Shapes of Semiflexible Polymer Rings

The shape of semiflexible polymer rings is studied over their whole
range of flexibility. Investigating the joint distribution of
asphericity and the nature of asphericity as well as their
respective averages, we find two distinct shape regimes depending
on the flexibility of the polymer. For a small perimeter to
persistence length the fluctuating rings exhibit only planar,
elliptical configurations. At higher flexibilities
three-dimensional, crumpled structures arise. Analytic calculations
confirm the qualitative behavior of the averaged shape parameters
and the elliptical shape in the stiff regime.