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