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 10,000 configurations per combination of radius and length (i.e. number of vertices). The lengths run from 10 through 90 by steps of 10. The radii are 1.0 through 3.0 by steps of 0.1 and 3.5, 4.0, and 4.5. The data set includes configurations with most pairs of length and radius from these sets. 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.

Citation/Other Information

Claus Ernst, Uta Ziegler, and Eric J. Rawdon; Configurations and knot types of random equilateral rooted polygons under spherical confinement with between 10 and 90 edges and radii between 1.0 and 4.5 (dataset), January 20, 2021.

Creative Commons License

Creative Commons Attribution-Share Alike 4.0 License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

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