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1answer
33 views

Example of using torus knots in experimental science

Can anyone give an example of using the theory of torus knot in experimental science? Thanks in advance!
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52 views

Infiniteness of a knot energy

I am going through the paper, Physical Knots, by Jonathan Simon. Initially, on page 10, he describes the electrostatic energy of two charged stick, X and Y in space as follows. $$ \int_{x \in X} ...
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19 views

Torsion energy as a component of physical energy of a knot

I am going through the paper, Recognizing knots Using Simulated Annealing by Ligocki and Sethian. This paper uses simulated annealing to solve the KNOT GENUS problem. It has used the concept of ...
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41 views

Invariance of the physical energy of a knot over Möbius transformations

I am going through the paper, Recognizing knots Using Simulated Annealing by Ligocki and Sethian. This paper uses simulated annealing to solve the KNOT GENUS problem. It has used two different ...
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55 views

What is the type of $u$ in this definition of knot?

I am going to quote from the second paragraph of the Introduction of Möbius Energy of Knots and Unknots by Michael H. Freedman, Zheng-Xu He and Zhenghan Wang. Let $\gamma = \gamma (u)$ be a ...
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49 views

Hamiltonian of one and two unknots

Recently I calculated the Ising Hamiltonian of a Hopf link. First, I colored the Hopf link in a checker board pattern and drew the Seifert surface from it. Considering the shaded regions as vertices ...
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148 views

Calculating the probability that a cord makes a knot

I use earphones to listen to music. The cord connected to the earphones often gets entangled in my pocket and makes a knot, which I always find hard to untangle. How can I define and calculate the ...