Spontaneous vortex formation by microswimmers with retarded attractions

Abstract

Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback, implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that do not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as the key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric, phoretic, and hydrodynamic interactions. Our results demonstrate how even most simple retarded interactions can foster emergent complex adaptive behavior in small active-particle ensembles.

Spontaneous velocity alignment of Brownian particles with feedback-induced propulsion (a)

“…Third, it seems promising to apply the present control scheme to active (rather than passive) Brownian particles. Indeed, the study of active particles with retardation effects due to feedback, inertia or other mechanisms is currently an emerging field [1,[21][22][23]40]. From a more general perspective, our work contributes to establishing a link between collective systems under time-delayed feedback and active matter [16].…”

“…clustering and swarming [1,[21][22][23], enriching the already complex collective behavior of active matter. However, so far, there is no comprehensive understanding of the role of time delay and its interplay with activity on structure formation and emergent dynamics of interacting, Brownian systems.…”

Micro/Nanorobotic Swarms: From Fundamentals to Functionalities

“…To date, different types of external fields have been applied to actuate micro/nanoagents (Figure ), including magnetic, − electric, − optical, − and acoustic fields. − In addition to these fields, chemical reaction − and topographical patterns − have also been investigated to power and guide the agents, respectively. Existing reviews have focused on individual micro/nanoagents, including their evolution, fabrication and functionalization, − modeling and motion control, − biomedical applications, − and environmental applications. − Compared with a single agent, micro/nanorobotic swarms have higher robustness (e.g., higher tolerance to the failure of a few agents), higher motion dexterity and flexibility, and better scalability.…”

Active particles with delayed attractions form quaking crystallites (a)

“…Introduction. -Recent experiments with synthetic microswimmers steered toward a fixed target have revealed a spontaneous vortex formation caused by a perceptionreaction delay [1]. The observed phenomenology can be attributed to the delay-induced aiming errors, akin to those associated with microswimmer navigation strategies employing "vision-cone" [2,3] or "acceptance-angle" [4,5] criteria.…”

“…In this letter, we numerically study a model system introduced and experimentally motivated in ref. [1]. We extend the analysis to particle numbers that are currently inaccessible to the experimental techniques [17] employed.…”