  We present a detailed numerical study of a microscopic artificial swimmer
realized recently by Dreyfus et al. in experiments [R. Dreyfus et al., Nature
437, 862 (2005)]. It consists of an elastic filament composed of
superparamagnetic particles that are linked together by DNA strands. Attached
to a load particle, the resulting swimmer is actuated by an oscillating
external magnetic field so that it performs a non-reciprocal motion in order to
move forward. We model the superparamagnetic filament by a bead-spring
configuration that resists bending like a rigid rod and whose beads experience
friction with the surrounding fluid and hydrodynamic interactions with each
other. We show that, aside from finite-size effects, its dynamics is governed
by the dimensionless sperm number, the magnitude of the magnetic field, and the
angular amplitude of the field's oscillating direction. Then we study the mean
velocity and the efficiency of the swimmer as a function of these parameters
and the size of the load particle. In particular, we clarify that the real
velocity of the swimmer is influenced by two main factors, namely the shape of
the beating filament (determined by the sperm number and the magnetic-field
strength) and the oscillation frequency. Furthermore, the load size influences
the performance of the swimmer and has to be chosen as a compromise between the
largest swimming velocity and the best efficiency. Finally, we demonstrate that
the direction of the swimming velocity changes in a symmetry-breaking
transition when the angular amplitude of the field's oscillating direction is
increased, in agreement with experiments.
