Department/School
Mathematics
Date
1-20-2021
Document Type
Dataset
Keywords
knot theory, confined knot, spherical confinement
Abstract
This data set consists of random equilateral confined knot configurations and their corresponding knot types. The configurations lie within spheres of different radii and are rooted at the origin (i.e. have one vertex at the origin). The algorithms used are described in the following articles. Yuanan Diao, Claus Ernst, Anthony Montemayor, and Uta Ziegler Generating equilateral random polygons in confinement. J. Phys. A, 44(40):405202, 2011. https://doi.org/10.1088/1751-8113/44/40/405202 Yuanan Diao, Claus Ernst, Anthony Montemayor, and Uta Ziegler Generating equilateral random polygons in confinement II. J. Phys. A, 45(27):275203, 2012. https://doi.org/10.1088/1751-8113/45/27/275203 Yuanan Diao, Claus Ernst, Anthony Montemayor, and Uta Ziegler Generating equilateral random polygons in confinement III. J. Phys. A, 45(46):465003, 2012. https://doi.org/10.1088/1751-8113/45/46/465003 The data set consists of 100,000 configurations per combination of radius and length (i.e. number of vertices). For length 30, the set has radii 1.0 through 3.0 by steps of 0.1, and 3.5, 4.0, and 4.5. For radius 3.0, the set has lengths 10 through 90 by steps of 10. All files are plain text. More details are included in the README.txt file within the zip archive. This material is based upon work supported by the National Science Foundation under Grant Nos. 1115722, 1418869, and 1720342 to Eric J. Rawdon and 1016420 to Claus Ernst and Uta Ziegler. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Creative Commons License
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Citation/Other Information
Claus Ernst, Uta Ziegler, and Eric J. Rawdon; Configurations and knot types of random equilateral rooted polygons under spherical confinement with (a) 30 edges and radii between 1.0 and 4.5, and (b) radius 3.0 and edges between 10 and 90 (dataset), January 20, 2021.