Random walks and polygons in tight confinement

Tangled Magnetic Fields in Astro- and Plasma Physics; Quantised Flux in Tightly Knotted and Linked Systems

Diao, Y.^1 ; Ernst, C.^2 ; Ziegler, U.^2

Department of Mathematics and Statistics, University of North Carolina Charlotte, Charlotte

NC

28223, United States^1

Department of Mathematics and Computer Science, Western Kentucky University, Bowling Green

KY

42101, United States^2

关键词: Crossing number;    Random polygon;    Random Walk;    Sphere of radius R;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/544/1/012017/pdf
DOI  :  10.1088/1742-6596/544/1/012017

来源: IOP

【 摘 要 】

We discuss the effect of confinement on the topology and geometry of tightly confined random walks and polygons. Here the walks and polygons are confined in a sphere of radius R ≥ 1/2 and the polygons are equilateral with n edges of unit length. We illustrate numerically that for a fixed length of random polygons the knotting probability increases to one as the radius decreases to 1/2. We also demonstrate that for random polygons (walks) the curvature increases to πn (π(n-1)) as the radius approaches 1/2 and that the torsion decreases to = πn/3 (= π(n-1)/3). In addition we show the effect of length and confinement on the average crossing number of a random polygon.