Title: Nonlinear parametric excitation effect induces stability transitions in swimming direction of flexible superparamagnetic microswimmers,
Abstract: Microscopic artificial swimmers have recently become highly attractive due to
their promising potential for biomedical applications. The pioneering work of
Dreyfus et al (2005) has demonstrated the motion of a microswimmer with an
undulating chain of superparamagnetic beads, which is actuated by an
oscillating external magnetic field. Interestingly, it has also been
theoretically predicted that the swimming direction of this swimmer will
undergo a $90^\circ$-transition when the magnetic field's oscillations
amplitude is increased above a critical value of $\sqrt{2}$. In this work, we
further investigate this transition both theoretically and experimentally by
using numerical simulations and presenting a novel flexible microswimmer with a
superparamagnetic head. We realize the $90^\circ$-transition in swimming
direction, prove that this effect depends on both frequency and amplitude of
the oscillating magnetic field, and demonstrate the existence of an optimal
amplitude, under which, maximal swimming speed can be achieved. By
asymptotically analyzing the dynamic motion of microswimmer with a minimal
two-link model, we reveal that the stability transitions representing the
changes in the swimming direction are induced by the effect of nonlinear
parametric excitation.