2008/08/31 by Shinya Saka, Hiroshi Takano
Chemical Engineering · Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Chemistry #Combinatorics #Crystallography #Delocalized electron #Force Microscopy Techniques and Applications #Loop (graph theory) #Material Dynamics and Properties #Mathematics #Physics #Rheology and Fluid Dynamics Studies #Ring (chemistry) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1143/jpsj.77.124802
15 pages, 19 figures, uses jpsj2.cls
arxiv created 2008/09/01 · openalex publication_date 2008/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two types of average structures of a single knotted ring polymer are studied by Brownian dynamics simulations. For a ring polymer with N segments, its structure is represented by a 3N -dimensional conformation vector consisting of the Cartesian coordinates of the segment positions relative to the center of mass of the ring polymer. The average structure is given by the average conformation vector, which is self-consistently defined as the average of the conformation vectors obtained from a simulation each of which is rotated to minimize its distance from the average conformation vector. From each conformation vector sampled in a simulation, 2N conformation vectors are generated by changing the numbering of the segments. Among the 2N conformation vectors, the one closest to the average conformation vector is used for one type of the average structure. The other type of the averages structure uses all the conformation vectors generated from those sampled in a simulation. In thecase of the former average structure, the knotted part of the average structure is delocalized for small N and becomes localized as N is increased. In the case of the latter average structure, the average structure changes from a double loop structure for small N to a single loop structure for large N, which indicates the localization-delocalization transition of the knotted part.