Figure 1

(Color online) (a) A body deforming its shape in a reciprocal fashion, such as a scallop, cannot move on average at low Reynolds numbers (left, $⟨V⟩=0$), whereas nonreciprocal deformation leads to net propulsion (right, $⟨V⟩\ne 0$). (b) Two force-free dimers interacting hydrodynamically. The dimers are composed of two solid spheres (more generally, bodies), of radii $\{a_1,a_2\}$ and $\{b_1,b_2\}$, have lengths ${\ell }_a\left(t\right)$ and ${\ell }_b\left(t\right)$, and are separated by the distance $d\left(t\right)$.Reuse & Permissions

Figure 2

(Color online) Dynamics of identical dimers interacting hydrodynamically. Units are chosen so that $\delta {\ell }_a\left(t\right)=\cos \left(t\right)$, $\delta {\ell }_b\left(t\right)=\sin \left(t\right)$. (a) Mean displacement, $⟨\int Vdt⟩$, for two mirror-images polar dimers ($a_1\ne a_2$, solid line); mean displacement for two mirror-images apolar dimers ($a_1=a_2$, dash-dotted line); mean distance, $\int \Delta Vdt$, between the two dimers (polar and apolar cases, dashed line). (b) Mean displacement (solid line) and mean separation distance (dashed line) for two identical polar dimers pointing in the same direction. (c) same as (b) but for dimers pointing in the opposite direction; note the change in the sign of the dimer-dimer effective interaction. (d) Comparison between the swimming speed of two active dimers and a single swimmer made of two rigidly connected dimers (constant $d$). In all figures, the lengths ${\ell }_a$ and ${\ell }_b$ oscillate with the same amplitude and frequencies, and a relative phase of $\pi ∕2$. In the chosen units, ${\overline{\ell }}_a={\overline{\ell }}_b=10$, ${\phantom{\mid }d\mid }_{t=0}=100$, $a_1=3$, $a_2=3∕2$ for the polar dimers and $a_1=a_2=2$ in the apolar case.Reuse & Permissions