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math.GT2021
The tightest knot is not necessarily the smallest
Alexander R. Klotz
In this note, we attempt to find counterexamples to the conjecture that the ideal form of a knot, that which minimizes its contour length while respecting a no-overlap constraint,…
cond-mat.soft2021
Flatness and Intrinsic Curvature of Linked-Ring Membranes
James M. Polson, Edgar J. Garcia, Alexander R. Klotz
Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from cate…
math.GT2021
The Ropelength of Complex Knots
Alexander R. Klotz, Matthew Maldonado
The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out the knot in three dimensional space without self-overlap, colloquially the minimum a…