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math-ph2013★ 14 cited
Euler elasticae in the plane and the Whitney--Graustein theorem
Sergey Avvakumov, Oleg Karpenkov, Alexey Sossinsky
In this paper, we apply classical energy principles to Euler elasticae, i.e., closed C^2 curves in the plane supplied with the Euler functional U (the integral of the square of the…
math-ph2011★ 6 cited
Energies of knot diagrams
Oleg Karpenkov, Alexey Sossinsky
We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel…