Localization and size distribution of a polymer knot confined in a channel

We have examined the behaviors of a knotted linear polymer in narrow channels using Langevin dynamics simulation to investigate the knot localization property in one-dimensional (1D) geometry. We have found that the knot is strongly localized in such a geometry. By observing the distribution function of the size of the localized knot, we found the scaling behavior of the fluctuation around the most probable size with the radius of confinement. Based on the analysis of the probability distribution of the knot size, we show that the strong localization behavior and the fluctuation around the most probable size can be encompassed by a simple argument based on virtual tubes composed of parallel strands and the overlap among them.