Tension-dependent wrapping phase diagram (source code)

= Tension-dependent wrapping phase diagram
{title2=$\xi_*=[(\bar w-2)/\bar\sigma]_{[0,2]}$}

For positive <membrane tension>, the bound-cap <energy> is convex in indentation. Its constrained <minimum> is the unconstrained value $(\bar w-2)/\bar\sigma$ clipped to $[0,2]$. No wrapping occurs at $\bar w\leq2$, partial wrapping at $2<\bar w<2+2\bar\sigma$, and full wrapping at $\bar w\geq2+2\bar\sigma$. At zero tension the expression is linear, with all indentations degenerate at $\bar w=2$. These phase boundaries belong to the specified cap model and can move when free-membrane and neck energies are included.