Controlling non-controllable scallops

Abstract A swimmer embedded on an inertialess fluid must perform a non-reciprocal motion to swim forward. The archetypal demonstration of this unique motion-constraint was introduced by Purcell with the so-called “scallop theorem”. Scallop here is minimal mathematical model composed two arms connected via hinge whose periodic (of opening and closing its arms) not sufficient achieve net displacement. Any source asymmetry in or forces/torques experienced such scallop will break time-reversibility imposed Stokes linearity lead subsequent propulsion scallop. However, little known about controllability time-reversible scalloping systems. Here, we consider individually non-controllable scallops swimming together. Under suitable geometric assumption configuration system, it proved that can be achieved as consequence their hydrodynamic interaction. detailed analysis control system equations carried out analytically means theory. We obtain analytic expression for controlled displacement after prescribed sequence controls function phase difference scallops. Numerical validation theoretical results presented predictions further agreement literature.