On this page, you will find links to software, other websites we have created for our data, and knot/link data. This page is essentially always under construction. Please visit my preprints and published papers page to find the papers and my collaborators.
Configurations
and knot types of random cylindrical knots used to model
knotting in extreme confinement
This data set consists of 3D coordinates and knot types. These configurations lie within a cylinder with the vertices alternating between the two endcap disks. We analyzed configurations with even numbers of edges, from 6 through 30. There are 1,000,000 samples per number of edges. See the README.txt for more information. The image to the left has configurations with 6, 18, and 30 edges, respectively. The configurations form a +3.1, 10.124, and a knot type with crossing number 27. This data set is used in the following paper (which also appears in the previous two entries).


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
This data set consists of 3D coordinates and knot types. For each analyzed edge/radius pair, there are 100,000 configurations. See the README.txt for more information. The image to the left is a unitlength edge equilateral 30gon rooted at the origin which is contained in a sphere of radius 2.0. It forms a negative trefoil. This data set is used in the following papers (all of which are listed in the previous entry as well).


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
This data set consists of 3D coordinates and knot types. For each analyzed edge/radius pair, there are 10,000 configurations. See the README.txt for more information. The image to the left is a unitlength edge equilateral 80gon rooted at the origin which is contained in a sphere of radius 1.5. It appears to be a knot with crossing number 61. This data set is used in the following papers.


Knot types of Petaluma knots for 5, 7, 9, 11, and 13 petals
This data set consists of the knot types of all Petaluma knots for 5, 7, 9, 11, and 13 petals. See the README.txt file in the zip file for information about how to decode what is there. The image shows the 7petal +8.19 knot for the permutation (1,5,2,6,3,7,4). The top left is the polygonal petal knot configuration when viewed from above; the top right is the same configuration, but viewed from the side; the bottom left is a smoothed version on the same configuration; the bottom right is the +8.19 knot viewed as a torus (4,3) knot.


Alexander polynomials and determinants for knot types through 16 crossings
This data set has the Alexander polynomial and determinants of all prime and composite knot types through crossing number 16. The documentation is in README.txt within the zip file. This data is not related to any particular publication. We just had it sitting around, so decided to post it. 

Knots aligned with respect to chirality axes
Follow this link to see tight and knotplot knot configurations through 10 crossings aligned with respect to the principle axes of chirality as defined in the paper below. This site also includes some knots tightened with certain symmetries enforced and includes images, eigenvalues, and coordinates. This data is related to the following publication.


Software to create disk image matrices
Follow this link to download the code to make pictures like the one on the left. The documentation for the program is there as well. This software is related to our work in the following publications.


Software to create triangular/square image matrices
Follow this link to download the software to make pictures like the one on the left. The documentation for the program is there as well. This software is related to our work in the following publications.


Tight knots at resolution one
Follow this link to see and download tight knots (i.e. minimized with respect to my definition of polygonal ropelength) at resolution one (i.e. the numbers of edges is about the same as their ropelengths). The polygons were ropelengthminimized using the freely available Ridgerunner package. This data is related to some ongoing projects, but is not a part of any published papers. Some related papers include:


LinkProt
The database LinkProt catalogs all linking in the RCSB Protein Data Bank. The database updates weekly so that it includes to most recently deposited proteins. Users can upload their own protein chains for automated analysis. This work is in collaboration with a number of people. See this page for the current list of authors. The following article summarizes the capabilities of LinkProt.


KnotProt
The database KnotProt catalogs all knotting in the RCSB Protein Data Bank. The database updates weekly so that it includes to most recently deposited proteins. Users can upload their own protein chains for automated analysis. This work is in collaboration with a number of people. See this page for the current list of authors. The following articles are related to our work with knotted proteins.


Tight knots and links
We tighten our knots using the freely available package
Ridgerunner
package.
We have visualizations
of the tightening process for knots and links
The tight knot files can be found
here
in the VECT format.
This arxiv
article describes some of our results as well as how
to interpret these images.


Upper bounds for equilateral stick numbers
We have produced candidates for the minimum equilateral stick number using KnotPlot. This work is in collaboration with Rob Scharein and appears in the paper:


Can computers discover ideal knots
Our original ropelength data used simulated annealing for ropelength minimization. The configurations, as well as a variety of spatial and topological measurements are available here. My former undergraduate researcher Michael Piatek did much of the work on the computations. The theoretical paper related to this work is:


Role of flexibility in entanglement
This work explores ropelength optimization with a hard bound on curvature. Our hope is to capture the shape of ropelength minimizers in physical materials with curvature constraints. Visualizations with associated spatial characters are available as is the paper published in Physical Review E, 70:011803, 2004. This work was in collaboration with Greg Buck and Michael Piatek did much of the work on the computations.


Energy, ropelength, and other physical aspects of equilateral knots
Energy optimized and ropelength optimized knots are available
with spatial characteristics. The associated paper appears
in Journal
of Computational Physics, 186(2):426456, 2003. 
This work has been supported by NFS DMS grant numbers 0074315, 0296098, 0311010, 0621903, 0810415, 1115722, 1418869, and 1720342. 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.