  We have examined the behaviors of a knotted linear polymer in narrow tubes
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 localized knot, we found the scaling behavior of the fluctuation
around the most probable size with 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 the virtual tubes composed of
parallel strands and overlapping among them.
