Hysteretic dynamics of active particles in a periodic orienting field

Abstract

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.

Body size affects the strength of social interactions and spatial organization of a schooling fish (Pseudomugil signifer)

“…The fish were confined into a large shallow circular arena (760 mm diameter) and filmed from above at high spatial and temporal resolution. The positions of fish were subsequently tracked using DIDSON tracking software [1]. On average 86% of fish were identified and tracked in our experiments, which is a similar level of accuracy as compared to other studies that track large numbers of individuals [9].…”

“…In sufficiently large collective systems, the behaviour of an individual can be dominated by the generic statistical effects of many individuals interacting, rather than its own behaviour [1]. Much of the progress in understanding collective motion of animal groups has involved applying ideas borrowed from the statistical physics of materials like magnets or fluids [2][3][4][5][6].…”

Diffusion of active particles with stochastic torques modeled asα-stable noise

“…Examples are the works on dicstyostelium [2], also under influence of chemotactic stimulus [3], on human motile keratinocytes and fibroblasts [4], on motile pieces of physarum [5], on flagellate eukaryotes (Euglena) [6], also in time dependent light fields [7], and on more complex organisms as gastropods [8], zooplankton [9], birds [10] and zebra-tail fish [11]. One has also considered motion in the presence of boundaries which might substantially change its effective properties [12,13].…”

Stationary Modes and Localized Metastable States in a Triangular Lattice of Active Particles

“…Suspensions of conservative and active solid particles ("swimmers") are also actively investigated [7,8]. Models of active particle ensembles interacting via common velocity field are used to investigate swimmers' dynamics [1,[9][10][11].…”