  In this paper we calculate the critical currents in thin superconducting
strips with sharp right-angle turns, 180-degree turnarounds, and more
complicated geometries, where all the line widths are much smaller than the
Pearl length $\Lambda = 2 \lambda^2/d$. We define the critical current as the
current that reduces the Gibbs free-energy barrier to zero. We show that
current crowding, which occurs whenever the current rounds a sharp turn, tends
to reduce the critical current, but we also show that when the radius of
curvature is less than the coherence length this effect is partially
compensated by a radius-of-curvature effect. We propose several patterns with
rounded corners to avoid critical-current reduction due to current crowding.
These results are relevant to superconducting nanowire single-photon detectors,
where they suggest a means of improving the bias conditions and reducing dark
counts. These results also have relevance to normal-metal nanocircuits, as
these patterns can reduce the electrical resistance, electromigration, and hot
spots caused by nonuniform heating.
