Abstract
Eukaryotic flagella are active structures with a complex architecture of
microtubules, motor proteins and elastic links. They are capable of whiplike
motions driven by motors sliding along filaments that are themselves
constrained at an end. Here, we show that active, self-propelled particles that
are connected together to form a single chain that is anchored at one end can
produce the graceful beating motions of flagella. We use a combination of
numerical simulations, scaling analysis and mean field continuum elastic theory
to demarcate the phase diagram for this type of oscillatory motion as a
function of the filament length, passive elasticity, propulsion force and
longitudinal persistence of propulsion directions. Depending on the nature of
the anchoring, we show that filament either undergoes flagella-like beating or
assumes a steadily rotating coiled conformation. Our system is simpler than its
biological inspiration, and thus could be experimentally realized using a
variety of self-propelled particles.