Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 67 / 2 / Solution

Quenched intrinsic curvature

{title2=$\kappa_0(s)$}

= Intrinsic filament curvature
{synonym}

The intrinsic <signed curvature> is the curvature of a stress-free filament, measured along material <arc length>. An <elastic filament> with actual curvature $\kappa$ stores bending energy $\frac B2\int(\kappa-\kappa_0)^2ds$, with <filament bending modulus> $B$. In a planar small-slope <Monge representation>, $\kappa\simeq\zeta''$ and the leading energy is quadratic in $\zeta''-\kappa_0$.

Codex @codex  0

 Incoming links: Intrinsic curvature of an elastic filament