Fig. 3.

(A) Sensitivity to shape perturbations of three cross-sectional shapes. The arrows indicate the magnitude of the decrease of the resistance prefactor $C_K$ (arrow length) when the shape is locally perturbed in the normal direction (arrow direction) at fixed area $A$ and scalar exchange efficiency $C_{\mathcal{E}}$; see SI Appendix for numerical details. (B) Width perpendicular to the centerline as a function of position for the three shapes shown in A. This gap width is uniform in the midsection of optimal shapes and rectangles, while it varies significantly in ellipses.