，从合成主动粒子的运动，到生物群体行为乃至舆论动力学（opinion dynamics）均涵盖在内。