= Polymerization-driven cantilever postbuckling
{title2=$F\simeq\pi^2B[1-3(\ell-d)/(2d)]/(4d^2)$}
A clamped filament touching a laterally sliding, moment-free wall has fixed projected gap $d$. For an inextensible small-amplitude elastica, parameterize its tip angle by $k=\sin(\theta_{\rm tip}/2)$. Then $\ell=\sqrt{B/F}K(k)$ and $d=\sqrt{B/F}[2E(k)-K(k)]$, where $K,E$ are complete elliptic integrals. Their small-$k$ expansions give the displayed decrease of wall force with excess contour length. It concerns the weakly buckled branch, before overhang or additional wall contact changes the boundary conditions.
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