7 papers
Pearl necklace knots with fewer vertices than an equivalent FCC lattice knot
Alexander R. Klotz
The pearl necklace number, , of a knot is the smallest number of unit spheres required to construct a knot if each sphere is tangent to two neighbors and no sphere overlaps wi…
Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height
Jay Pantone, Alexander R. Klotz, Everett Sullivan
A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and has a trapped endpoint. We show that the generating function en…
Efficient Detection of Borromean Linking in Ellipses
Jonathan Strange, Ryan Blair, Alexander R. Klotz
We describe a method by which the number of intersections one ellipse makes inside the plane of another can be determined. The method is based on applying a transformation that rev…
Geometric considerations for energy minimization of topological links and chainmail networks
Alexander Klotz
Knot and link energies can be computed from sets of closed curves in three dimensional space, and each type of knot or link has a minimum energy associated with it. Here, we consid…
Ropelength-minimizing concentric helices and non-alternating torus knots
Alexander R. Klotz, Finn Thompson
An alternating torus knot or link may be constructed from a repeating double helix after connecting its two ends. A structure with additional helices may be closed to form a non-al…
The space writhes and signatures of polymer knots
Finn Thompson, Maria Maalouf, Alexander R. Klotz
The space writhe of a knot is a property of its three-dimensional embedding that contains information about its underlying topology, but the correspondence between space writhe and…