Knots
Sorry, this page is PERMANENTLY under construction
- I guess, as every other page. Come back again, new stuff will be
(hopefully) added soon. However, a couple of interesting images are
here:
This
shows a summary of Monte Carlo data from many works of different authors
on knotting probability as a function of polymer length. The notations
for some knots are shown in the inset. What is striking is the fact
that the probability of trivial knot (or "no knot") decays exponentially
with chain length. This fact is easy to understand; this is because
most of the knots are forming on small spatial scales.
And here is the smallest possible knot on the cubic lattice, it has
24 nodes:
Meanwhile, here is the preprint of my
most recent work on knots.