Polymers in spatially confined conditions have different configurations than unconfined polymers. The confinement influences the possible configurations and thus influences the average geometry of the arrangements. This presentation gives one answer to how the level of confinement, the polymer length and its knotting affect the average geometric configurations (with a focus on average curvature and average torsion) based on an empirical study.

The study uses equilateral, freely-joined, random polygons rooted at the origin. The knot type of each polygon was determined as well as information for the total curvature, total torsion, average crossing number, and writhe.

This is joint work with Y. Diao, C. Ernst, and E. Rawdon.