Control and controllability of microswimmers by a shearing flow

Most probable path of an active Brownian particle

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager-Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the ℓ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

Driving a Microswimmer with Wall-Induced Flow

Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. Recent advances in artificial magnetic cilia carpets offer the potentiality to use a similar wall-generated background flow to steer bio-hybrid microrobots. In this paper, we provide some ground theoretical and numerical work assessing the viability of this novel means of swimmer guidance by setting up a simple model of a spherical swimmer in an oscillatory flow and analysing it from the control theory viewpoint. We show a property of local controllability around the reference free trajectories and investigate the bang-bang structure of the control for time-optimal trajectories, with an estimation of the minimal time for suitable objectives. By direct simulation, we have demonstrated that the wall actuation can improve the wall-following transport by nearly 50%, which can be interpreted by synchronous flow structure. Although an open-loop control with a periodic bang-bang actuation loses some robustness and effectiveness, a feedback control is found to improve its robustness and effective transport, even with hydrodynamic wall-swimmer interactions. The results shed light on the potentialities of flow control and open the way to future experiments on swimmer guidance.